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May
16

The Pricing of Commodity Options

The present research will prove particularly useful to option traders. The analysis proposed by the HyperVolatility Team will explain, in a few bullet points, how the most popular commodity options pricing models behave and what the practical divergences in terms of prices are. The present study is very valuable to anyone interested in trading options because most trading platforms allow the trader to choose the model via which the theoretical value of the options will be calculated and consequently shown (the HyperVolatility Forecast Service provides market projections for many asset classes. Send an email to info@hypervolatility.com and get a free 14 days trial). The pricing models that will be analyzed are the Barone–Adesi –Whaley, the Bjerksund & Stensland (the 2002 version), the Black–76, the Binomial Tree and the classic Black–Scholes–Merton one. The models have been tested against each other and the following charts graphically show the divergence of 1 pricing model with respect to all others. The research has been performed assuming that the underlying asset (S) is a WTI crude oil futures contract, that the volatility (σ) is 20%, that the interest rate (r) is 0.5% and that the Cost of Carry is 0 (which is normal when dealing with commodity options).

As previously mentioned, the study will examine 1 pricing model at the time and, in order to avoid confusion and make things simpler, we decided to list the most important aspects below each graph:

Barone Adesi Whaley model

1) The Barone-Adesi-Whaley model overprices options when compared to other formulas. The pricing spread with respect to other models is on average between 0.06% and 0.08%

2) The Barone-Adesi-Whaley prices tend to get closer to other models as the expiration increases

3) The Barone-Adesi-Whaley model, on average, tends to overprice options with respect to the Binomial Tree (~ 0.16% higher) for short maturities. The trend is higher for out-of-the-money options and particularly for put options

4) The prices derived from the Bjerksund & Stensland model are always lower than Barone-Adesi-Whaley prices. The difference is bigger for 1 month options (~ 0.16%)

5) The Black-76 performs as well as the Black–Scholes–Merton model, however, their results overlap and that is why the Black-76 curve is not visible

6) The difference with the Black–Scholes–Merton model becomes larger as the expiration increases but it is not higher than 0.1%

 

Bjerksund & Stensland model

1) The Bjerksund & Stensland model under–prices options in respect to other models. On average the difference ranges between 0.05% – 0.06%

2) The under–pricing tends to reduce as the expiration increases

3) The Bjerksund & Stensland  model produces prices which are lower than the Barone–Adesi–Whaley one for any expiration

4) The Black–Scholes–Merton model approximates to the Bjerksund & Stensland one from the 8th month onwards

5) The Black–76 performed as well as the Black–Scholes–Merton model and that is why the overlapped curve cannot be seen  in the chart

6) The Binomial Tree approach shows the highest differential with respect to the Bjerksund & Stensland model. The divergence in pricing oscillates around 0.15%

 

Black-76 model

1) The Black–76 model over–prices options only with respect to the Bjerksund & Stensland one (almost 0.05%)

2) The divergence between Black–76 and Bjerksund & Stensland attenuates when longer expirations are approached

3) The Barone–Adesi–Whaley model prices are slightly higher than Black–76 ones and the discrepancy augments with the passage of time (between 0.08% and 0.1% for 10 months and 1 year expiring options respectively)

4) The Binomial Tree approach, if we exclude the short term, delivers higher prices than the Black–76 model but the divergence oscillates around the interval 0.03% – 0.04%

5) The Black–76 model performed as well as the Black–Scholes–Merton one and that is why the BSM curve is flat to 0. Needless to say that the Black–Scholes–Merton curve suggests that there is no difference in pricing

 

Binomial Tree model

1) The Binomial Tree under–prices options with respect to other models in the short term (around 2.5%) but the divergence is much lower for longer dated derivatives

2) The Barone–Adesi–Whaley model and the BSM model perform as well as the Black–76 one therefore their curves are hidden in the chart

3) The Bjerksund & Stensland model provided higher prices for short dated options but in the long term the Binomial Tree approach shows a slight over–pricing tendency with respect to the former. However, the spread is no higher than 0.04% – 0.05%

 

Black Scholes Merton model

1) The performances of the Black–Scholes–Merton formula with respect to other pricing models match perfectly well with the outcome generated by the Black–76 model

2) The above reported chart is identical to the graph extrapolated for the Black–76 model, in fact, the green curve does not move from the 0 axis

If you are interested in trading options you might want to read also the HyperVolatility researches entitled “Options Greeks: Delta, Gamma, Vega, Theta, Rho” and “Options Greeks: Vanna, Charm, Vomma, DvegaDtime”

The HyperVolatility Forecast Service enables you to receive the statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at info@hypervolatility.com with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial.

Apr
26

The US Dollar Index

The Dollar Index is a very useful yet simple to understand tool for currency, commodity and equity traders. The index measures the fluctuations of the US Dollar against a basket of different currencies: Euro, Japanese Yen, Canadian Dollar, British Pound, Swedish Krona and Swiss Franc (the Forecast Service provides market projections for currencies and many other asset classes. Send an email to info@hypervolatility.com and get a free 14 days trial). In practical terms, the Dollar Index tries to quantify how much the US dollar is appreciating or depreciating with respect to some of the most important and traded currencies in the world. The reason the Dollar Index is a valuable instrument for many traders is primarily due to its correlation to other asset classes and particularly risky assets.

As previously mentioned, the Index tracks the performance of the American dollar against a basket of other currencies, however, each exchange rate has a different weight. Specifically, the Index is a weighted geometric mean whose components and respective weights are the following: Euro (56.7%), Japanese Yen (13.6%), British Pound (11.9%), Canadian Dollar (9.1%), Swedish Krona (4.2%) and Swiss Franc (3.6%). The Index has 100 as a benchmark value therefore every reading below this threshold would imply a depreciation of the American currency against the basket, primarily the Euro, while any value above it is obviously indicating an appreciation. It goes without saying that the reason the Dollar Index has been trading below the 100 level for so long is the axiomatic consequence of the strength of the Single currency. It is clear that the Euro, whose weight in the Dollar Index calculation is 56.7%, is the most important currency since its impact is by far the heaviest. Obviously, every appreciation of the Single currency will impact negatively on the performance of the dollar and the next chart evidently displays such relationship:

Dollar Index

The above reported chart evidently displays the natural inverse relationship between the 2 markets and the obvious contrary fluctuations can be used to hedge potential currency based portfolios. In particular, the Euro, which is considered to be a risky asset, is positively correlated to equity indices therefore a drop in the Single currency would automatically correspond to a rise in the Dollar index. However, the positive correlation amongst Euro futures and other equity indices (such as E-Mini S&P500, DAX or Nasdaq futures) would suggest that a down trend in the Single currency is likely to be accompanied by a retracement in many risky assets. Therefore, the Dollar Index, being a “contrarian market by default”, could be very useful to detect market nervousness and cover unstable positions in equities. In order to better understand how much the American currency is linked to its components we will analyze the volatility fluctuations of the most important exchanges: Euro, British Pound and Japanese Yen futures. The reason we chose these 3 currencies is related to their weights, in fact, the combination of the aforementioned asset classes is responsible for 82.2% of the Dollar Index’s oscillation (Euro 56.7% + Japanese Yen 13.6% + British Pound 11.9%).

Dollar Index

The calculation tracks the volatility performance of the Dollar Index, Euro futures, Japanese Yen futures and British Pound futures. It is evident that the oscillations are more or less correlated, in fact, the volatility decreased for all asset classes in January, April – May, August – September and November – December but drastically augmented in February, June – July and October. Undoubtedly, every market behaved differently in the short term but the macro movements are very correlated each other. This information is very important to forex traders because it proves that the Dollar Index, in terms of magnitude, moves as much as the other currencies implying that it could be used as a hedging tool when the Euro or the British Pound are in downtrend (the behaviour of the Japanese Yen is different and it will be treated separately later on). Let’s have a look at the relationships amongst the aforementioned exchanges from a quantitative point of view:

Dollar Index

The table presents the correlation and covariance of each asset class against the Dollar Index and the results stress what have been previously stated: the Index obviously has an extremely strong negative correlation to the price of the Euro (-0.93) and a strong negative correlation to the price of the British Pound (-0.66). However, Euro and British Pound volatilities display a strong positive connection to the Dollar Index, in fact, the correlation coefficients are +0.79 and +0.69 respectively. The positive connection in volatility is an obvious consequence of the fact that the rise in the Dollar Index will always be proportioned to the depreciation of the remaining currencies, hence, the movement will be fairly similar in terms of magnitude. The covariance of Euro and British Pound prices with respect to the value of the dollar (the covariance measures the mutual variability of 2 random variables) is negative, -0.16 and -5.04 respectively, which is another natural consequence of the appreciation of the American currency against European exchanges. On the other hand, the volatility covariance is positive, 1.95 and 1.73 respectively, implying that Euro and British Pound volatilities rise when the volatility of the Dollar Index rises and vice versa. The reason volatilities move in the same direction is because both markets observe a leverage effect process: the volatility tends to rise when the price action is in downtrend. Specifically, a drop in Euro and British Pound futures would probably cause an increase in market volatility but a rise in the Dollar Index would increase its volatility too. In other words, risky assets such as Euro or British Pound futures follow a leverage effect process while the Dollar Index is governed by an inverted leverage effect: the volatility increases with a larger buying pressure and decreases in case of a sell–off. Consequently, If Euro and British Pound futures are plunging they are effectively depreciating against the Dollar. Therefore, the volatilities of the 2 European asset classes, following a leverage effect process, will increase while the appreciation of the Dollar will push the Dollar Index up and the buying pressure would increase its variance too.

The Japanese Yen, instead, needs a different approach. First of all, it is necessary to remind that the Asian currency is often used as a hedging tool in portfolio management because many market participants rush to buy Yen when equities drop. Secondly, it is important to point out that the “safe haven role” played by the Japanese Yen has a clear implication: the volatility rises when the market heads north (if you are interested in hedging portfolio risk you may want to read the HyperVolatility research entitled “Portfolio Hedging: Risky Assets vs Safe Havens”). As we can see, Japanese Yen futures, as well as the Dollar Index, are popular assets when equity indices and single stocks are plummeting and their volatilities are both driven by an inverted leverage effect process. The positive price correlation between Dollar Index and Japanese Yen futures (+0.10) and the weak covariance (-0.26) evidently proves the point just made. The price correlation is clearly very low and the negative, although feeble, covariance indicates that the buying pressure was sometimes stronger for the Asian currency. The numbers suggest that in 2012 the Dollar Index and Japanese Yen futures have been both used as a hedging tool but in a diverse fashion because the buying pressure was evidently different.

Conclusions

The Dollar Index is a very simple to understand tool for traders and it is worth monitoring when investing. Here are some important points to bear in mind:

1) The benchmark value for the Dollar Index is 100. If the Index is below this level the dollar is depreciating against other currencies while a reading above this threshold implies an appreciation of the American currency

2) The Dollar Index is a weighted geometric mean whose components and respective weights are the following: Euro (56.7%), Japanese Yen (13.6%), British Pound (11.9%), Canadian Dollar (9.1%), Swedish Krona (4.2%) and Swiss Franc (3.6%)

3) The Euro is the currency that influences Dollar Index’s fluctuations the most

4) The volatility of the Dollar Index rises with an increasing buying pressure and decreases when the market goes down

5) Euro, Japanese Yen and British Pound are responsible for the 82.2% oscillations in the Dollar Index

6) The Dollar Index can be effectively used to hedge positions in Euro and British Pound futures

7) Japanese Yen futures do not show much correlation to the Dollar Index because of their “safe haven” characteristics

8) The Dollar Index, given its “contrarian nature” is a rather good asset to hold when risky assets (equities, stocks, etc) plunge

The HyperVolatility Forecast Service enables you to receive the statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at info@hypervolatility.com with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial.

Apr
14

Options Greeks: Vanna, Charm, Vomma, DvegaDtime

The present article deals with second order Options Greeks and it constitutes the second part of a previously published article entitled “Options Greeks: Delta,Gamma,Vega,Theta,Rho”. Before getting started it is important to highlight the great contribution that Liying Zhao (Options Analyst at HyperVolatility) gave to this report. All the calculations and numerical simulations that will be shown and commented are entirely provided by Mr Zhao.

Second-order Greeks are sensitivities of first-order Greeks to small changes in different parameters. Mathematically, second-order Greeks are nothing else but the second-order partial derivatives of option prices with respect to different variables. In practical terms, they measure how fast first order options Greeks (Delta, Vega, Theta, Rho) are going to change with respect to underlying price fluctuations, volatility, interest rate changes and time decay. Specifically, we will go through Vanna, Charm (otherwise known as Delta Bleed), Vomma and DvegaDtime. It is important to point out that all charts have been produced by assuming that the underlying asset is a futures contract on WTI crude oil, the ATM strike (X) is 100, risk-free interest rate (r) is 0.5%, implied volatility is 10% while the cost of carry (b) is 0 (which is the case when dealing with commodity options).

Vanna: Vanna measures the movements of the delta with respect to small changes in implied volatility (1% change in implied volatility to be precise). Alternatively, it can also be interpreted as the fluctuations of vega with respect to small changes in the underlying price. The following chart shows how vanna oscillates with respect to changes in the underlying asset S:

Options VannaThe above reported chart clearly shows that vanna has positive values when the underlying price is higher than strike (in our case S>$100) and it has negative values when the underlying moves just below it (S<$100). What does that imply? The graph highlights the fact that vega moves much more when the underlying asset approaches the ATM strike ($100 in our case) but it tends to approximate 0 for OTM options. Consequently, the delta is very sensitive to changes in implied volatility when the ATM area is approached. However, it is important to point out that delta will not always increase if the underlying moves from, say, $80 to $100 because in many risky assets (stocks, equity indices, some currencies and commodities) the implied volatility is inversely correlated to the price action. As a result, if WTI futures go from $80 to $100 the implied volatility will probably head south and such a phenomenon would decrease vanna which, in turn, would diminish the value of delta.

Charm (or Delta Bleed): Charm measures delta’s sensitivity to a small movement in time to maturity (T). In practical terms, it shows how the delta is going to change with the passage of time. The next chart displays graphically the relationship between the aforementioned variables:

Options Charm

The chart suggests that, like in the case of vanna, the charm achieves its highest absolute values when the options are around the ATM area. Therefore, slightly in-the-money or out-of-the-money options will have the highest charm values. This makes sense because the greatest impact of time decay is precisely on options “floating” around the ATM zone. In fact, deep ITM options will behave almost like the underlying asset while OTM options with the passage of time will approach 0. Consequently, the deltas of slightly ITM or OTM options will be the most eroded by time. Charm is very important to options traders because if today the delta of your position or portfolio is 0.2 and charm is, for instance, 0.05 tomorrow your position will have a delta equal to 0.25. As we can clearly see, knowing the value of charm is crucial when hedging a position in order to keep it delta – neutral or minimize portfolio risk.

Vomma: Vomma measures how Vega is going to change with respect to implied volatility and it is normally expressed in order to quantify the influence on vega should the volatility oscillate by 1 point. The fluctuations of vomma with respect to S are shown in the next chart:

Options VommaAs displayed in the above reported chart out-of-the-money options have the highest vomma, while at-the-money options have a low vomma which means that vega remains almost constant with respect to volatility. The shape of vomma is something that every options trader should bear in mind while trading because it clearly confirms that the vega that will be influenced the most by a change in volatility will be the one of OTM options while the relationship with ATM options will be almost constant. This makes sense because a change in implied volatility would increase the probability of an OTM options to expire in-the-money and this is precisely why vomma is the highest around the OTM area.

DvegaDtime: DvegaDtime is the negative value of the partial derivative of vega in terms of time to maturity and it measures how fast vega is going to change with respect to the time decay. The next chart is a visual representation of its fluctuations with respect to the underlying asset S:

Options DvegaDtime

The above reported graph clearly displays that the influence of time decay on volatility exposure measured by vega is mostly felt in the ATM area especially for options with short time to maturity. The fact that DvegaDtime is mathematically expressed as negative derivatives makes sense because time decay is clearly a price that every options holder has to pay. In order to make things easier have a look at the plots of vega and theta because you will immediately realize that both volatility and time decay have their highest and lowest values in the ATM area. It goes without saying that ATM options have the highest volatility potential and therefore vega will be effected the most by the passage of time when the strike of our hypothetical options and the underlying price gets very close.

The HyperVolatility Forecast Service enables you to receive the statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at info@hypervolatility.com with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial.

Apr
01

Options Greeks: Delta,Gamma,Vega,Theta,Rho

First of all I would like to give credit to Liying Zhao (Options Analyst at HyperVolatility) for helping me to conceptualize this article and provide the quantitative analysis necessary to develop it. The present report will be followed by a second one dealing with second order Greeks and how they work.

Options are way older than one might imagine. Aristotele mentioned options for the first time in the “Thales of Miletus” (624 to 527 B.C.), Dutch tulip traders began trading options at the beginning of 1600 while in 1968 stock options have been traded for the first time at the Chicago Board Options Exchange (CBOE). The pricing of options has always attracted academics and mathematicians but the first breakthrough in this field was pioneered at the beginning of the 1900 by Bachelier. He literally discovered a new way to look at option valuation, however, the real shift between academia and business occurred in 1973 when Black, Scholes and Merton developed the most popular and used option pricing model. Such a discovery opened an entire new era for both academics and market players. Being one of the most crucial financial derivatives in the global market, options are now widely adopted as an effective tool to leverage assets or control portfolio risk. Nowadays, it is easy to find articles, researches and studies on option pricing models but this article will instead focus on options Greeks and in particular first-order Greeks (derived in the BSM world). Options Greeks are important indicators for assessing the degree of risk coming from exogenous variables, in fact, they measure option premium’s sensitivities to small changes in different parameters. Mathematically, Greeks are the partial derivatives of the option price with respect to different factors such as volatility, interest rate and time decay.

The purpose of this article is to explain, as clearly as possible, how Options Greeks work but we will concentrate only on the most popular ones: Delta, Gamma, Vega (or Kappa), Theta and Rho. It is worth mentioning that all the charts that will be presented have been extrapolated by assuming that the underlying is a WTI futures contract, that the options have a strike price (X) of 100, that the risk-free interest rate (r) is 0.5%, that the cost of carry (b) is 0 while implied volatility is 10%.

Delta: Delta measures the sensitiveness of the option’s price to a $1 fluctuation in the underlying asset price. The chart displays how the Delta moves in respect to the underlying price S and time to maturity T:

options delta

The chart clearly shows that in-the-money call options have much higher Delta values than out-of-the-money options while ATM options have a Delta which oscillates around 0.5. Call options have a Delta which ranges between 0 and 1 and it gets higher as the underlying approaches the strike price of the option which means that out-of-the-money call options will have a Delta close to 0 while ITM options will have a Delta fluctuating around 1. Many traders think of Delta as the probability of an option expiring in-the-money but this interpretation is not correct because the N(d) term in its formula expresses the probability of the option expiring ITM but only in a risk-neutral world.  In real trading conditions higher Delta calls do have a higher probability to expire ITM than lower Delta ones, however, the number itself does not provide a reliable source of information because everything depends on the underlying. The Delta simply expresses the exposure of the options premium to the underlying: a positive Delta tells you that the premium will rise if the underlying asset will trend higher and it will decrease in the opposite scenario. Put options, instead, have a negative Delta which ranges between -1 and 0 and the below reported chart displays its fluctuation in respect to the underlying asset.

put option delta

It is easy to notice that as the underlying asset moves below the $100 threshold (the strike price of our hypothetical put option) the Delta approaches -1, which implies that ITM put options have a negative Delta close to -1, while OTM options have a Delta oscillating around 0. In practical trading the value of the Delta is very important because it tells you how the options premium is going to change in the case the underlying moves by $1. Let’s assume you purchase a 100 call options on crude oil with a Delta of +0.5 and the premium was $1,000.  If the option is at-the-money the WTI (the underlying asset) will be at $100 but if oil futures go up by $1 dollar to $101 the premium of your long call will move to $1,500. The same applies to put options but in this case the ATM Delta will be -0.5 and your long put option position will generate a profit if WTI futures move from $100 to $99.

Gamma: Gamma measures Delta’s sensitivity to a $1 movement in the underlying asset price and it is identical for both call and put options. Gamma reaches its maximum when the underlying price is a little bit smaller, not exactly equal, to the strike of the option and the chart shows quite evidently that for ATM option Gamma is significantly higher than for OTM and ITM options.

option gamma

The fact that Gamma is higher for ATM options makes sense because it is nothing but the quantification of how fast the Delta is going to change and an ATM option will have a very sensitive Delta because every single oscillation in the underlying asset will alter it.

How Gamma can help us in trading? How do we interpret it?

Again, the value of Gamma is simply telling you how fast the Delta will move in the case the underlying asset experience a $1 oscillation. Let’s assume we have an ATM call option on WTI with a Delta of +0.5 while futures prices are moving around $100 and Gamma is 0.08, what does that imply? The interpretation is rather simple: a 0.08 gamma is telling us that our ATM call, in the case the underlying moves by $1 to $101, will see its Delta increasing to +0.58 from +0.5

Vega (or Kappa): Vega is the option’s sensitivity to a 1% movement in implied volatility and it is identical for both call and put options. The below reported 3-D chart displays Vega as a function of the asset price and time to maturity for a WTI options with strike at 100, interest rate at 0.5% and implied volatility at 10% (the cost of carry is set to 0 because we are dealing with commodity options).

option vega

The chart clearly highlights the fact that Vega is much higher for ATM options than for ITM and OTM options. The shape of Vega as a function of the underlying asset price makes sense because ATM options have by far the highest volatility potential but what does Vega really tell us in real trading conditions? Again, Vega (or Kappa) measures the dollar change in case of a 1% shift in implied volatility, therefore, an at-the-money WTI options whose value is $1,000 with a Vega of , say, 100 will be worth $1,100 if the implied volatility moves from 20% to 21%. Vega is a very important risk measure for options traders because it estimates how your P/L is going to change as a function of implied volatility. Implied volatility is the key factor in options pricing because the price of a single options will vary according to this number and this is precisely why implied volatility and Vega are essential to options trading (the HyperVolatility Forecast service provides analytical, easy to understand projections and analysis on volatility and price action for traders and investors).

Theta: Theta measures option’s sensitivity to a small change in time to maturity (T). As time to maturity is always decreasing it is normal to express Theta as negative partial derivatives of the option price with respect to T.  Theta represents the time decay of option prices in terms of a 1 year move in time to maturity and to view the value of Theta for a 1 day move we should divide it by 365 or 252 (the number of trading days in one year). The below reported chart shows how Theta moves:

option theta

Theta is evidently negative for at-the-money options and the reason behind this phenomenon is that ATM options have the highest volatility potential, therefore, the impact of time decay is higher. Think of an option like an air balloon which loses a bit of air every day. The at-the-money options are right in the middle because they could become ITM or they could get back into the OTM “limbo” and therefore they contain a lot of air, consequently, if they have got more air than all other balloons they will lose more than others when the time passes. Let’s look at a practical example. Let’s assume we are long an ATM call option whose value is $1,000 and has a Theta equals to -25, if the day after both the underlying price and volatility are still where they were 1 day before our long call position will lose $25.

Rho: Rho is the option’s sensitivity to a change in the risk-free interest rate and the next chart summarises how it fluctuates with respect to the underlying asset:

option rho

ITM options are more influenced by changes in interest rates (negative Rho) because the premium of these options is higher and therefore a fluctuation in the cost of money (interest rate) would inevitably cause a higher impact on high-premium instruments. Furthermore, it is rather clear that long dated options are much more affected by changes in interest rates than short-dated derivatives. The below reported chart displays how Rho oscillates when dealing with put options:

put option rho

The Rho graph for put options mirrors what it has been stated for calls: ITM have a larger exposure than ATM and OTM put options to interest rate changes and long term derivatives are much more affected by Rho than in the short term (even in this case the 3-D graph displays negative values). As previously mentioned Rho measures how much the option’s premium is going to change when interest rates move by 1%. Hence, an increase in interest rates will augment the value of a hypothetical call option and the rise will be equal to Rho. In other words, the value of the call option will increase by $50 if interest rates move from 5% to 6% and our WTI call option has a premium of $1,000 but Rho equals 50.

As stated at the beginning of the present report this is only the first part and a second article dealing with second order Greeks will be posted soon.

Feb
15

HyperVolatility – End of the Year Report 2012

Dear All, we are pleased to announce you that the HyperVolatility End of the Year Report 2012 has been finally completed and it can be downloaded for free by clicking the following link:

HYPERVOLATILITY END OF THE YEAR REPORT 2012

As always, our analysis focuses on the most important financial markets in the world in addition to a complete and accurate examination of the macroeconomic indicators over the 2012. Therefore, the first part of the study is focused on equity markets, currency , commodity and government bond futures. The HyperVolatility Team performed for each asset class calculations regarding price fluctuations, market volatility, inter-market analysis and price distribution. All quantitative studies are accompanied by a chart and an easy to understand explanation.

On the other hand, the second part of the HyperVolatility End of the Year Report 2012 is entirely dedicated to macroeconomic factors, their fluctuations and potential influence on financial markets and global economy. The macroeconomic study focuses on 1 indicator at the time and inspects its oscillations over the 2012 in Western European countries, USA, Japan, Australia and the top emerging markets in the world (Brazil, Russia, India, China)

Please read carefully our Legal Disclaimer. The HyperVolatility End of the Year 2012 table of contents is the following:

1) Legal Disclaimer; 2) Euro Futures; 3) Japanese Yen Futures; 4) WTI Crude Oil Futures; 5) Gold 100 Futures; 6) E- Mini S&P500 Futures; 7) DAX Futures; 8) FTSE/MIB Futures; 9) German Bund Futures; 10) Treasury Bond Futures; 11) VIX Index; 12) GDP Growth Rate; 13) Unemployment Rate; 14) Inflation Rate; 15) Debt to GDP Ratio; 16) Credit Rating; 16.A) Appendix

A more ink-saving version of the HyperVolatility Enf of the Year Report 2012 is available upon request. Send us an email at info@hypervolatility.com

We take this opportunity to remind you that market projections and statistical analyses of the aforementioned classes can be obtained on a weekly basis thanks to the HyperVolatility Forecast Service (We guarantee you a 14 day free trial)

Feb
06

The Oil Arbitrage: Brent vs WTI

It is no secret that the most important crude oils in the world are the European Brent (extracted by 15 oil fields located in the East Shetland Basin in the North Sea) and the American WTI which is extracted in the US and delivered at the Cushing in Oklahoma. It is well known that the Brent Crude oil has become the global benchmark and it is used to price crude oils worldwide. Although they are extracted in geographically distant locations the chemical composition of WTI and Brent is not exceptionally different because both of them are considered to be “sweet oils” which means that both contain a low concentration of sulphur: 0.37% for the Brent and 0.24% for the WTI. This small introduction is necessary to understand that the supply/demand forces driving price fluctuations are dissimilar and the discrepancy is even clearer if we add that the Brent is exported in the whole Europe and worldwide while the WTI does not leave the US.

The Brent/WTI arbitrage (the word arbitrage is a misnomer because we are buying and selling two different asset classes) is a fairly popular trading technique within the energy sector and its aim is to profit from price discrepancies. The strategy is reasonably simple and it consists of contemporarily selling the WTI and buying the Brent (short arb) or selling the Brent and buying the WTI (long arb). Clearly, this is a spread trading technique rather easy to implement and control because both Brent and WTI futures share the same size (1,000 barrels) while the tick value (1 cent per barrel) equals to $ 10 for both contracts.

How does the trade work? Let’s assume that a trader decides to sell WTI and buy Brent futures (short arb). He sells the WTI at $ 100 and buys the Brent at $ 110 and he will make money if the 2 asset classes will move in opposite directions. If the WTI drops to $ 97 while the Brent closes at $ 112 our hypothetical trader would have made a $ 3,000 profit from the WTI and $ 2,000 from the Brent for each contract traded.

What happens if WTI and Brent move in the same direction? The strategy would still be profitable if the price augment in the Brent market outweighs the rise in WTI futures. If the Brent gains $ 3 and the WTI $ 1.5, the trader would make a $ 3,000 profit from the long Brent position but he would lose $ 1,500 on the short WTI contract which implies that the overall profit would be equal to $ 3,000 – $ 1,500 = $ 1,500

As you can see the trade would still show a profit because in our example WTI and Brent experienced different volatilities and consequently their fluctuations were not symmetrical in terms of magnitude (the first moved 3 dollars and the second only $ 1.5). However, should the Brent had moved lower and the WTI higher the short WTI / long Brent position would have lost money.

The chart #1 shows how the most important oils oscillated since 2009 until 2011:

Brent and WTI futures

It is evident that until 2011both WTI and Brent were moving symmetrically but for some fundamental reasons, such as global demand and some logistic problems with the WTI, the prices started to diverge and the spread became rather large. On the other hand, the narrowing of the arb from September 2011 onwards is mainly due to an increased demand and to the construction of the Seaway pipeline which facilitates the transportation of the WTI from the Cushing in Oklahoma to Freeport in Texas. Let’s have a look at the WTI/Brent spread now:

Brent / WTI spread

The chart #2 shows very clearly that since 2009 until the beginning of 2011 the differential oscillated following a mean reverting process (because it always tended to get back to the 0 line) and it used to fluctuate within fixed boundaries (because it rarely surpassed the $ 2.5 threshold and infrequently remained below the – $2 level for an extended period of time). However, the scenario has quite changed because in 2011 the Brent/WTI spread increased substantially and achieved the $ 25 level. If we go back to the first chart we can immediately understand what caused such a high spread: the Brent price kept increasing while WTI futures prices kept dropping.

How can a trader take advantage of such divergence? When the trade should be triggered?

Buying or selling the oil arb is up to the trader and it depends on fundamental data such as supply/demand forces, industrial productivity, etc but it is possible to identify when the trade could have a higher probability of success. The chart #3 will help us prove our point:

Brent / WTI correlation

The graph shows the correlation (which fluctuates within -1 and 1) between Brent and WTI since 2009 until the end of the 2011 and its interpretation is straightforward: the higher the correlation, the stronger the relationship between the 2 asset classes. The correlation on average is rather high which means that Brent and WTI tend to experience similar fluctuations, although with different volatilities, but there is a second important characteristic that it is very useful in practical terms: the correlation is mean reverting because it tends to drop and then explode again.

In practical terms, all the time the correlation index drops the relationship between Brent and WTI weakens, hence, the probability of dissimilar fluctuations amplify. Conversely, an increasing correlation would imply the opposite scenario.

We now know that a plunge in the correlation index would increase the probability of maximizing our profits because it would highlight that the relationship between the 2 asset classes is not going to be strong and that the spread will likely expand.  However, in real trading conditions we will need specific entry points, some numerical thresholds to look at in order to trigger our trades and the following tables should be a valuable tool for anyone interested in trading the oil arb:

Brent / WTI spread price distribution

Bear in mind that these are not trading recommendations but merely a guide and the price / correlation levels refer to the period 2009 – 2011.

The table #1 represents the price distribution of the Brent/WTI spread. The outcome of our research shows that the lowest price achieved by the spread is $ -5.42 (which means that the Brent was lower than the WTI) while the highest point was $ 26.84. The percentage row displays the percentage of observations below the reported price levels. In other words, the 24.97% of  total observations were below the $ -0.36, almost 50% of the Brent/WTI spread prices were below the $ 2.28 level while the price fluctuated below the $10.98 threshold in the 74.77% of cases. Now let’s see what the correlation key points are:

Brent / WTI correlation distribution

On average the correlation is around 0.82 but in the 25% of cases it dropped to 0.62 and it remained lower than 0.91 almost the 80% of the time. The extreme points are -0.35 and 0.99 that have been touched only once.

 Strategy Analysis

1)   The Brent/WTI spread fluctuated within $ 2 and $ 2.3 most of the time

2)  The correlation is usually fairly strong and it frequently oscillates around 0.78 and 0.82

3)  In order to have a reliable entry point both price and correlation should be out of their ranges. We should be in a situation where there is an evident mismatch

4)  Entry points are signalled by a breakthrough of the aforementioned price and correlation levels because if the arb price is higher than $ 2.3 and the correlation is lower than 0.78 then the probability of success is higher. Needless to say that good opportunities arise also when the arb price is lower than $ 2 dollars and the correlation is higher than $ 0.8

In our HyperVolatility Forecast Service we dig deeper through news and calculations. We provide financial forecasts based on volatility analysis and statistics that you will not find in a retail trading platform. The HyperVolatility Forecast Service enables you to receive the statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at info@hypervolatility.com with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial.

Oct
05

Portfolio Hedging: Risky Assets vs Safe Havens

The credit crunch changed the game and we all know it. Financial markets have been completely reshaped, in fact, the old way to invest is not yielding the results it used to and the composition of market participants have been totally revolutionised (perhaps permanently). The attention towards the management of portfolio risk augmented dramatically soon after the 2008 – 2009 and words like “safe havens” and “risky assets” started to consistently appear on many financial newspapers; but how the “safe havens” relate to “risky assets” nowadays? Which markets can today still be considered to be “safe”? The continuous weekly analysis of inter-market relationships that we perform, here at HyperVolatility, brought us to write this research. Let’s proceed with order.

Risky assets are all those markets that are traded mainly for speculative purposes so in this category we primarily find equity indices (S&P500, DAX, Dow Jones, FTSE100, Nikkei225, etc), stocks (Apple, Microsoft, Amazon, etc), some currencies (essentially Euro vs US Dollar and Yen vs US Dollar) and the most popular commodities such as WTI Crude Oil (this list is far from being exhaustive). Clearly, some of the aforementioned markets are more prone to speculation than others because of the nature of their market players (for instance equity indices are mainly traded by hedge funds, banks and retail traders whilst WTI Crude Oil is traded even by large commercial players that enter futures or options positions purely to hedge their physical exposure) so the way they move and react to market news and changes in the fundamentals vary vastly. On the other hand, the “safe assets” are the ones that fund managers and traders use in order to limit losses during sharp retracements in equity indices. In other words, they are employed in portfolio management as a sort of insurance. The markets that have historically played this role are Gold, Japanese Yen, US Dollar, Swiss Franc, Treasuries such as the American Treasury Bond or the German Bund and the “more recent” VIX Index (the adjective “recent” refers to the fact that the VIX Index could not be traded in the past). The reason they are called “safe havens” is because they tend to rise when risky assets fall, consequently, they are inversely correlated to equity indices and stocks; but is it really so? Do they really provide a valuable parachute against crash landings?

In order to answer the above mentioned questions we take 2 risky assets, E-Mini S&P500 and Crude Oil futures, and we compare their fluctuations against American Treasury Bond futures, German Bund futures, Gold futures, Japanese Yen futures and the VIX Index (the weekly analysis of all the aforementioned markets is covered by the HyperVolatility Forecasts service, send us an email at info@hypervolatility.com to know more). The study of the inter-market relationships has been performed using the correlation analysis and the dataset consists of weekly data for the years 2010, 2011 and 2012 (the last observation for the 2012 has been registered on the 24th of August 2012). Let’s examine E-Mini S&P500 futures:

As we can clearly see from the above reported chart the American index is negatively correlated to all the “safe havens”, which means that while E-Mini S&P00 futures were retracing the safe assets were going up and vice versa. Nevertheless, the correlation index fluctuated a lot throughout last years and the fact that Gold and Japanese Yen futures show an incredibly strong positive correlation in 2010 proves what it has been just stated. Therefore, any hypothetical fund manager or trader willing to hedge any S&P500 long position with these instruments would have obtained fairly poor results in 2010. However, it is worth noting that in 2011 and 2012 the futures on the Asian currency performed fairly well and proved to be moderately good when offsetting the risk coming from long positions on risky assets whilst gold futures worked out well only in 2011. Additionally, the futures on the German Bund had a fairly good negative correlation in 2011 but the performances registered in 2010 and 2012 are not really encouraging which means that there were extended periods of time where both instruments (E-Mini S&P500 and German Bund futures) were moving in the same direction. The same thing can be said for Treasury Bond futures, which display a more solid negative correlation in 2012 than German Bund, but the overall performance is still not that good. The only market which showed a constant and reasonably robust negative correlation with E-Mini S&P500 futures is the VIX Index that can be traded via VIX futures and options offered by the CBOE. Let’s now see if the scenario is different for WTI Crude Oil futures:

The chart displays a significant negative correlation and all the “safe havens” seem to be very good when hedging crude oil positions, although, in 2012 there is a considerable positive relationship with Gold futures (we will explain why later). Specifically, Japanese Yen futures and the VIX Index both show a negative relationship which was evidently much stronger in 2011 than it is now and the analysis manifestly highlights that the best products to use, when hedging any crude oil position, are definitely Treasury Bond and German Bund futures because the negative coefficients that they display are very solid and the inverse rapport seems to be quite stable over time.

So, why are Gold futures a sub-optimal choice? There are no definite answers to that but there are two contributing factors which could help to explain what is happening:

1) The CME increased margin calls for gold futures in August 2011, hence, many traders could not afford to keep their positions open anymore and had to cut them. This resulted in a large drop in gold prices, even if investors were heavily using them to hedge against the massive plunge that risky assets experienced over the summer of 2011, and by looking at the above reported chart it is easy to notice that in 2011 Gold futures were the worst performers (the correlation is still negative but it is definitely weaker than the one registered for the remaining “safe havens”)

2) Gold prices are still used for hedging purposes; the only problem is that they are now employed to counterbalance a different type of risk: over-inflation. In particular, gold futures are being purchased to cope with a higher inflation that can be caused by the “expansive monetary policies” recently adopted by the Fed and the ECB (the Fed will purchase 40 billion dollars worth of mortgage backed securities on a monthly basis and the ECB just launched an apparently unlimited bond buying programme). This explains the uptrend in gold prices and the positive correlation with the so-called risky assets in 2012

According to our findings the best markets to use when hedging positions on E-Mini S&P500 futures are the VIX Index, Treasury Bond and Japanese Yen futures whilst Crude Oil futures are best covered by Treasury Bond and German Bund futures with the Asian currency and the VIX being the 3rd best option (they are equally good so we can both place them at the 3rd place in our ranking).

Conversely, Gold prices proved to be the worst performer and the least reliable market, amongst all the “safe havens” analysed in the present research, when trying to minimise the downside risk on equity indices and risky assets.

 

The HyperVolatility team provides weekly volatility forecasts directly delivered at your email address. Send us an email at info@hypervolatility.com to know more and join our promotional campaign. WE GUARANTEE YOU A ONE MONTH AND A HALF FREE MEMBERSHIP FROM THE MOMENT YOU SIGN UP WITH US.

 

May
29

HyperVolatility Forecasts: BIG NEWS

Dear HyperVolatility readers,

we would like to inform you that the forecasting service is now carried on a personal basis only. Hence, if you want to receive market analysis based on quantitative methods and statistics in order to support your investment decisions please do not hesitate to send us an email at hypervolatility@gmail.com and let us know which asset class you would like to receive the projections for. You can choose up to 3 markets from the following list:

1) VIX Index

2) E-Mini S&P500 Futures

3) Crude Oil Futures

4) Gold Futures

5) German Bund Futures

6) Treasury Bond Futures (30 years)

7) DAX Futures

8) FTSE/MIB Futures

9) Euro Futures

10) Japanese Yen Futures

You will receive 1 report every week containing the statistical analysis, which will be explained to you in details, for the 3 markets of your choice.

Are you tired of reading the same non-sensical market commentaries? do you want to know how volatile the market and your portfolio are going to be in the next week? are you looking for a more scientific approach to investing and trading?

if you answered YES to these questions we are probably a good match for you

The studies we provide are extremely useful for both futures and options traders therefore everyone can benefit from our researches.

Remember that our approach does not consist in interpreting the market according to our view of things but in LETTING THE DATA SPEAK

The service will become fee-based in a couple of months time but we guarantee you a 2 free months membership from the moment you sign up with us. You will not be forced to upgrade to the fee-based service and there are no legal commitments.

In other words, you will receive a total of 8 reports containing 24 analysis and forecasts related to the asset classes you chose completely free of charge.

We believe in a genuine and sincere type of business model: you like us, you like our analysis, you stay with us. As simple as that.

Also, there are many promotions for those of you who will manage to bring us more readers and subscribers, in fact, you could end up paying absolutely nothing for your forecasts. Send us an email at hypervolatility@gmail.com to know more.

We will keep posting articles on our blog and if you want us to go through a specific market or product please let us know and we will try to address your request as soon as possible.

It is important to point out that:

1) WE DO NOT OFFER PRE-PACKAGED, LOW QUALITY, IMPOSSIBLE TO MODIFY – TYPE OF SERVICES

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HYPERVOLATILITY: DO NOT LIMIT YOUR RISK, TRADE IT 

Apr
21

Trading Gold & Silver: A Realized Volatility Approach

First of all, I’d like to thank Nick Pritzakis for editing and revising the article.

Now, gold and silver are amongst the most heavily traded commodities in the world. Not only that, interest towards precious metals has been growing at an exponential rate. Many investors, institutional and retail…use them as a way to diversify their portfolios. Of course, this is an attempt to reduce their exposure to the equity markets, as well as hedge against the potential fear of inflation.
In fact, many market participants rush to buy precious metals, particularly gold, during sharp retracements in the equity market, as well as, when we’ve had political instability and the threat of war.
It’s no secret that gold and silver are “safe havens”, the financial parachute that investors and traders use during a crash landing.
But are they really safe? Are they still a good investment or just another bubble waiting to pop? You see, rather than blindly accepting what journalists and financial advisors tell us, we’ve decided to investigate these markets further, by using a more scientific approach called quantitative analysis.
The chart below displays the volatility fluctuations in gold futures over the last 2 years (January 2010 to 18th of April 2012). As you can see, there are two volatility estimators: close-to-close and the Yang Zhang estimator (“YZ”). The close-to-close is the volatility obtained by modelling closing prices each day. The Yang Zhang is the volatility extracted using high, low, close and opening prices and then weighted for the overnight risk.

 

There is significant evidence that the close-to-close volatility (left hand axis) tends to be higher than the YZ volatility (right hand axis). At first glance, we can observe that the average volatility for the market is 18% (for the close-to-close) while it drops to 7.5% (for the YZ volatility). By the way, the VIX averages around the 13%.

So what are these numbers telling us? Can we draw a verdict? Well, the overnight risk is greater than the intra-day one. In other words, gold prices are likely to experience big jumps from one day to another… and then trade within a narrow range during the day (everything else being equal).
And actually, we saw this last summer when we had a big price spike in gold… while the equity markets were getting crushed. And believe it or not, the volatility rose as gold prices were increasing.
Wait…What? But isn’t volatility connected to market crashes? Doesn’t volatility mean only confusion and uncertainty?
The quick answer would be” yes” but the correct one is “it depends”.

Sure, volatility tends to explode during market crashes. And, this type of relationship is called asymmetric effect (or leverage effect), and it’s particularly strong in equity markets.
However, in currencies and commodities the dynamics are a lot more complicated. You see, there is a tendency for volatility to pop as prices go up. Now, at this point, it’s a typical feature, not only in the gold and silver market, but also in the Swiss Franc, Japanese Yen, T-Bonds, German Bunds and other government debt securities…just to name a few.
Here’s something else.
The chart suggests that the volatility in gold futures is mean reverting. Therefore, it will tend to collapse towards its long term average over time. This, of course implies that short volatility strategies can profit… if kept on long enough. On the other hand, long volatility strategies can potentially be profitable if entered when the close-to-close volatility touches the 10% level or when the YZ volatility is trading around the 4% threshold.
It’s important to note here… that volatility is dynamic. What’s worked in the past or is currently working now does not mean that it will continue to work. And as always, past performance is not indicative of future results.

Moving on. What about the Silver?

The chart shows some similarities with gold. For example, we did see an explosion in volatility last summer as silver prices were increasing. Now, if we analyze the difference amongst the close-to-close (left hand axis) and the YZ (right hand axis) volatility, we’ll find a pattern which we saw earlier from the gold market. Once again, the overnight risk is greater than the intra-day moves.

As you may know, the silver market is extremely volatile… a lot more then the gold market. In fact, the average close-to-close volatility is around 40% (left hand axis) while the YZ volatility fluctuates around the 17% level.

And actually, like gold, silver volatility tends to be mean reverting.

Also, last summer, the close-to-close volatility touched 85% …in July 2011 and November 2011 it touched 100%. Of course, long volatility strategies would have been pretty sweet had you put them on before these big moves.

Finally, we’ve looked at both markets individually; it’s time to look at them together.

Closing Thoughts:

1) The silver market is twice as volatile as the gold market.

2) Overnight risk is big, the majority of the large movements occur overnight…not intraday.

3) The volatility is mean reverting in both markets and it follows a symmetric effect (it increases with buying pressure)

4) The volatility in gold is smoother.

Strategy Analysis: For Option Traders


Now, these are not trading recommendations, but a basic guide under the present volatility regime. Remember, volatility is dynamic and past results are not indicative of future results.

1) Long straddles or strangles are favourable when the realized volatility is around 20% for the silver and 10% for gold

2) Iron condors and butterflies positions are favorable when the realized volatility achieves the 35% – 40% for silver and 15% – 20% for gold.

3) Long volatility strategies are favorable when kept for a short period of time.

4) Short volatility strategies may take up to a month and a half to show consistent returns.

5) Call options tend to benefit from a one-two punch. When the futures price rises, implied volatility tends to rise with it.

In this report we tried to provide a quantitative approach to trading gold and silver using realized volatility data. Of course, there are many ways you can trade them and other factors to consider.

 

 

 

Feb
12

HyperVolatility – End of the Year Report 2011

Dear All, we are pleased to announce you that the HyperVolatility End of the Year Report 2011 has been finally completed and it can be downloaded for free by clicking the following link:

HYPERVOLATILITY END OF THE YEAR REPORT 2011

In the first part, the study is focused on equity markets, currency and commodity futures. Each analysis is divided into 2 parts: in the first one we go through the overall performance of the particular asset under examination whilst in the second one we focus on intraday and close-to-close volatilities which have been calculated using the TGARCH model.

The second part is entirely centred on the macroeconomic factors and their influence on financial markets. We try to pull together the big picture by singularly studying the most important exogenous variables which affected financial prices over the 2011. This examination has been carried on the major economies in the world in order to keep an eye on the global status of the economy.

Please read carefully our Legal Disclaimer. To give you an idea of what you can expect we report here the table of contents:

1) Legal Disclaimer; 2) Euro Futures; 3) British Pound Futures; 4) Swiss Franc Futures; 5) Japanese Yen Futures; 6) (WTI) E-Mini Crude Oil Futures; 7) Gold 100 Futures; 8) Yen, Australian Dollars and Commodities; 9) DJ EuroStoxx50 Futures; 10) E- Mini S&P500 Futures; 11) German Bund Futures; 12) Correlation Matrix Analysis; 13) Correlation Matrix Appendix; 14) Unemployment Rate; 15)Inflation Rate; 16) Gross Domestic Product; 17) Debt to GDP; 18) BRIC Economies: a brief summary; 19) Macroeconomic Data

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