### The VIX Index: step by step

The VIX Index has been introduced by the CBOE in January 1993 and since then it has become the most popular and well known volatility index in the world. The VIX is an index extracted from S&P500 options and its calculation has been changed in September 2003 in order to obtain observations not linked or dependant from any model idiosyncrasy. The present study, inspired by the paper written and compiled by the CBOE, will show how to calculate the VIX Index in a step–by–step fashion. There will be ample explanations about how the index works and we will break down the formula in order to provide a better understanding of the function and weight of every component. Let’s start with the general formula for the VIX Index:

$\dpi{120}&space;\bg_white&space;\large&space;\sigma&space;^2&space;=&space;\frac{2}{T}\sum_\imath&space;\frac{\Delta&space;K_\imath}{K_\imath&space;^2}&space;e^&space;R^T&space;Q&space;(K_\imath&space;)-&space;\frac{1}{T}&space;\left&space;[&space;\frac{F}{K_0}-1&space;\right&space;]^2$                                     (1)

Where

$\dpi{120}&space;\bg_white&space;\large&space;\sigma$ = $\dpi{120}&space;\bg_white&space;\frac{VIX}{100}\Rightarrow&space;VIX&space;=&space;\sigma&space;x&space;100$

T = Time to expiration

F = Forward Index price (the ATM strike price)

K0=  First strike price below the Forward price F

Ki= Strike of the ith out–of–the–money option. A call option strike will be considered if Ki>K0 while a put option strike will be used if Ki=K0

ΔKi = it is the midpoint between the strike prices. Specifically, the strikes used will be on both the sides of Ki. In other words, ΔK for the lowest strike is just the difference between the lowest strike and the penultimate strike of the option chain while ΔK for the highest strike is equivalent to the difference between the highest strike and the strike immediately below the top one. The formula is the following $\dpi{120}&space;\bg_white&space;\Delta&space;K_\imath&space;=&space;\frac{K_\imath_+_1&space;-&space;K_\imath_-_1}{2}$

R = Risk free interest rate (the interest rate used is usually the Treasury Bond yield that more closely matches the option expiration date)

Q (Ki) = The midpoint of the spread between bid price and ask price for each option with a strike Ki

This is the formula that it is currently employed to calculate the most famous risk management index in the world. Before we provide any real example it is necessary to clarify some points. First of all, the VIX index is calculated using 2 expirations: the front month and the second front month contracts. In our study we will be using S&P500 option prices recorded on the 10th of October 2013 and therefore the front month options will be those expiring on the 18th of October 2013 (which will provide us with information about the volatility in the near term) while the second front month options will expire on the 15th of November 2013 and they will provide us with information about the volatility in the medium term. It is important to point out that near term options must have at least 7 days to expiration and when this criteria is no longer met the model automatically rolls to the next available contract. Let’s give an example, our front month options expire on the 18th of October while the medium term options will expire on the 15th of November, hence, on Friday the 12th the VIX will mechanically roll. At this point, the front month options used will be the ones expiring on the 15th of November while the second front month options employed in the calculation will become those expiring in December. This measure has to be adopted in order to avoid mispricing issues that commonly happen when options are about to expire. Another important detail to mention is that T (time to expiration) is calculated in minutes using calendar days, consequently, the time to expiration will be given by

$\dpi{120}&space;\bg_white&space;T&space;=&space;\frac&space;{M_c_u_r_r_e_n_t_&space;\hspace&space;{1&space;mm}_d_a_y&space;+&space;M&space;_s_e_t_t_l_e_m_e_n_t&space;\hspace&space;{1&space;mm}_d_a_y&space;+&space;M_o_t_h_e_r&space;\hspace&space;{1&space;mm}_d_a_y_s&space;}{Minutes\hspace&space;{1&space;mm}in&space;\hspace&space;{1&space;mm}a\hspace&space;{1&space;mm}&space;year}$                                  (2)

M current day= minutes remaining until midnight of the same day

M settlement day= minutes remaining from midnight until 08:30 am on SPX settlement day

M other days= total minutes in the days between current day and settlement day

If we assume that the data have been recorded exactly at 08:30 am on the 10th of October and that options will expire at 08:30 am of the 18th of October:

$\dpi{120}&space;\bg_white&space;T_1&space;=\frac&space;{930+510+1,920}{525,600}&space;=&space;0.0246575$

$\dpi{120}&space;\bg_white&space;T_2&space;=\frac&space;{930+510+3,540}{525,600}&space;=&space;0.1013699$

Needless to say that T1 and T2 refer to near term and medium term options respectively. The yield for 1 month Treasury Bills as of the 9th of October 2013 was 0.27% and therefore, given that our October options expire in 9 days while the November options will expire in 37 days, we will use this figure for both near and medium terms.

We now need to determine the F price of the index and in order to do so we take the strike price at which puts and calls have the smallest difference in absolute terms. The below reported table displays call and put prices with their absolute differential:

The red back–grounded figures are the strike prices at which calls and puts have the lowest difference, however, the two expiration dates have 2 different strike prices: ATM for October options is at 1,650 while ATM for November options is 1,655. In order to simplify calculations, and given the fact that the difference is extremely small, we will take 1,650 as F price because it is the front month contract. We can calculate F using the following formula:

$\dpi{120}&space;\bg_white&space;F&space;=&space;Strike&space;\hspace&space;{1&space;mm}Price&space;+&space;e^R^T&space;x&space;(&space;Call&space;\hspace&space;{1&space;mm}Price&space;-&space;Put&space;\hspace&space;{1&space;mm}&space;Price)$                                 (3)

Obviously, there will be two forward index values, F1 and F2 , the first for near term and the second one for medium term options respectively:

$\dpi{120}&space;\bg_white&space;F_1:&space;1,650+&space;e^(^0^.^0^0^2^7&space;\hspace&space;{1mm}^x&space;\hspace&space;{1mm}^0^.^0^2^4^6^5^7^5^)x&space;(23.75&space;-&space;22.7)&space;=&space;1,651.05$

$\dpi{120}&space;\bg_white&space;F_2:&space;1,650+&space;e^(^0^.^0^0^2^7&space;\hspace&space;{1mm}^x&space;\hspace&space;{1mm}^0^.^1^0^1^3^6^9^9^)x&space;(39.75&space;-&space;37.3)&space;=&space;1,652.45$

Now we have both  F1 and F2 , so we can identify K0 which is the strike price immediately below the forward prices. In our case, the closest strike right below F1 and F2 is 1,650. Consequentially, K0,1= 1,650 and K0,2 = 1,650.

The next step is to select all put options whose strike is lower than K0 and all call options whose strike is higher than K0. The selection excludes every option with a bid equal to 0 and it terminates when there are 2 consecutive strike prices that equal zero:

The above reported table explains very well what stated before. In the month of October the lowest puts are at 790 and 795 but the two red back–grounded options cannot be accepted in our calculation because there are two consecutive 0 in their bid prices and therefore they are our stopping point. In other words, no option with a lower than 800 strike price will be considered into the calculation of the VIX. The same principle applies to calls and in fact 2,095 and 2,100 are the highest call option strike prices that will be considered. The same procedure will be applied to November options. It is important to point out that the option chains will rarely have the same amount of strikes available because according to volatility fluctuations the number of strikes that will be priced by market makers will vary. It goes without saying that high volatility explosions will obligate market makers to price even Far–Away–From–The–Money options on both sides because the demand for these instruments will rise. Consequentially, the number of strikes that will be used for the purpose of calculating the VIX will vary according to volatility fluctuations and swings in S&P500 futures. The following table lists the options that will be used for calculating the volatility index:

The ATM strike is highlighted in blue. The put options in the near term contract that will be used start from strike 800 until strike 1,645 while the call options range from strike 1,655 until strike 2,100. The medium term strikes, instead, goes from 985 until 1,645 for put options and from strike 1,655 until strike 2,100 for calls. We now calculate the specific weight that every single strike will have in the calculation by using the following formula and we will take the 800 put as an example:

$\dpi{120}&space;\bg_white&space;\frac{\Delta&space;K_8_0_0&space;\hspace&space;{1&space;mm}Put}&space;{K^2_8_0_0&space;\hspace&space;{1&space;mm}Put}&space;e&space;^R^T^1&space;Q(800&space;Put)$                        (4)

Please bear in mind that Q is the midpoint between bid and ask while ΔK is the difference between the last option’s strike and the closest next strike, hence, in our case ΔK is (805 – 800) = 5. Let’s proceed with the calculation:

$\dpi{120}&space;\bg_white&space;\frac{5}{(800)^2}\hspace&space;{2&space;mm}2.71828&space;^(^0^.^0^0^2^7&space;\hspace&space;{1&space;mm}^x&space;\hspace&space;{1&space;mm}&space;^0^.^0^2^4^6^5^7^5^)&space;(0.05)=&space;0.000000390651$

The next table summarizes the contribution of each option strike to the overall computation of the VIX Index:

Now, the weights need to be added up and multiplied by 2/T1 for the near term and by 2/T2for the medium term and by performing this calculation we would have 0.074319519775 for the near term and 0.041553088 for the medium term.

The equation (1) that we presented at the beginning of this study is almost completed, in fact, the final part is the only one yet to be estimated. Let’s proceed:

$\dpi{120}&space;\bg_white&space;\frac{1}{T_1}&space;\left&space;[&space;\frac{F_1}{K_0}-1&space;\right&space;]^2&space;=&space;\frac&space;{1}{0.0246575}&space;\left&space;[\frac&space;{1,651.05}{1,650}-1&space;\right&space;]^2&space;=&space;0.000016423$

$\dpi{120}&space;\bg_white&space;\frac{1}{T_2}&space;\left&space;[&space;\frac{F_2}{K_0}-1&space;\right&space;]^2&space;=&space;\frac&space;{1}{0.1013699}&space;\left&space;[\frac&space;{1,652.45}{1,650}-1&space;\right&space;]^2&space;=&space;0.000021750$

We can now complete the calculation by subtracting the two members of equation (1):

Near Term σ21 : 0.074319519775 – 0.000016423 = 0.074303096

Medium Term σ22 : 0.041553088 – 0.000021750 = 0.041531338

The final VIX computation is given by the following formula:

$\dpi{120}&space;\bg_white&space;VIX&space;=&space;100&space;\hspace&space;{1&space;mm}&space;x&space;\hspace&space;{1&space;mm}\sqrt\left&space;\left&space;\{&space;T_1&space;\sigma_1^2&space;\left&space;[&space;\frac{N_T_2-N_3_0}{N_T_2&space;-&space;N_T_1}\right]&space;-&space;T_2\sigma&space;_2^2&space;\left&space;[&space;\frac{N_3_0&space;-&space;N_T_1}{N_T_2&space;-&space;N_T_1}&space;\right&space;]\right&space;\}&space;x&space;\frac&space;{N_3_6_5}{N_3_0}$

The second term of the equation is nothing but the computation of the square root of the 30 day average of σ21 and σ22which are subsequently multiplied by the first term 100.  The weights of σ21 and σ22 are less than 1 or almost equal to 1 when the near term options have less 30 days and the medium term options have more than 30 days to expiration. However, it is worth noting that when the VIX rolls both near and medium term options have more than 30 days to expiration. Let’s now conclude the VIX estimation:

NT1= minutes left before the settlement of near – term options

NT2= minutes left before the settlement of medium – term options

N30= number of minutes in 30 days

N365=  number of minutes in a year composed by 365 days

If we plug in the numbers we have the following outcome:

$\dpi{120}&space;\bg_white&space;\sqrt\left&space;\{&space;0.0246575&space;\hspace&space;{1&space;mm}x&space;\hspace&space;{1&space;mm}0.074303096&space;\hspace&space;{1&space;mm}&space;x&space;\left&space;[&space;\frac{53,280&space;-&space;43,200}{53,280&space;-&space;12,960}\right]&space;+&space;0.1013699&space;\hspace&space;{1&space;mm}&space;x&space;\hspace&space;{1&space;mm}&space;0.041531338&space;\hspace&space;{1&space;mm}x&space;\hspace&space;{1&space;mm}\left&space;[&space;\frac{43,200&space;-&space;12,960}{53,280&space;-&space;12,960}&space;\right&space;]\right&space;\}&space;\hspace&space;{1&space;mm}&space;x&space;\hspace&space;{1&space;mm}&space;\frac&space;{525,600}{43,200}$

This leads to the very last step: VIX = 100 x 0.209736087 = 20.9%

Now, the number we came out with is fairly accurate but it is limited to the moment in which the option prices have been “frozen”. Consequentially, the aforementioned procedure and calculation, in order to be precise, has to be automated and repeated every instant because any changes in option premiums will inevitable affect the final assessment of the VIX.

The HyperVolatility Forecast Service enables you to receive 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.

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### The Volatility Smile

Option markets are multidimensional, in fact, options spreads can be created using different strikes, different maturities or different type of options (calls / puts). Besides, option traders cannot track instantaneous price changes on the entire option chain, hence, it is easy to derive that the most important factor in option trading is not the price of the option itself. The variable that has to be accurately tracked and monitored at all times is, in fact, what drives and determines the price of the option: volatility. In reality, there are different types of volatilities but the one extracted from option premiums is called implied volatility (the volatility extracted from futures prices is instead referred to as realized volatility) and its shapes and fluctuations are crucial to any market player involved in options trading. The present research will try to describe the dynamics of the implied volatility shape and to analyze its most common evolutions: Smile, Smirk and Forward Skew. In particular, the implied volatility figures used in the present examination have been extracted from front month WTI option premiums traded on the 30th of August 2013 which expire in October. All calculations and charts have been respectively performed and created with the HyperVolatility Option Toolbox. The following chart displays the so–called volatility smile:

(Source: HyperVolatility Option Toolbox)

As we can see from the above reported graph, the curve is higher at the extremes but rather low in the middle (bear in mind that the At–the–Money strike was \$107.5). This is the typical shape for a front month implied volatility curve where the high demand for ITM calls and OTM puts as well as for ITM puts and OTM calls drives the volatility higher. In many cases, you will hear that the volatility for Out–of–the–Money options is higher but such statement is clearly incorrect because without further specification it implies that only OTM puts and calls experience such high volatility. The chart evidently shows that the volatility for ITM and OTM options is higher but, for obvious reasons, the volatility for the strike where a call option is In–the–Money will be almost as high as the volatility for the Out–of–the–Money put option and vice versa. Consequentially, saying that Away–from–the–Money options (both calls and puts) have a higher implied volatility than At–the–Money options is without a doubt the most correct statement. The most natural questions at this point would be: Why? What does a smile–shaped curve tell us?

The most obvious thing to say is that the volatility on AFTM options is higher because investors tend to trade them more often and they consequently push the volatility on the upside. The reason why investors buy wings is that ITM options have more intrinsic value than the ATM ones while OTM options have more extrinsic value than an option struck At–the–Money. Consequentially, the presence of an implied volatility smile–shaped curve is typical of more speculative markets. The smile suggests that, when large volatility shifts happen, many market players rush to buy OTM options for speculative reasons while ITM options are primarily purchased to stabilize portfolio gains. The next chart shows how the curve moves:

(Source: HyperVolatility Option Toolbox)

Many researches on implied volatility curve dynamics showed that the 75% of volatility changes can be defined by a total shift, up or down, of the entire curve as you can see from the chart. A further 15% of the movements consist of curve twisting (the right hand side of the curve goes deeper down while the left side gets pulled on the right or vice versa) while the remaining 10% is the product of a change in convexity (wings getting wider or tighter).

Smile–shaped curves are frequently found in equity index options, stock options and popular commodities / currencies (Euro, WTI, Gold, etc). Nevertheless, it is worth noting that the shape of the curve can even evolve over time. This concept can be better explained by looking at the following chart:

(Source: HyperVolatility Option Toolbox)

The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility. This phenomenon is commonly found in equity markets and risky assets. In this simulation the ATM strike is 116 and its volatility is 13.1% but OTM puts and ITM calls are much more expensive because they are trading above the 70% level. As previously mentioned, the implied volatility curve can change and evolve and a volatility smile can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened. Smirks are simply telling us that lower strikes are more traded than higher strikes and OTM puts as well as ITM calls are being heavily traded. If the market is heading south, a smile would easily evolve into a smirk because of the great buying pressure generated by market players rushing to buy OTM puts to protect their portfolios. The purchase of ITM calls, even during market crashes, makes sense because ITM call options have already an established intrinsic value and they have the highest probability to expire In–the–Money; in other words they are safer. However, in the event of market downtrends the evolution of a volatility smile into a smirk would predominantly be caused by the large buying volume on OTM puts.

The Volatility smile, nevertheless, can go through another metamorphosis whose final output is the so–called forward skew:

(Source: HyperVolatility Option Toolbox)

The forward skew is nothing but a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls. This type of curve is more frequently found in commodity markets, particularly agricultural products, than equity indices or stock options. Even in this case the increase in volatility is provoked by an augment in demand for these options. However, the strong buying pressure concentrated on OTM calls is often the main cause of such shape. Let us break it down. Many players in commodity markets are commercials (mining and energy companies, grain / wheat / sugar / coffee producers) and therefore a disruption in the supply chain of a particular commodity can generate serious problems. A shortage in oil supply due to geopolitical variables, a disappointing crop due to a frost or to challenging meteorological conditions, continuous strikes in a particularly large mine are all factors that would force companies to buy as quickly as possible the commodity they need in order to lock in the order. Consequentially, the remarkable buying pressure on OTM calls would inevitably drive their price up and that is why the implied volatility of higher strikes is more elevated than others.

Let us now summarize the main concepts in order to avoid confusion:

1) An implied volatility smile means that Away–from–the–Money options have a higher implied volatility than At–the–Money options

2) Implied volatility smile–shaped curves are typical of highly speculative markets

3) Many researches on implied volatility curve dynamics showed that the 75% of all volatility changes consist of a shift, up or down, of the entire curve

4) Smile–shaped curves are frequently found in equity index options, stock options and the most popular commodities / currencies

5) The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility

6) Volatility smile curves can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened

7) The forward skew is a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls

8) The forward skew curve is more frequently found in commodity markets (particularly in agricultural products)

9) The formation of a forward skew curve is often the consequence of a shortage in the supply chain due to transportation issues, geopolitical problems, adverse meteorological conditions, etc

The HyperVolatility Forecast Service enables you to receive 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.

### Commodity Volatility Indices: OVX and GVZ

The present research will examine the most popular commodity volatility indices proposed by the CBOE: the OVX and the GVZ. It is important to point out that this study is the second component of a bigger research whose first part is entitled “Equity Volatility Indices: VIX, VXN, VXD, RVX” . The analysis will follow the structure presented in the first half and it is aimed to provide pivotal volatility levels. (The HyperVolatility Forecast Service provides market projections for the VIX, Gold, WTI crude oil and many other asset classes. Send an email to info@hypervolatility.com and get a free 14 days trial). Before getting started it is worth reminding that the OVX is a volatility index based on the performance of the options written on the USO (United States Oil Fund) while the GVZ is calculated on options written on the SPDR Gold Shares Trust. The next chart displays the ranking of both commodity volatility indices:

The most important levels to observe are the 25%, the median and the 75% ones. The OVX has a median value fluctuating around 32.8% while the GVZ is much lower and, on average, it does not get higher than 18.1%. In case of low volatility environments the OVX remains around the range 29% – 30% while the GVZ tends to oscillate around 16%. On the other hand, high volatility days would probably see the OVX moving around 37% while the GVZ does not usually surpass the 21.3%. These levels are crucial to anyone who wants to trade oil or gold volatilities because they will provide buy / sell signals for options traders. Let’s list some of them (remember these are not recommendations but only a general rule):

1) Long Gold or WTI Oil volatility when the OVX is below 30% and the GVZ is around 16%

2) Range trading strategies, such as condors or butterflies, should be adopted when the OVX is higher than 35% and the GVZ is above 19%

3) If the OVX or the GVZ are fluctuating around their median levels, it implies that some major movement is about to occur. Therefore long volatility strategies could be implemented when the OVX is around 30% – 31% and the GVZ is in the 17% – 18% interval.

The fact that a volatility index has a high value does not mean that it is the most volatile one. We already tried to address this issue when dealing with equity volatility indices so now we will attempt to explain such a phenomenon for commodity volatilities too. The next chart plots the volatilities for the OVX and GVZ indices:

The chart clearly displays the volatility of both commodity volatility indices. The relationship between the OVX and the GVZ is positive, in fact, the correlation between the 2 indices is +0.77 while the correlation between the volatility of the OVX and the volatility of the GVZ is +0.62. It is interesting to notice that the 10% – 13% interval is a key mean reverting level in both markets because all the time the volatility of the OVX or GVZ touched this level both asset classes experienced a major volatility explosion. The next chart shows the distribution ranking for the volatility of commodity volatility indices:

The distribution ranking demonstrates that the GVZ, although lower than the OVX in volatility points, is more volatile than the OVX index. Specifically, GVZ’s volatility oscillates on average around the 18% while the OVX’s oscillation rate does not go higher than 13.3%. In low volatility environments the oil volatility index’s fluctuations rate is not lower than 10.6% while gold’s index oscillations rarely gets lower than 13.9% (these are the mean reverting points for the volatility of commodity volatilities). On the other hand, volatility explosions are not higher than 20.7% for the volatility of the OVX and 22.5% for the GVZ. Now we can improve on the list of buy/sell signals we previously mentioned (again these are not trading recommendations but only a general guide):

1) Long Gold or WTI Oil volatility when OVX’s volatility is around 10% – 11% or when GVZ’s volatility is within 13% – 14%

2) Condors or butterflies, should be entered when OVX’s volatility is higher than 19% – 20% and the GVZ’s one is above the 20% – 21% interval

3) If OVX and GVZ volatilities are oscillating around their median values some long volatility strategies are definitely safer than selling straddles or naked options. Hence, when the volatility of the OVX is around 13% – 14% and the volatility of the GVZ is in the 18% – 19% interval, it is a good risk management practice to hedge the portfolio against a potentially higher degree of market fluctuations

If you are interested in trading gold futures or options you might want to read our research “Trading Gold and Silver: A Realized Volatility Approach”

Instead, if you are looking to trade WTI oil futures or options you will find the research “The Oil Arbitrage: Brent vs WTI” very helpful

### Equity Volatility Indices: VIX, VXN, VXD, RVX

The present research will go through the most popular equity volatility indices proposed by the CBOE. The aim of the research is to identify how they fluctuate and to quantify the magnitude of their movements. The actual study will be followed by a second one entirely focused on commodity volatilities and the examined asset classes will be Gold and WTI Crude Oil (the HyperVolatility Forecast Service provides market projections for the VIX, Gold, WTI crude oil and many other asset classes. Send an email to info@hypervolatility.com and get a free 14 days trial). The great attention towards volatility indices and the remarkable popularity gained by VIX futures are surely undeniable but what is the risk involved in these markets? What is the volatility index that best fits your trading style and portfolio needs? Do you know how the VIX performs compared to other volatility indices? The HyperVolatility team trades and analyzes volatility movements on a daily basis on different asset classes and the present study is a summary of some of our findings. The examined data sample goes from January 2011 until April 2013 and the present research will examine 4 equity volatility indices: the VXN (Nasdaq 100), the VXD (Dow Jones), the RVX (Russell Index) and the VIX (S&P500). The first chart displays the distribution ranking of each index and it is a good approximation of how volatile the aforementioned indices can be:

The graph clearly indicates that, on average, almost all indices move within the 18% – 22% interval (the RVX is the only one above this range as its median is 23.43%). The lowest fluctuations, for all indices, are concentrated within the 9% – 12% range (the VXD is the only index showing a figure lower than 10%) while the wildest volatility explosions tend to group around the 45% – 48% area (the RVX again is the only outsider with a 58.84% peak). Statistically speaking, the most important intervals to consider are the 25%, the median and the 75% ones because they represent the most common spectrum of oscillation. Consequently, in case of low volatility most of the indices will tend to move within the 15% – 18% range (the RVX does not go below 20% though) while in high volatility environments equity volatility indices will tend to oscillate between 20% and 24% (the RVX is again the only outsider with 28.1%). The RVX is definitely the index showing the highest figures, which is normal given the fact that it tracks the volatility of less liquid stocks, but is it really the most volatile one? The answer is no because the fact that the RVX has an average value of 23.43% does not mean that it experiences the highest degree of fluctuations; it simply implies that the RVX is constantly higher than the others. In order to clarify this issue it is necessary to quantify the magnitude of the equity volatility indices’ movements. The next chart displays the volatility of the volatility indices. This time, however, the oscillations are expressed in monthly volatility because the CBOE indices are already annualized:

The chart evidently shows that the most volatile equity index, amongst those proposed by the CBOE since 2011 so far, is the VIX and not the RVX. The second most volatile is the VXD and the least volatile is the RVX. How is this possible? Wasn’t the RVX the index showing the highest values? The explanation is simple. The VIX and VXD indices have a higher variability rate because a fairly good amount of moves tend to be large, fast and powerful. On the other hand, the RVX has a lower variability because it tends to fluctuate more often around its mean value and consequently the dispersion is lower. The next graph, which plots the ranking of the dispersion rate for the volatility of CBOE equity volatility indices, will help to expand more this concept:

The graph confirms what previously stated: the VIX and the VXD are, on average, the most volatile indices. The 3rd index is the VXN while the RVX is the one that experiences the lowest degree of diffusion. The dispersion of the VIX and VXD is the largest even for small and large moves indicating that these 2 volatility indices move a lot more quickly than the others. Almost all indices do not go over the 30% threshold but when large market moves happen the monthly volatilities reach 50% and in some cases, like the VIX, 60%. To sum up, the VIX and VXD are the most volatile indices while the VXN and RVX ranked 3rd and 4th respectively (it is worth reminding that the sample analyzed goes from January 2011 until April 2013). Financial markets have different risk dimensions and equity volatility indices make no exception. The next table tries to provide empirical evidence to quantify 1 of those dimensions: the intraday risk

Before getting started it is important to point out that the numbers reported in the table are volatility points. The intraday risk, on average, is around 1.35% for all equity volatility indices but the RVX reaches 1.5%. On the other hand, the table suggests that very large market moves can push equity volatility indices up or down by 13%, 14% or 15% in one single day.

However, one question, given the above mentioned results, would be particularly appropriate: wasn’t the RVX the least volatile index? If that is true, how come the intraday risk is higher?

The RVX index is more “dangerous” than other volatility indices as far as intraday risk is concerned. Nevertheless, even if the RVX fluctuates more wildly during trading hours its mean reverting pressure is higher in the medium term. In other words, the RVX is fairly volatile on a daily basis but it tends to mean revert towards its mean much more quickly than other indices. Furthermore, violent volatility bursts or aggressive drops tend to counterbalance themselves more effectively and in the medium term they result in a lower dispersion of the RVX with respect to its mean. The aforementioned phenomena explain why the RVX has a higher value in terms of volatility points but it is generally less volatile than the VIX or the VXD.

Conclusions

1) On average all indices tend to oscillate within the 18% – 22% interval

2) In case of low volatility, indices will tend to move within the 15% – 18% range while in high volatility environments the equity volatility indices will likely oscillate between 20% and 24%

3) The RVX is definitely the index showing the highest value in terms of volatility points but it is the less volatile because the mean reverting pressure is higher in the medium term

4) The most volatile equity indices, amongst those proposed by the CBOE, are the VIX and the VXD

5) The dispersion rate for the VIX and VXD indices is the largest even for small and large moves which means that they oscillate more quickly and frequently than others

6) Intraday risk is around 1.35% for all equity volatility indices but the RVX reaches 1.5%

The HyperVolatility Forecast Service enables you to receive 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.

### 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.

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.

### Long Volatility = Shorting the Underlying

Trading Volatility is considered to be an extremely risky business by the average investor because of its complexity.
I have read many articles and opinions written by sham experts and disguised traders about trading options and volatility. Funnily enough, I found out that most of them complain about the fact that volatility trading does not work and therefore you should be using other strategies in order to have consistent profits.
Obviously, this is not true and the majority of traders and investors don’t understand the great advantage that an accurate forecasting of volatility can give. Let’s break it down.
Over the last 10 years many academic researches about volatility presented a multitude of models and every “inventor” had to fight in order to promote the reliability of his/her model against its competitors. However, put aside the debates about which model is the best, it is evident that all of them had to agree about the fact that volatility increases much more when the market drops!!!

In technical jargon, options traders use the sentence “I am long volatility” when they think that in that moment volatility is cheap and it is worth buying; but what they really mean by saying that?
In practice, buying volatility means selling the underlying asset. What? Are you crazy?

Let me be more precise. If you are an options trader and you think that volatility is cheap you are probably assuming that the estimation of volatility that you are getting is rather low (regardless if you are using the VIX, stochastic volatility models or technical volatility indicators). Since volatility is mean-reverting you are probably expecting a sharp market movement either up or down. However, since an increase in volatility usually drives the market down and an augment of its value during an up movement is more often than not a “fake head” it is easy to understand that: buying volatility is effectively shorting the underlying.

For the sake of precision, it must be said that this is not always the case and that a rise in volatility could initially welcome even a steady and robust upward movement.

Nevertheless,the last time analysts, econometricians and quantitative traders said that volatility was too cheap was before the credit crunch occurred and since then the volatility decreased to a level which is even lower than what it was during the great bull market which lately faded out.
What are you going to do then?
Will you buy volatility or short the underlying? Ooops, sorry !!!

### Volatility Trading : Why ?

Over the last 10 years financial markets went through several changes and, as a consequence, many different trading techniques that were considered to be extremely efficient and profitable are now generating increasing losses.

The financial downturn completely twisted the way investors and traders look at markets and many analysts, mathematicians, econometricians and portfolio managers are talking about a new market paradigm.

In other words, nothing will be like it used to.

In my opinion, we will get back to “normal” trading conditions in terms of psychological approach to risk  in a 3-5 years time.

The reality is that the markets are not going to trend as fluently as they used to. Retracements, pull backs and temporary drops will occur more frequently and more violently. The old strategies cannot cope with that any more because the sub-structure of the market is not the same anymore.

Think of it. It’s like driving a car. Let’s assume we have 2 cars: the 1st one designed and constructed in the 1920 and the second one in the 2010.  Are they similar?  Breaks, gears and the steering wheel are still going to be there but the way you drive itwill be different. You can measure the speed more accurately, you can drive faster , you have much more technology there and the same thing happens in the market. You cannot win the competition with an old car. You can try but you will be inevitably left behind.

Volatility is the answer to the modern investment ‘s needs. As time goes by financial markets become more and more volatile so why not trading volatility considering it as an asset?

Financial press continuously states that volatility is increasing in the markets. So, why not taking advantage of it ?

As a matter of fact, just a restricted and well educated elite of traders know how to expertly profit from volatility changes over time. The truth is that volatility trading is DIFFICULT !!! It is not as easy as it might seem and many readings and lots of effort is required in order to gain an edge over the crowd.

The good side of it is that VOLATILITY TRADING IS PROFITABLE !!!

Markets will experience wider swings and sharper retracements which old-fashion techniques will not be able to capture anymore and therefore we have to update our knowledge to surf  those waves rather than being overcome by events.

There are many ways to trade volatility and, if correctly  interpreted, some volatility technical indicators can prove quite useful. However,  many researches demonstrated that when measuring volatility some mathematical models and econometric techniques outperform all the others in terms of accuracy.

Consequently, the more we know the better because more accurate forecasts will inevitably lead to more profitable trades.

So, Why would anyone trade volatility?   the answer is simple: IT WORKS !!!