Statistical Distributions of the Volatility Index

VIX related products (ETNs, futures and options) are becoming popular financial instruments, for both hedging and speculation, these days.  The volatility index VIX was developed in the early 90’s. In its early days, it led the derivative markets. Today the dynamics has changed.  Now there is strong evidence that the VIX futures market leads the cash index.

In this post we are going to look at some statistical properties of the spot VIX index. We used data from January 1990 to May 2017. Graph below shows the kernel distribution of spot VIX.

[caption id="attachment_313" align="aligncenter" width="564"] Kernel distribution of the spot VIX index[/caption]

It can be seen that the distribution of spot VIX is not normal, and it possesses a right tail.

We next look at the Q-Q plot of spot VIX. Graph below shows the Q-Q plot. It’s apparent that the distribution of spot VIX is not normal. The right-tail behavior can also be seen clearly. Intuitively, it makes sense since the VIX index often experiences very sharp, upward spikes.

[caption id="attachment_314" align="aligncenter" width="564"] Q-Q plot of spot VIX vs. standard normal[/caption]

It is interesting to observe that there exists a natural floor around 9% on the left side, i.e. historically speaking, 9% has been a minimum for spot VIX.

We now look at the distribution of VIX returns. Graph below shows the Q-Q plot of VIX returns. We observe that the return distribution is closer to normal than the spot VIX distribution. However, it still exhibits the right tail behavior.

[caption id="attachment_315" align="aligncenter" width="564"] Q-Q plot of VIX returns vs. standard normal[/caption]

It’s interesting to see that in the return space, the VIX distribution has a left tail similar to the equity indices. This is probably due to large decreases in the spot VIX after sharp volatility spikes.

The natural floor of the spot VIX index and its left tail in the return space can lead to construction of good risk/reward trading strategies.

Post Source Here: Statistical Distributions of the Volatility Index

Volatility, Skew, and Smile Trading

Peter Carr recently gave a talk on volatility trading at the Fields institute.

Summary:

In general, an option’s fair value depends crucially on the volatility of its underlying asset. In a stochastic volatility (SV) setting, an at-the-money straddle can be dynamically traded to profit on average from the difference between its underlying’s instantaneous variance rate and its Black Merton Scholes (BMS) implied variance rate. In SV models, an option’s fair value also depends on the covariation rate between returns and volatility. We show that a pair of out-of-the-money options can be dynamically traded to profit on average from the difference between this instantaneous covariation rate and half the slope of a BMS implied variance curve. Finally, in SV models, an option’s fair value also depends on the variance rate of volatility. We show that an option triple can be dynamically traded to profit on average from the difference between this instantaneous variance rate and a convexity measure of the BMS implied variance curve. Our results yield precise financial interpretations of particular measures of the level, slope, and curvature of a BMS implied variance curve. These interpretations help explain standard quotation conventions found in the over-the counter market for options written on precious metals and on foreign exchange.

In this talk, Carr discussed which options you should trade when

• You know the realized volatility will exceed 10% and yet the ATM volatility is currently below 10%
• You know that the correlation of every IV with the underlying will realize positive and yet an OTM call’s IV is currently below an equally OTM put’s IV
• You know that IVs are themselves volatile and yet 3 IVs currently plot linearly

Click here to watch

Post Source Here: Volatility, Skew, and Smile Trading