Volatility, Skew, and Smile Trading

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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

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