Volatility trading, or the misnomer volatility arbitrage, is a trading strategy that aims to capture the difference between an option’s implied volatility and the realized volatility of the underlying. Sometimes this is a stand-alone strategy, but the concepts behind it are important for all option traders, as every position they take will inescapably expose them to volatility risk. In this chapter we show how to hedge options to isolate the volatility component. We also look at how we can expect our profit and loss to evolve as a function of time.
We see in Chapter 4 that the fair price for an option is related to the standard deviation of the underlying’s returns. But the option market is forward-looking: the volatility that is used in option pricing models is in some sense the option markets forecast of volatility over the lifetime of the option. We can also make a forecast using the historical statistics of the underlying.
If our estimate of volatility differs significantly from that implied by the option market then we could trade the option accordingly. If we forecast volatility to be higher than that implied by the option, we would buy the option and hedge in the underlying market. Our expected profit would depend on the difference between implied volatility and realized volatility. Equation 5.23
implies that instantaneously this profit would be proportional to
But from the relationship between gamma and vega (equation 5.32
) we can ...