Volatility arbitrage

Volatility arbitrage, a.k.a. Vol Arb, is a trading strategy in which a delta neutral portfolio of an option and its underlying security are traded and held for long periods of time. The objective is to take advantage of differences between the implied volatility of the option, and a forecast of future realized volatility of the option's underlier. Over the holding period, the portfolio will be continually re-hedged as the underlier's price changes to keep the portfolio delta neutral. The profitability of the strategy is determined by whether the hedging required by the price changes is in line with expectations or not.

Overview

To a professional option trader engaging in volatility arbitrage, an option contract is a way to speculate in the volatility of the underlier rather than a directional bet on the underlier's price. So long as the trading is done delta-neutral, buying an option is a bet that the underlier's future realized volatility will be high, while selling an option is a bet that future realized volatility will be low. Because of put call parity, it doesn't matter if the options traded are calls or puts. This is true because put-call parity posits an risk neutral equivalence relationship between a call, a put and some amount of the underlier. Therefore, being a long a delta neutral call is the same as being long a delta neutral put.

Forecast Volatility

To engage in volatility arbitrage, a trader must first forecast the underlier's future realized volatility. This is typically done by computing the historic daily returns for the underlier and generating rolling x-day volatility samples, where x is a value such as 21 (trading days in one month) to 252 (trading days in one year). A trader may either view a chart of these volatility graphs and develop a feel for what the true volatility should, or, alternatively, he may employ an algorithm that uses estimation techniques. Either way, the trader must determine a baseline volatility estimate for the underlier. For example, after reviewing a graph showing rolling 252-day realized volatility over the past year, a trader may decide that the appropriate volatility for IBM stock is 15%. That is, based on past movements, IBM stock is most likely to be 11% higher or lower from it's current price one year from today.

Market (Implied) Volatility

As described in option valuation techniques, there a number of factors that are used to determine the theoretical value of an option. However, it practice, the only two inputs to the model that change during the day are the price of the underlier and the volatility. Therefore, the theoretical price of an option can expressed as:

$C=f(S,\sigma ,\cdot )\,$

where $S\,$ is the price of the underlier, and $\sigma \,$ is the estimate of future volatility. Because the theoretical price function $f(\cdot )\,$ is a monotonically increasing function of $\sigma \,$, there must be a corresponding monotonically increasing function $g()\,$ such that expresses the volatility implied by the option's market price ${\bar {C}}\,$, or

$\sigma _{\bar {C}}=g({\bar {C}},\cdot )\,$

Or, in other words, there exists no more than one implied volatility $\sigma _{\bar {C}}\,$ for each market price ${\bar {C}}\,$ for the option.

Because implied volatility of an option can remain constant even as the underlier's value change, traders often use it as a measure of relative value rather than the option's market price. For instance, if a trader can buy an option whose implied volatility $\sigma _{\bar {C}}\,$ is 10%, it's common to say that the trader can "buy the option for 10%". Conversely, if the trader can sell an option whose implied volatility is 20%, it is said the trader can "sell the option at 20%".

For example, assume a call option is trading at $1.90 with the underlier's price at $45.50, yielding an implied volatility of 17.5%. A short time later, the same option might trade at $2.50 with the the underlier's price at $46.36, yielding an implied volatility of 16.8%. Even though the option's price is higher at the second measurement, the option is still considered cheaper because the implied volatility is lower. The reason this is true is because the trader can sell stock need to hedge the long call at a higher price.

Mechanism

To engage in volatility arbitrage, a trader looks for options where the implied volatility is either significantly lower than or higher than the estimate of