Volatility arbitrage

Overview

To an 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. If a trader buys options as part of a delta-neutral portfolio, he is said to be long volatility. If he sells options, he is said to be short volatility. 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 a risk neutral equivalence relationship between a call, a put and some amount of the underlier. Therefore, being long a delta neutral call results in the same returns 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 for a given past sample such as 252 days, the number of trading days in a year. The trader may also use other factors, such as whether the period was unusually volatile, or if there are going to be unusual events in the near future, to adjust his forecast. For instance, if the current 252-day volatility for the returns on a stock is computed to be 15%, but it's known that an important patent dispute will likely be settled in the next year, the trader may decide that the appropriate forecast volatility for the stock is 18%. That is, based on past movements and upcoming events, the stock is most likely to be 18% higher or lower from its current price one year from today.

Mechanism

Armed with a forecast volatility, and capable of measuring an option's market price in terms of implied volatility, the trader is ready to begin a volatility arbitrage trade. A trader looks for options where the implied volatility, sigma_ar{C} , is either significantly lower than or higher than the forecast realized volatility sigma ,, for the underlier. In the first case, the trader buys the option and hedges with the underlier to make a delta neutral portfolio. In the second case, the trader sells the option and then hedges them.

Over the holding period, the trader will realize a profit on the trade if the underlier's realized volatility is closer to his forecast than it is to the market's forecast (i.e. the implied volatility). The profit is extracted from the trade through the continual re-hedging required to keep the portfolio delta neutral.

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