Volatility arbitrage, a.k.a. Vol Arb, is a trading strategy in which a delta neutral portfolio of an option and its underlier 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. In volatility arbitrage, volatility is used as the unit of relative measure rather than price - that is, traders attempt to buy "volatility" when it's low and sell "volatility" when it's high. Volatility most frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon. ... In economics, arbitrage is the practice of taking advantage of a state of imbalance between two or more markets: a combination of matching deals are struck that capitalize upon the imbalance, the profit being the difference between the market prices. ... Look up Trade in Wiktionary, the free dictionary Trade centers on the exchange of goods and/or services. ... Delta neutral refers to a portfolio containing options, that has been hedged so that its overall value will not change for small changes in the underliers price. ... In finance, an option is a contract whereby one party (the holder or buyer) has the right but not the obligation to exercise a feature of the contract (the option) on or before a future date (the exercise date or expiry). ... In finance, an underlying is an investment from which a derivative security is derived. ... In financial mathematics, the implied volatility of a financial instrument is the volatility implied by the market price of a derivative based on a theoretical pricing model. ... Volatility most frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon. ...

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. In financial mathematics, put-call parity defines a relationship between the price of a European call option and a European put option - both with the identical strike price and expiry. ... A call option is a financial contract between two parties, the buyer and the seller of this type of option. ... A put option (sometimes simply called a put) is a financial contract between two parties, the buyer and the seller of the option. ... In Economics, the term risk neutral is used to describe an individual who cares only about the expected outcome of an investment, and not the risk (variance of outcomes or the potential gains or losses). ...

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.

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, in 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 be expressed as:

where is the price of the underlier, and is the estimate of future volatility. Because the theoretical price function is a monotonically increasing function of , there must be a corresponding monotonically increasing function that expresses the volatility implied by the option's market price , or

Or, in other words, when all other inputs including the stock price are held constant, there exists no more than one implied volatility for each market price for the option.

Because implied volatility of an option can remain constant even as the underlier's value changes, traders 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 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 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 needed to hedge the long call at a higher price.

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, is either significantly lower than or higher than the forecast realized volatility , 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.