In finance , volatility arbitrage or vol arb is a type of statistical arbitrage that is implemented by trading a delta neutral portfolio of an option and its underlying. The objective is to take advantage of differences between the implied volatility [1] of the option, and a forecast of future realized volatility of the option's underlying.

In volatility arbitrage, volatility rather than price is used as the unit of relative measure, i. To an option trader engaging in volatility arbitrage, an option contract is a way to speculate in the volatility of the underlying rather than a directional bet on the underlying'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 underlying's future realized volatility will be high, while selling an option is a bet that future realized volatility will be low.

Because of the 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 underlying. Therefore, being long a delta- hedged call results in the same returns as being long a delta-hedged put.

Volatility arbitrage is not "true economic arbitrage" in the sense of a risk free profit opportunity. It relies on predicting the future direction of implied volatility.

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Even portfolio based volatility arbitrage approaches which seek to "diversify" volatility risk can experience " black swan " events when changes in implied volatility are correlated across multiple securities and even markets. Long Term Capital Management used a volatility arbitrage approach.

To engage in volatility arbitrage, a trader must first forecast the underlying's future realized volatility. This is typically done by computing the historical daily returns for the underlying for a given past sample such as days the typical number of trading days in a year for the US stock market. 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.

As described in option valuation techniques, there are 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 underlying and the volatility.

Therefore, the theoretical price of an option can be expressed as:. Because implied volatility of an option can remain constant even as the underlying's value changes, traders use it as a measure of relative value rather than the option's market price. Even though the option's price is higher at the second measurement, the option is still considered cheaper because the implied volatility is lower.

This is because the trader can sell stock needed to hedge the long call at a higher price. 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.

In the first case, the trader buys the option and hedges with the underlying to make a delta neutral portfolio. In the second case, the trader sells the option and then hedges the position. Over the holding period, the trader will realize a profit on the trade if the underlying's realized volatility is closer to his forecast than it is to the market's forecast i.

The profit is extracted from the trade through the continuous re-hedging required to keep the portfolio delta-neutral. From Wikipedia, the free encyclopedia. Application to Skew Risk". Inside Volatility Arbitrage, The Secrets of Skewness. Credit spread Debit spread Exercise Expiration Moneyness Open interest Pin risk Risk-free interest rate Strike price the Greeks Volatility.

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