Volatility arbitrage
Encyclopedia
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 underlier
. 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 rather than price is used as the unit of relative measure, i.e. traders attempt to buy volatility when it is low and sell volatility when it is high.
, 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-hedged
call results in the same returns as being long a delta-hedged put.
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 and is 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 and be yielding an implied volatility of 16.5%. 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.
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 the position.
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 continuous re-hedging required to keep the portfolio delta-neutral.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, volatility arbitrage (or vol arb) is a type of statistical arbitrage
Statistical arbitrage
In the world of finance and investments, statistical arbitrage is used in two related but distinct ways:* In academic literature, "statistical arbitrage" is opposed to arbitrage. In deterministic arbitrage, a sure profit can be obtained from being long some securities and short others...
that is implemented by trading
Trade
Trade is the transfer of ownership of goods and services from one person or entity to another. Trade is sometimes loosely called commerce or financial transaction or barter. A network that allows trade is called a market. The original form of trade was barter, the direct exchange of goods and...
a delta neutral
Delta neutral
In finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged due to small changes in the value of the underlying security...
portfolio of an option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
and its underlier
Underlying
In finance, the underlying of a derivative is an asset, basket of assets, index, or even another derivative, such that the cash flows of the derivative depend on the value of this underlying...
. The objective is to take advantage of differences between the implied volatility
Implied volatility
In financial mathematics, the implied volatility of an option contract is the volatility of the price of the underlying security that is implied by the market price of the option based on an option pricing model. In other words, it is the volatility that, when used in a particular pricing model,...
of the option, and a forecast of future realized volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
of the option's underlier. In volatility arbitrage, volatility rather than price is used as the unit of relative measure, i.e. traders attempt to buy volatility when it is low and sell volatility when it is high.
Overview
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 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 the put–call parityPut–call parity
In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option in a frictionless market —both with the identical strike price and expiry, and the underlying being a liquid asset. In the absence of liquidity, the existence of a...
, it doesn't matter if the options traded are calls
Call option
A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...
or puts
Put option
A put or put option is a contract between two parties to exchange an asset, the underlying, at a specified price, the strike, by a predetermined date, the expiry or maturity...
. This is true because put-call parity posits a risk neutral
Risk neutral
In economics and finance, risk neutral behavior is between risk aversion and risk seeking. If offered either €50 or a 50% chance of each of €100 and nothing, a risk neutral person would have no preference between the two options...
equivalence relationship between a call, a put and some amount of the underlier. Therefore, being long a delta-hedged
Hedge (finance)
A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...
call results in the same returns as being long a delta-hedged 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 historical daily returns for the underlier for a given past sample such as 252 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. For instance, if the current 252-day volatility for the returns on a stock is computed to be 15%, but it is known that an important patent dispute will likely be settled in the next year and will affect the stock, the trader may decide that the appropriate forecast volatility for the stock is 18%.Market (Implied) Volatility
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 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 , orOr, 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 and is 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 and be yielding an implied volatility of 16.5%. 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 the position.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 continuous re-hedging required to keep the portfolio delta-neutral.
See also
- Delta neutralDelta neutralIn finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged due to small changes in the value of the underlying security...
- Hedge (finance)Hedge (finance)A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...
- Implied volatilityImplied volatilityIn financial mathematics, the implied volatility of an option contract is the volatility of the price of the underlying security that is implied by the market price of the option based on an option pricing model. In other words, it is the volatility that, when used in a particular pricing model,...
- Option (finance)Option (finance)In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
- Statistical arbitrageStatistical arbitrageIn the world of finance and investments, statistical arbitrage is used in two related but distinct ways:* In academic literature, "statistical arbitrage" is opposed to arbitrage. In deterministic arbitrage, a sure profit can be obtained from being long some securities and short others...
- Volatility (finance)Volatility (finance)In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
- Volatility smileVolatility SmileIn finance, the volatility smile is a long-observed pattern in which at-the-money options tend to have lower implied volatilities than in- or out-of-the-money options. The pattern displays different characteristics for different markets and results from the probability of extreme moves...