Volatility Arbitrage - Market (Implied) Volatility

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