The volatility of an asset price is a measure of how uncertain one is about future asset price movements. It is a key parameter to calculate Value at Risk, to optimize portfolio and to value derivatives. Volatility is one of the factors that determines option price. The premiums of both call and put options increase as volatility increases. Therefore, overestimated volatility values produce overestimated option premiums. Moreover, volatility is the only input used in the Black-Scholes model that cannot be observed in the market or a priori determined in a contract. Thus, properly calculating volatility becomes extremely important. There are two basic ways to estimate volatility. The first method uses historical prices, while the second technique, known as implied volatility, employs option prices to find the option’s market estimate of the underlying asset standard deviation.

This paper explores the impact of volatility estimation methods on theoretical option values based upon the Black-Scholes-Merton (BSM) model. Iterative techniques are applied, based on daily S&P index options. Additionally, using option data on S&P 500 Index listed on the Chicago Board of Options Exchange, historical volatility can be estimated. Generally, the method used for computing implied volatility works as follows. First, a rough guess is made as to what the implied volatility could be. This guess is used along with other input parameters to compute the Black-Scholes value. Then, the guess is modified to produce a new guess of volatility, and a new Black-Scholes value that is closer to the market price.

JEL Classifications: C0, C01, C2, C58, D53, G0, G13, G17

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