How to Calculate European Call Options


An option is the right, but not the obligation, to buy or sell a security in the future. There are several types of option categories, but the most common are European and American. An American option can be exercised at any time during the life of the option. The majority of exchange traded options are American. In contrast, a European option can only be exercised at the end of its life; that is, investors in European options must ride the wave of price fluctuations until the maturity date. This makes European options less valuable to the buyer.

Review option terms. There are two types of options: calls and puts. A call gives an investor the right, but not the obligation, to buy the underlying asset at a given price. A put gives the investor the right, but not the obligation, to sell the underlying asset at a given price.

Use the Black Scholes option pricing model to calculate price. According to this model, at maturity, a call option is worth C_T = max(0,S_T-X), and a put option is worth P_T = max(0,X-S_T). Where "S_T" equals the underlying asset at the maturity date. In this formula, "S" equals the price of the underlying asset (stock price), "X" equals the exercise (strike) price, "R" equals the risk-free interest rate (compounded), and sigma equals the standard deviation of the underlying asset. "t" equals the current date, and "T" equals the maturity date, and "T-t" equals the time to maturity. This is a very complicated formula which takes a knowledge of higher level computational finance in order to compute.

Use a calculator provided by the Chicago Board Options Exchange (CBOE). Due to the complex nature of the Black Scholes formula, the CBOE has provided a calculator (see the link in the Resource section). The CBOE is one of the largest exchange houses for options in the world.

Work through an example. You are interested in Indexed Options (the second tab). Click on European, and enter the price, strike price, volatility (use the calculator provided on the right), annual interest rate (use 10-year treasuries as a proxy), and the annual dividend yield. In the box at the bottom, you will need to enter the expiration month, year, or the days to expiration. The box on the right will update automatically with pricing.

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