7. As shown in proposition 7, Chapter 13, a European option on a stock should be priced by netting out from the underlying asset price all the dividends to be paid before the option matures. Merton (1973) shows that for the case of an asset with price S paying a continuously compounded dividend yield k, this approach leads to the following call-option-pricing formula:

where This formula is often applied to the pricing of options on indexes, where the aggregation of many stock dividends makes the continuous-dividend assumption an appropriate approximation. Use this formula to price a call option on an index whose current price is S = 500 when the option's maturity T = 1, the dividend yield is k = 2.2 percent, its standard deviation σ = 20 percent, and the interest rate r = 7 percent.