European Option Model on Asset with Continuous Cash Payouts (Index Option)

Some assets have numerous distribution of cash payouts. An example is a broad-based stock market index portfolio (say SP500), in which nearly everyday one component stock or another will pay a dividend. Merton (1973) has derived a variant of the Black-Scholes model for an asset that pays dividends continuously. The payput can be treated as a constant proportion of the asset price.

The following demonstrates the computation of option prices with the underlying asset that pays continuous dividends. Suppose dividend yield before the option expired is 10%. Based on all other parameters value, the call price and the put price are, $6.254 and $2.075, respectively. The delta for the call and put are 0.6702 and -0.3074, respectively.