The Black-Scholes Formulas

European Options on Dividend Paying Stocks We can use the Black-Scholes formulas replacing the stock price by the stock price less the present value of the dividends

Problem on dividend paying European stock Consider a European call option on a stock with ex-dividend dates in two months and five months. The dividend on each ex-dividend date is expected to be $0.50. The current share price is $40, the exercise price is $40, the stock price volatility is 30 percent per annum, the risk-free interest is 9 percent per annum, and the time to maturity is six months. What is the price of call option on this European dividend paying stock?

American Calls An American call on a non-dividend- paying stock should never be exercised early An American call on a dividend-paying stock should only ever be exercised immediately prior to an ex-dividend date

Black’s Approach Set the American price equal to the greater of two European prices: The 1st European price is for an option maturing at the same time as the American option The 2nd European price is for an option maturing just before the final ex- dividend date

Problem Consider an option on a dividend paying American stock when the stock price is $ 30, the exercise price is $29, the risk free interest rate is 5 percent per annum, and the time to maturity is four months. The stock price is due to go ex-dividend is 50 cents. What is the price of the call option?