A stock will pay a dividend D at t = tD < T, where an American-style call option expires at t = This problem values the call option by using binomial trees. Because the dividend has known value, fort to the stock has a non-random component equal the value of dividend, discounted to time t The dividend is paid at tp, and fort t the stock price no longer includes this non-random component. To apply the binomial tree method, we construct a binomial tree for the random component of the stock. Then we construct a binomial tree for the stock S by adding the non-random component to the tree for S Finally we construct the call option values, based upon the binomial tree of stock values by working back from t-T. Let So 86.5 stock price at t 0 K 90 strike price for call option r 0.0175 risk-free interest rate ? 0.21 volatility D- 0.56 value of dividend (dollars) tp 0.125 time dividend is paid (years "ex-date") T 0.166667 expiration time ( years ) M 2number of subintervals of time for binomial trees 0.166667 time increment Let s model the "random part. Then S(t) - De- S(t) 0t