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(1 point) A stock will pay a dividend D att = tp to 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 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 option T 0.0175 risk-free interest rate o 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 = 2 number of subintervals of time for binomial trees 0.166667 time increment At 2 Let S model the "random" part. Then s(t) = S(t) - Der(tp-t) S(t) 0 will increase to $; 11 = u, with probability p, or ;t1 = a, with probability 1 p where = decrease to u = et = 1.0625, d=e 0.941176, p=(erat - d)/(u d) = 0.496884. Then values of the "random part" Sare as follows: 52 97.019 91.31 85.94 85.94 So 80.88 76.12 Since 5 -|*, s + Der(tp-+-) ) 0 to 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 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 option T 0.0175 risk-free interest rate o 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 = 2 number of subintervals of time for binomial trees 0.166667 time increment At 2 Let S model the "random" part. Then s(t) = S(t) - Der(tp-t) S(t) 0 will increase to $; 11 = u, with probability p, or ;t1 = a, with probability 1 p where = decrease to u = et = 1.0625, d=e 0.941176, p=(erat - d)/(u d) = 0.496884. Then values of the "random part" Sare as follows: 52 97.019 91.31 85.94 85.94 So 80.88 76.12 Since 5 -|*, s + Der(tp-+-) ) 0