The current price of a stock is $50.Every month,the stock price will rise by a factor of 1.2 or fall by a factor of 0.8;and a $1 risk-free investment will be worth $1.03.A dividend as a proportion 0.01 of the stock price is paid each period.What is the price of a six-month American put option at a strike of $51?
A)$7.51
B)$7.91
C)$8.11
D)$8.51

Question

Quizplus · Accepted Answer

To make things easier,we create a recursive function for the option value as done in the preceding questions,except that this function will handle proportional dividends:
> OptionValue2 = function(S,K,u,d,R,cp,am,div,n){
+ q = (R*(1-div)-d)/(u-d)
+ if (n==0){ optval = max(0,cp*(S-K))}
+ else { optval = max(am*cp*(S-K),
(q*OptionValue2(S*u,K,u,d,R,cp,am,div,n-1)
+(1-q)*OptionValue2(S*d,K,u,d,R,cp,am,div,n-1))/R)}
+ }
>
> print(OptionValue2(50,51,1.2,0.8,1.03,-1,1,0.01,6))
[1] 7.909438

The Current Price of a Stock Is $50