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.Dividends are paid as a proportion of 0.02 of the stock price.What is the early-exercise premium on the 49-strike,six-month American call?
A)$0.00
B)$0.02
C)$0.06
D)$0.11

Question

Quizplus · Accepted Answer

Using the same function as the previous question,we price the American and European calls:
> 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)}
}
>
> call_A = OptionValue2(50,49,1.2,0.8,1.03,1,1,0.02,6)
> call_A
[1] 10.31880
> call_E = OptionValue2(50,49,1.2,0.8,1.03,1,0,0.02,6)
> call_E
[1] 10.20391
> call_A - call_E
[1] 0.1148866

The Current Price of a Stock Is $50