The current price of a stock is $50.This includes the value of a dividend of $2 that will be paid three months from now.In three months,the net of dividend stock price will rise by a factor of 1.2 or fall by a factor of 0.8.The risk-free rate of interest is 0.0834% per month (simple interest).Using the technique of Schroder (1988),what is the price of a six-month American call option at a strike of $51?
A)$3.62
B)$4.12
C)$4.62
D)$5.12

Question

Quizplus · Accepted Answer

The following calculations give theAnswer:
> u = 1.2
> d = 0.8
> R = 1.000834
> S_0_net = 50 - 2/1.000834^3
> S_0 = 50
> S_u_net = S_0_net*u
> S_d_net = S_0_net*d
> S_uu_net = S_u_net*u
> S_ud_net = S_u_net*d
> S_dd_net = S_d_net*d
> S_u = S_u_net + 2
> S_d = S_d_net + 2
> C_uu = max(0,S_uu_net-51)
> C_ud = max(0,S_ud_net-51)
> C_dd = max(0,S_dd_net-51)
> c(C_uu,C_ud,C_dd)
[1] 18.12719 0.00000 0.00000
> q = (R-d)/(u-d)
> C_u = (q*C_uu+(1-q)*C_ud)/R
> C_u
[1] 9.154118
> C_u = max(C_u,S_u-51)
> C_u
[1] 9.154118
> C_d = 0
> C_0 = (q*C_u+(1-q)*C_d)/R
> C_0
[1] 4.622773

The Current Price of a Stock Is $50