In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.The risk-free gross return per time step is 1.001668.If a 98-strike call option is trading at $2,how much arbitrage profit can you make in present value terms?
A)$2.09
B)$4.09
C)$6.09
D)$12.09

Question

Quizplus · Accepted Answer

First price the call.
> u = 1.1
> d = 0.9
> R = 1.001668
> q = (R-d)/(u-d)
> q
[1] 0.5083403
> call = (110-98)*q/R
> call
[1] 6.089925
Short the replicating portfolio of the call and collect an amount of $6.09,and buy the call at $2.At inception the net cash inflow is $4.09.At maturity the position nets off to zero no matter what the final price.Hence in present value terms,the arbitrage profit is $4.09.

In a One-Period Binomial Model,assume That the Current Stock Price