Consider a binomial world in which the current stock price of 80 can either go u

Question

Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. Answer questions 3 through 6 about a call with an exercise price of 80 What would be the call's price if the stock goes up? a. 3.60 8.00 5.71 d. 4.39 non e of the above 4.What would be the call's price if the stock goes down? 8.00 3.60 0.00 9.00 none of the above d. What is the hedge ratio? 0.429 0.714 0.571 0.823 none of the above d.

Explanation / Answer

Here,

u=1+10%=1.1

d=1-8%=0.92

t=1

r=4%

S=80

Probability of upmove=(e^(rt)-d)/(u-d)=(e^(0.04*1)-0.92)/(1.1-0.92)=0.67

Call price if stock gies up=max(80*1.1-80,0)=8

Call price if stock gies down=max(80*0.92-80,0)=0

hedge ratio=(Call up price-Call down price)/(S*(u-d))=(8-0)/(80*(1.1-0.92))=0.56

Theoretical price=0.67*8+(1-0.67)*0=5.15

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