A stock with a current price of $300, can go either up by 20%, or down by 15%. You have the opportunity to buy an American call option on this stock for $65, which matures at the end of one period, with an exercise price of 275.
a- Please draw the trees of the stock and option values
b- What is the price of the call option today if the risk free rate is 8%.
c- What is your decision for this investment opportunity? Explain your answer
Given:
Spot price,
American call option
Two period.
Exercise, x=275
Risk free rate, r=8%
Solution:
Risk neutral probability
(a) Binomial tree for american call:
So, we select 120.36
(2)
Se, we select 14.40.
(3)
So we select 74.38.
(b) Price of the call option =74.38
(c) Given American coll option price =$ 65
Calculated American calloption price = $74.38
As given American call option price and calculated American call option price are diffecent, there is a scope of profit from this investment.
Buy the American call option al lower of the above prices.
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