question archive DIY is trading at $550 per share
DIY is trading at $550 per share
Subject:FinancePrice:2.86 Bought7
DIY is trading at $550 per share. The stock price will either increase by 5% or decrease by 15% in the first month. If the price increases in the first month, it will go up by $120 or down by $180 in the second month. If the price decreases in the first month, it will go up by $45 or down by $60 in the second month. The risk-free interest rate is 5% per month. a. Using the replicating portfolio approach, find the price of a 1-month put option that has an exercise price of $500. b. Using the risk neutral probability approach, find the price of a 1-month call option that has an exercise price of $500. c. Using either approach, find the price of a 2-month put option that has an exercise price of $500.
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ANSWER
Let the portfolio hold X number of shares and one put.
The price at the end = 577.5 or 467.5
The payoff for the prices = 27.5x-0 or -82.5x+32.5
As per replicating portfolio approach
27.5x=-82.5x+32.5
x= 0.29
Put value of x in any of the payoffs
The value at expiry= 7.975
The value of option= 7.975e^ (-0.05x1)
= 7.586
Let the portfolio hold X number of shares and one put.
Price at the end = 577.5 or 467.5
Payoff for the prices = 27.5x-0 or -82.5x+32.5
As per replicating portfolio approach
27.5x=-82.5x+32.5
x= 0.29
Put value of x in any of the payoffs
The value at expiry= 7.975
The value of option= 7.975e^ (-0.05x1)
= 7.586
