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.

 

Value of option = 7.586

Step-by-step explanation

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

Value at expiry= 7.975

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

Value at expiry= 7.975

Value of option= 7.975e^(-0.05x1)

= 7.586