Question

You are evaluating a two-year put option on RACE (Ferrari), who currently has a stock price of $40/share. The risk-free rate is 6%. The tree of RACE's stock prices for the next two years is the following: 49 44. 41 40 40 32 1. Find the value of a European put option with a strike price of $42. 2. Find the value of an American put option with a strike price of $42 (assume that you can exercise the option at year 1 or year 2, but you can't exercise the option today).

Answer 1

1. Value of European Put Option with strike price of $42

Value of European put option at expiration is the greater of

• Zero
• Exercise Price
• reduced by value of underlying

Applying the above, the option can be exercised only at the end of year 2 and exercise price must be greater than the underlying  

Greater of zero or exercise price - value of underlying

• $42 - $41 = $1
• $42 - $40 = $2
• $42 - $32 = $10

Put option has zero intrinsic value when the price goes to $49 as the strike price is $42

2. Value of an american put option with strike price of $42 with an option to exercise at year 1 and year 2 but not at spot

Value of a put option = greater of zero or exercise price - value of underlying

• $42 - $36 = $6
• $42 - $41 = $1
• $42 - $40 = $2
• $42 - $32 = $10

Put option has zero intrinsic value when the price of the underlying exceeds strike price ie., $42