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ID: 2737436 • Letter: H

Question

home / study / business / finance / questions and answers / 1. compute the price of an american call option ... Question 1. Compute the price of an American call option with strike K=110 and maturity T=.25 years. 2. Compute the price of an American put option with strike K=110 and maturity T=.25 years. 3. Is it ever optimal to early exercise the put option of Question 2? 4. If your answer to Question 3 is "Yes", when is the earliest period at which it might be optimal to early exercise? (If your answer to Question 3 is "No", then you should submit an answer of 15 since exercising after 15 periods is not an early exercise.) 5. Do the call and put option prices of Questions 1 and 2 satisfy put-call parity? 6. Compute the fair value of an American call option with strike K=110 and maturity n=10 periods where the option is written on a futures contract that expires after 15 periods. The futures contract is on the same underlying security of the previous questions. 7. What is the earliest time period in which you might want to exercise the American futures option of Question 6? 8. Compute the fair value of a chooser option which expires after n=10 periods. At expiration the owner of the chooser gets to choose (at no cost) a European call option or a European put option. The call and put each have strike K=100 and they mature 5 periods later, i.e. at n=15.

Explanation / Answer

Calculate the price of an American call option and put option:

STOCK PRICE: 100

STRIKE PRICE: 110

INTEREST RATE 0.1 for 10t : 0.02

NO OF TREE NODES : 15

CONE Dry YIELD 0.015 for 1.5t: 0.01

VOLATILITY PER YEAR 0.3 for 30t : 0.30

TIME TO EXPIRATION IN DAYS : 90

AMERICAN PUT PRICE (bin. tree): 12301230000I

EUROPEAN PUT PRICE (bin. tree): 12234727711'

AMERICAN CALL PRICE (bin. tree): 2.5295864850.

EUROPEAN CALL PRICE (bin. tree): 23295864850:

Note:

The value of the stock price, interest rate, and volatility is not given. Hence,
it is assumed to be the stock price is 100, interest rate is 2%, and volatility is 30%.