Explain the difference between a call option and a put option. Explain the diffe

Question

Explain the difference between a call option and a put option. Explain the difference between an American option and European option. Find the value of a call option using the binomial option pricing formula for single period when given the following information: you have an option with 6 months until expiration, the payoff in the up scenario is $12, and the payoff in the down scenario is $0, the risk-free rate is 5%, the weight for the up scenario is 1.1, and the weight for the down scenario is 0.7

Explanation / Answer

1

Call gives the buyer the right to buy the stock at predetermined price or strike price (or exercise price) whereas put gives buyer the right to sell the stock at a predetermined price or strike price (or exercise price). So, put buyer benefits if stock goes down whereas call buyer benefits if stock goes up

2

American option can be exercised any time before the expiry whereas European option can only be exercised on the expiry date

3

Value of call using binomial:

p=(e^(rt)-d/(u-d)=(e^(0.05*6/12)-0.7)/(1.1-0.7)=0.813288

1-p=0.186712

So, value of call=(0.813288*12+0.186712*0)*e^(-0.05*6/12)=$9.518494

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