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

Call option: An option that gives the holder the right to buy an underlying asset from another party at a fixed price over a specific period of time.

Put Option: An option that gives the holder the right to sell an underlying asset to another party at a fixed price over a specific period of time.

For a call option with physical delivery, upon exercise the underlying asset is delivered to the call buyer, who pays the call seller the exercise price. For a put option with physical delivery, upon exercise the put buyer delivers the underlying asset to the put seller and receives the strike price

That buying a call option is consistent with a bullish point of view and buying a put option is consistent with a bearish point of view

American Style option: Option contract that can be exercised at any time up to the option’s expiration date.

European style option: Option contract that can only be exercised on the option’s expiration date.

Binomial Model

Step 1

We compute risk neutral probability

Up probability=1+Risk free rate-down scenario/up scenario-down scenario

Up probability=1+.05-0.7/1.1-0.7

Up probability=0.875

Down probability=1-Up Probability

Down probability=1-0.875

Down probability=0.125

Step 2

Call value=up Probability× up payoff+ down probability × down payoff/(1+risk free rate)^N

Call value=12× 0.875 + 0×.125/ (1+.05) ^0.5

Call value=$10.25

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