You are to price options using a binomial model. The expiration is in 3 weeks an

Question

You are to price options using a binomial model. The expiration is in 3 weeks and we will use a time step of 1/52 (1 week). So there are 3 time steps (one more than the in-class examples). The price of a stock is S(0) = $48. The risk-free rate is r=6%. The strike is X=50 and K = 5%.

A) Determine the price of a call and put and verify that the lower bounds and put-call parity are met.

B) Determine the value of the put with the addition that it can be redeemed for $1. What is the redemption option worth?

C) Determine and explain (short answer) what happens to the (original) call and put price when K changes to 3% (Don’t forget p changes too!).

D) Determine and explain (short answer) the price of the call and put when S(0) changes to 50. From this, estimate the change in option price per $1 change in the underlying stock price.

Explanation / Answer

B ) IF Put option can be redeemed at 1 then its Average price would be (1 + 4.2273 ) / 2 = 2.6137

C) If K decrease to 3 % , it means premium will decease and so Price of Call and Put option will decrease.

D) as Spot and Strick price both are same, so there is no profit in option at maturity. however before maturity, Call option will in profit, as current present value of Strike Rate will be less than 50 due to discount factor, and so Call option will have some profit.

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