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4. Consider six months European put option with a strike price of $100 on a stock with current price $100. There are two time steps and in each time step the stock price either moves up by 10% or moves down by 10%. Risk-free interest rate is Y-5% (on 3 months (a) Find the current option price. (b) Compute the number of shares of stock which should be held by the replicating portfolio at time 0 and 1 (after 3 months)

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Answer #1

Answer to part (a)

Price Expectation after 3 month Exercise pricePut availed or not Put Value Not, being EP lower than at increase of 10% 100 current price 100 Yes at decrease of 10 90 10 Current Option Price C1 *P+C2( 1-p)/(1+r) Where C1 C2 Put value at high Put Value at low Probabilty at high Risk Free rate Computation of Probability Spot Price(1+Interest Rate) - Lower Rate Higher Rate Lower Rate l.e 100(1+1.25%)-90/110-90-.5625 Putting prob calculated above in current option price formula 0*.562 5+10(1-5625)/1+1 .25%-4.32 Therefore Value of Current Option Price is 4.32

Part (b) No. of stock would be 0.50.

i.e. Change in Put value/ Change in Share value = 0-10/110-90=0.50

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