Question 1. Consider a two-step binomial tree, where a stock that pays no dividends has current price 100, and at each time step can increase by 20% or decrease by 10%. The possible values at times T = 2 are thus 144, 108 and 81. The annually compounded interest rate is 10%.a) Calculate the price of a two-year 106-strike European put using risk-neutral probabilities.b) Calculate the price of a two-year 106-strike European put using replication.c) Calculate the price of a two-year 106-strike American put using replication, and hence verify that the American put has price strictly greater than the European.d) Calculate the prices of a two-year 86-strike European put and American put. What is different from part (c)?

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Asked Nov 18, 2019
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Question 1. Consider a two-step binomial tree, where a stock that pays no dividends has current price 100, and at each time step can increase by 20% or decrease by 10%. The possible values at times T = 2 are thus 144, 108 and 81. The annually compounded interest rate is 10%.

a) Calculate the price of a two-year 106-strike European put using risk-neutral probabilities.

b) Calculate the price of a two-year 106-strike European put using replication.

c) Calculate the price of a two-year 106-strike American put using replication, and hence verify that the American put has price strictly greater than the European.

d) Calculate the prices of a two-year 86-strike European put and American put. What is different from part (c)?

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Expert Answer

Step 1

Hi There, Thanks for posting the question. But as per Q&A guidelines, we have to answer the first question when multiple sub-parts given under single question. Hence, I have answered the first question below.

Step 2

Calculate the risk neutral probabilities as follows:

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(1 1d) (1+ и) - (1-d) (1+10%)-(1-10%) (1+20%)-(1-10%) 1.1-0.9 1.2-0.9 0.2 0.3 -0.666666666666667 or 66.67% 1- 166.67% = 33.33%

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Step 3

The two stage Black-Scholes...

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$144.00 $0 P* 120.00 $ 0 $100.00 $108.00 $ 1.74 P $90.00 5.76 P $ 81.00 P $19.00

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