please answer c) only 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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please answer c) only

 

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

c.

Strike Price = 106

Spot or Current Price = 100

Call Price = 23.73

 

Calculation of Price of a 2-year 106-strike American put is as follows:

American Put Price = Call Price+Strike Price - Spot Price
23.73+106-100
= 29.73
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American Put Price = Call Price+Strike Price - Spot Price 23.73+106-100 = 29.73

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Step 2

Working Note:

Strike Price = 106

Spot or Current Price = 100

Calculation of American Call Price in different scenarios is as follows:

Call Price 2nd Year (+,+) = Max (Spot Price-Strike Price,0) = Max (144-106,0) = 38
Call Price 2nd Year (+,-) and (-,+) = Max (Spot Price-Strike Price,0) = Max (108-106,0)= 2
Call Price 2nd Year (-,-) Max (Spot Price-Strike Price,0) = Max (81-106,0) = 0
Call Price 1st Year (+) = Max (Spot Price -Strike Price,0) = Max (120 -106,0) = 14
Call Price 1st Year (-) Max (Spot Price-Strike Price,0) = Max (90-106,0) = 0
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Call Price 2nd Year (+,+) = Max (Spot Price-Strike Price,0) = Max (144-106,0) = 38 Call Price 2nd Year (+,-) and (-,+) = Max (Spot Price-Strike Price,0) = Max (108-106,0)= 2 Call Price 2nd Year (-,-) Max (Spot Price-Strike Price,0) = Max (81-106,0) = 0 Call Price 1st Year (+) = Max (Spot Price -Strike Price,0) = Max (120 -106,0) = 14 Call Price 1st Year (-) Max (Spot Price-Strike Price,0) = Max (90-106,0) = 0

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Step 3

Probability ...

38
0.50 x
(1.1)
2
2
+0.50x
14
+0.50x
Call Price 0.50x -
(1.1)
(1.1)
(1.1)
15.70+0.83+ 0.83 +6.37
-23.73
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38 0.50 x (1.1) 2 2 +0.50x 14 +0.50x Call Price 0.50x - (1.1) (1.1) (1.1) 15.70+0.83+ 0.83 +6.37 -23.73

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