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Use a 2-step binomial tree to price an american style put option when the current stock...

Use a 2-step binomial tree to price an american style put option when the current stock price is $50 and the stock price will move up or down by 20 percent at each time(that is, the ending stock price are $72,$48, and $32). The strike price on the option is $52 and the risk-free interest rate is 5 percent per step. Please report your answer to two decimal places.

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Expert Solution

Using excel to derive call option

Call option
Stock Value 50
Excerise Value(X) 52
Risk free Rate 5%
Up Factor 1.2
Down factor 0.8
Probability of Up 0.625 (Formula = (1+Risk free rate- Down Factor)/(Up factor - Down Factor)
Probability of Down 0.375 Formula = (1-Probability of up)
S2+ 72.00 Formula = S1+*Up Factor
C2+ 20.00 (Max Value of (0,S2-X)
S1+ 60.00 Formula = Stock Value*Up Factor
C1+ 11.90 (Formula= (C2+*Probability of Up + C2+*Probability of Down fact)/(1+5%)
S2- 48.00 Formula = S1+* Downfactor Factor
Stock Value(S0) 50 C2- 0.00 (Max Value of (0,S2-X)
S1- 40.00 Formula = Stock Value*Down Factor
C1- 0
S2- 32.00 Formula = S1+*Up Factor
C2- 0.00 (Max Value of (0,S2-X)
Call option in Year 0 7.09 (Formula = Probability of Up*C1 + Probability of Down * C1-)/1.05

Call Option price = 7.09

jeff jeffy answered 1 year ago
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