Question

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.

Answer 1

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