Question

Below is a two-period price tree for a share of stock in Ameren Corp (AEE) Today In 6 Months In 1 Year $91.96 $83.60 $76 < > $79.42 $72.20 $68.59 Using the binomial model, calculate the value today of a call option on AEE stock with a strike price of $75. You may assume that the 6-month risk-free rate is 4.0%.

Answer 1

Given, Current Stock price, K = $ 76

Strike Price, So = $ 75

6 month risk free rate, r = 4%

Time step, n = 2

Here we have to value the European Call option.

Note: The call option is exercised when stock market price on the date of maturity is greater than K.

The value of the option at the terminal can be calculated using the following formula

Fuu = Max St - K,0

Fu = Max 91.96 – 75, 0 = Μαα16.96, 0 = 16.96-

Similarly we can calculate at other terminals too. Refer the attached picture below

Today In 6 Months In 1 Year $91.96 fuu = $ 16.96 $83.60 fu = $ 8.6 $76 >$79.42 fud= $ 4.42 1-P $72.20 < fd = $ 0 1-P 69.fdd = 0 $68.59

First of all we have to calculate the value of u and d

83.6 ณ - 1 S 1
,
72.2 d= 76 = 0.95

Now, we have to calculate the probability of upward and downward movement.

P= et – d 4 - d

= P= 0.04xl - 0.95 1.1 -0.95

P = 0.6054

1 - P = 1 - 0.6054 = 0.3946

The value of call option can be calculated using the following formula

f = P2 x fuu +2P(1 – P) fud + (1 - P)2 x faal xe-nrT

+ f = 10.60542 x 16.96 + 2 x 0.6054 x 0.3946 x 4.42 + 0.39462 x 01 x E-2x0.04x1

G f = $ 7.6875

Price of call option = $ 7.6875

Note; In the question it is given that 6 month risk free rate is 4%. Therefore I have considered 6 month time period as 1. Since, rate of interest is for 6 month time period.

If the interest rate is expressed as 4% per annum then the Time period, T = 1/2 years.

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