Question

In: Finance

You are attempting to value a call option with an exercise price of $109 and one...

You are attempting to value a call option with an exercise price of $109 and one year to expiration. The underlying stock pays no dividends, its current price is $109, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $88. The risk-free rate of interest is 12%. Calculate the call option’s value using the two-state stock price model.

Solutions

Expert Solution

c0= Call price = [c1+ + (1-)c1- ]/ (1+r)
p0= Put price = [p1+ + (1-)p1- ]/ (1+r)
Where
∏= Risk neutral probability = (1+r-d)/(u-d)
r= risk free interest rate = 12.0000%
u= up factor =                          1.1927
d= Down factor =                          0.8073
∏= Risk neutral probability =
=                          0.5000
1- ∏= =                          0.5000
S0 = Stock price today = 109
S1+ = = 109*1.1927 = 130
S1- = = 109*0.8073 = 88
X = Exercise price = 75
c1+ = = Max(0, S1+ - X)
= Max(0, 130 - 75) = 55
c1- = = Max(0, S1- - X)
= Max(0, 88 - 75) = 13
c0= (0.5*55 + 0.5*13) /(1+0.12 ) = 30.36

Answer is:

30.36


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