Question

Assume spot Swiss franc is $0.7200, the three-month forward rate is $0.7400, the annualized three-month Eurodollar rate is 5.0 percent, and the annualized volatility of the Swiss franc is 14.0 percent. Use the European option-pricing model to value a three-month European call option with a striking price of $0.7320.

Answer 1

Strike price (K) - $0.7320

Volatility (σ) - 14 % or 0.14

Interest rate (r) - 5 % or 0.05

Spot Price (S) - $0.7200

Time (T) - 3 month or 0.25

d​​​​​​1 = [ In (S/K) + 0.5 ( σ)2(T) ] / (σ)​​​​

d​​​​​​1 = [ln(0.7200/0.7320) + 0.5(0.14)2(0.25)]/(0.14)SQRT(0.25)= 0.263867

d​​​​​​2 = d​​​​​​1 - (σ)​​​​

d2 = d1 - 0.14*SQRT(0.25)

d 2= 0.263867 - 0.07= 0.193867

N(d1) = 0.604059
N(d2) = 0.57686
C = Call option

C = [72.00(0.604059) - 72.00(0.57686)]e-(0.05)(0.25)

C = 1.934

value of three-month European call option = 1.934

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