Consider a European put option on a currency. The exchange rate is $1.15 per unit of the foreign currency, the strike price is $1.25, the time to maturity is one year, the domestic risk-free rate is 0% per annum, and the foreign risk-free rate is 5% per annum. The volatility of the exchange rate is 0.25. What is the value of this put option according to the Black-Scholes-Merton model?
Value of put option = N(-d2)*K*e^(-Rd*t)-(S*e^(-Rf*t))*N(-d1) | ||||||
Where | ||||||
S = Current price = | 1.15 | |||||
t = time to expiry = | 1 | |||||
K = Strike price = | 1.25 | |||||
Rd=Doms. Curr. Rate%= | 0.0% | Rf = Forgn. Curr. Rate%= | 5.0% | |||
σ = Std dev = | 25% | |||||
d1 = (ln(S/K)+(r-Rf+σ^2/2)*t)/(σ*t^(1/2) | ||||||
d1 = (ln(1.15/1.25)+(0-0.05+0.25^2/2)*1)/(0.25*1^(1/2)) | ||||||
d1 = -0.208526 | ||||||
d2 = d1-σ*t^(1/2) | ||||||
d2 =-0.208526-0.25*1^(1/2) | ||||||
d2 = -0.458526 | ||||||
N(-d1) = Cumulative standard normal dist. of -d1 | ||||||
N(-d1) =0.658556 | ||||||
N(-d2) = Cumulative standard normal dist. of -d2 | ||||||
N(-d2) =0.7449 | ||||||
Value of put= 0.7449*1.25*e^(-0*1)-1.15*e^(-0.05*1)*0.658556 | ||||||
Value of put= 0.21 |
Consider a European put option on a currency. The exchange rate is $1.15 per unit of...
Consider a European put option on a currency. The exchange rate is $1.15 per unit of the foreign currency, the strike price is $1.25, the time to maturity is one year, the domestic risk-free rate is 0% per annum, and the foreign risk-free rate is 5% per annum. The volatility of the exchange rate is 0.25. What is the value of this put option according to the Black-Scholes-Merton model? Please provide your answer in the unit of dollar, to the...
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