Suppose that the spot price of the Canadian dollar is US $0.75 and that the Cana

Question

Suppose that the spot price of the Canadian dollar is US $0.75 and that the Canadian dollar/ US dollar exchange rate has a volatility of 4% per annum. The risk-free rates of interest in Canada and the United States are 9% and 7% per annum, respectively. Calculate the value of a European call option to buy one Canadian dollar for US $0.75 in 9 months. Use put-call parity to calculate the price of a European put option to sell one Canadian dollar for US $0.75 in 9 months. What is the price of a call option to buy US $0.75 with one Canadian dollar in 9 months?

Explanation / Answer

d1=[ln(So/X)+(r-q+.5*sigma^2)*T]/[sigma*sqrt(T)]

d1=[ln(.75/.75)+(0.07-0.09+.5*0.04^2)*0.75]/[0.04*sqrt(.75)]

d1=[(-0.02+.0008)*0.75]/[0.04*sqrt(.75)]

d1=-0.41569

d2=[ln(So/X)+(r-q-.5*sigma^2)*T]/[sigma*sqrt(T)]

d2=[ln(.75/.75)+(0.07-0.09-.5*0.04^2)*0.75]/[0.04*sqrt(.75)]

d2=-0.4503

call option value=0.75*exp(-0.09*0.75)*N(-0.41569)-0.75*exp(-0.07*0.75)*N(-0.4503)

call option value=0.75*exp(-0.09*0.75)*0.3388-0.75*exp(-0.07*0.75)*0.3262

call option value=$0.0054

Put call parity: S0*exp(-q*T)+price of put = call option value+X*exp(-r*T)

=>price of put = call option value+X*exp(-r*T)-S0*exp(-q*T)

=>price of put =0.0054+0.75*exp(-0.07*0.75)-0.75*exp(-0.09*0.75)

price of put =$0.0160

price of a call option to buy US $0.75 with one Canadian dollar in 9 months is same as the price of a put option to sell one Canadian dollar in 9 months for US $0.75 which is $0.0160.

current StockPrice S0 0.75 annual return volatility sigma 4.00% effective annual risk-free rate r 7% Exercise Price X 0.75 Time to Maturity(yrs) T 0.75 Foreign Canadian Yield q 9.00% d1 d1=[ln(So/X)+(r-q+.5*sigma^2)*T]/[sigma*sqrt(T)] -0.4157 d2 d2=[ln(So/X)+(r-q-.5*sigma^2)*T]/[sigma*sqrt(T)] -0.4503 N(d1) N(d1)=NORM.S.DIST(d1,TRUE) 0.3388 N(d2) N(d2)=NORM.S.DIST(d2,TRUE) 0.3262 call option value c=S0*exp(-qT)*N(d1)-X*exp(-rT)*N(d2) $          0.0054

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