Question

1.Suppose that the spot price of the Canadian dollar is U.S. $0.95 and that the Canadian dollar/U.S. dollar exchange rate has a volatility of 8% per annum. The risk-free rates of interest in Canada and the United States are 4% and 5% per annum, respectively.(6 points)

N(0.0429)=	0.5171		N(-0.0264)	0.4895
N(-0.0429)=	0.4829		N(-0.0264)=	0.5105
N(0.1429)=	0.5568		N(0.0736)	0.5293
N(-0.1429)=	0.4432		N(-0.0736)=	0.4707
N(0.2429)=	0.5960		N(0.1736)	0.5689
N(-0.2429)=	0.4040		N(-0.1736)=	0.4311

a.Calculate the value of a European call option to buy one Canadian dollar for U.S. $0.95 in nine months. (4 points)

b. Use put-call parity to calculate the price of a European put option to sell one Canadian dollar for U.S. $0.95 in nine months. (2 points)

Answer 1

1. Using Black –Scholes model

S_{0 =} 0.95 , K =0.95 , r =0.05 , rf = 0.04 , = 0.08 , T =0.75

           

D1=( ln(0.95/0.95) + (0.05-0.04+0.0064/2)*0.75) /(0.08*0.75^^1/2) = 0.1429

D2= D1- (0.08*0.75^^1/2) = 0.0736

N(D1)= 0.5568 N(D2) = 0.5293           from table

Value of the call

c = 0.95e^-0.04×0.75×0.5568 - (0.95e^-0.05×0.75×0.5293) = 0.0290     = 2.90 cents

b) Using put call parity

P + S₀e^-rfT = C + Ke^-rT                P = price of put

P = 0.029 + 0.95e^-0.05*9/12 - 0.95e^-0.04*9/12 = 0.0221 = 2.21 cents