Question

Suppose the current exchange rate is $1.62/£, the interest rate in the united states is 4.5%, the interest rate in the United Kingdom is 4%, and the volatility of the $/£, exchange rate is 16%.

(a) Using the Black-Scholes formula, calculate the price of a six-month European call option on the British pound with a strike price of $1.60/£

The price of a six-month European call option is__________ $ (round to five decimal places).

Answer 1

We use Black-Scholes Model to calculate the value of the currency call option.

The domestic currency value of a call option into the foreign currency is:

C = (S0 * e-rf*T)*N(d1) - (K * e-rd*T)*N(d2)

where :

S0 = current spot rate

K = strike price

N(x) is the cumulative normal distribution function

rd = domestic risk-free simple interest rate

rf = foreign risk-free simple interest rate

T is the time to maturity in years

σ = volatility of underlying currency

d1 = (ln(S0 / K) + (rd - rf + σ2/2)*T) / σ√T

d2 = d1 - σ√T

First, we calculate d1 and d2 as below :

· ln(S0 / K) = ln(1.62 / 1.60). We input the same formula into Excel, i.e. =LN(1.62 / 1.60)

· (rd - rf + σ2/2)*T = (0.045 - 0.04 + (0.162/2)*0.50

· σ√T = 0.16 * √0.50

d1 = 0.1885

d2 = 0.0753

N(d1) and N(d2) are calculated in Excel using the NORMSDIST function and inputting the value of d1 and d2 into the function.

N(d1) = 0.5747

N(d2) = 0.5300

Now, we calculate the values of the call option as below:

C = (S0 * e-rf*T)*N(d1) - (K * e-rd*T)*N(d2) , which is (1.62 * e(-0.04 * 0.50))*(0.5747) - (1.60 * e(-0.045 * 0.50))*(0.5300)    ==> $0.08348

Price of call option is $0.08348