Question

Suppose the current exchange rate is $1.42/€, the interest rate in the United States is 3.50%, the interest rate in the EU is 6%, and the volatility of the $/€ exchange rate is 17%.

(a). Using the Black-Scholes formula, calculate the price of a three-month European call option on the Euro with a strike price of $1.45/€.

The price of a three-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 put 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(1.42 / 1.45). We input the same formula into Excel, i.e. =LN(1.42 / 1.45)

· (rd - rf + σ2/2)*T = (0.035 - 0.06 + (0.172/2)*0.25

· σ√T = 0.17 * √0.25

d1 = -0.2770

d2 = -0.3620

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) = 0.3909

N(d2) = 0.3587

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 (1.42 * e(-0.06 * 0.25))*(0.3909) - (1.45 * e(-0.035 * 0.25))*(0.3587)    ==> $0.03125

Price of call option is $0.03125