Question

1. The current EUR/CAD exchange rate is 1.10. The current European interest rate (c.c.) is -0.4%(!), and the current USD interest rate (c.c.) is 0.8%. The volatility of the EUR/USD exchange rate is something like 15%.

a) What is the 3-month forward EUR/USD exchange rate?

b)Which currency is (expected to be) getting stronger

c) If you thought the forward EUR/USD exchange rate was too high, would you prefer a 3-month call on 10000 Euros or a 3-month put on 10000 Euros (both struck at the same forward exchange rate from a) )?

d) What would your option of choice cost you?

e) What would the actual exchange rate have to be (in 3 months time) for you to break even?

Answer 1

a) The current EUR/USD rate is 1.1

Assume the interest rates and volatility given are annualized rates.

The 3 month fwd rate is computed by Spot rate * (1 + Foreign Interest rate*90/360)/ (1+ Domestic Interest rate *90/360)

= 1.1 * (1+ (-0.4%*0.25))/(1+ (0.8%*0.25)) = 1.1033

b) EUR is going to be stronger as the domestic interest rate is lower for EUR

c) If I feel the fwd price of 1.1033 is too high now, which means the actual price is much less than this, I would buy a put option to sell EUR at 1.1033 USD and buy at a lower price.

d)The European put option price is calculated using the Black scholes formula -

P =

K *e-rd+T* N(-2) - S*e-rf*T* N-d1)

where K = Strike Price = 1.1033

rd = Domestic Interest rate = -0.4%

S= Current price = 1.1

rf = Foreign Interest rate = 0.8%

N(d) is cumulative normal distribution function

T = 90/360 = 0.25

d1 =

(Ln(S/K)+(rd - rf +02/2)* T)/0 * sqrt(T)

d2 =

d1 - 0 * sqrt(T)

$\sigma$ - Volatility of Fx Intereste rate = 15%

Plugging the values,

N(-d2) = 0.546744

N(-d1) = 0.516926

Put option premium = 0.603827 - 0.567483 = 0.036344

the Put option premium is = 0.0363 is the option premium.

Since the underlying is 10000 Euros, the cost is 363 Euros.

e) The break even price is when I recover the price I pay for buying the option is covered in the exchange rate.

1.1033-0.036344 i.e 1.066956.