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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A bank prices a European call on euros with the dollar as the domestic currency. The USD risk-free rate is 4% and the EUR risk-free rate is 2%. In the Garman-Kohlhagen version of the Black-Scholes-Merton model, which treatment is correct?

The exchange rate is treated as a stock paying a continuous yield equal to the foreign risk-free rate, here 2% for the euro, while the strike is discounted at the domestic dollar rate of 4%. Holding euros earns foreign interest, which works like a dividend yield.

  1. ATreat the exchange rate as a stock with a dividend yield of 4%, and discount the strike at 2%.
  2. BTreat the exchange rate as a stock with a dividend yield of 2%, and discount the strike at 4%.Correct
  3. CTreat the exchange rate as a stock with a dividend yield of 6%, and discount the strike at 4%.
  4. DTreat the exchange rate as a stock with zero dividend yield, and discount the strike at 2%.

Explanation

The foreign currency earns the foreign risk-free rate, which acts as a continuous dividend yield, so q = 2%. The domestic risk-free rate of 4% is used for discounting and the drift. The first option reverses the two rates. The third adds the rates together. The fourth ignores the foreign interest altogether.

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