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FRM Part I · FRM Exam Part I · Exotic Options

An exchange option gives the holder the right to exchange asset B for asset A at maturity, so payoff is max(A_T - B_T, 0). Under the Margrabe approach the volatility used in the pricing formula depends on which inputs?

The effective volatility depends on both assets' volatilities and their correlation, through the square root of sigma A squared plus sigma B squared minus two times rho times the two volatilities. The risk-free rate does not enter this volatility term, and correlation cannot be ignored.

  1. AOnly the volatility of asset A
  2. BThe volatilities of A and B and the correlation between them, and no risk-free rate for the volatility termCorrect
  3. CThe volatility of A and B only, ignoring correlation
  4. DThe strike price and the risk-free rate only

Explanation

The effective volatility is sqrt(sigma_A^2 + sigma_B^2 - 2 rho sigma_A sigma_B). It depends on both volatilities and their correlation, not on the risk-free rate. Ignoring correlation (option C) would misstate the volatility of the ratio A/B.

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