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, with payoff max(S_A - S_B, 0). Asset A has volatility 30%, asset B has volatility 40%, and their correlation is 0.5. Using the Margrabe approach, what is the volatility of the ratio S_A/S_B used in the pricing formula?
The relevant volatility is about 36.1%. It is the square root of 0.09 plus 0.16 minus 2 times 0.5 times 0.3 times 0.4, which is 0.13, capturing the correlation between the two assets.
- A36.1%Correct
- B10.0%
- C50.0%
- D35.0%
Explanation
Variance = 0.30^2 + 0.40^2 - 2(0.5)(0.30)(0.40) = 0.09 + 0.16 - 0.12 = 0.13. Volatility = sqrt(0.13) = 0.3606, or 36.1%. Option 3 (50%) ignores correlation and takes the root of the sum 0.25; option 4 averages the volatilities.
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