FRM Part I · FRM Exam Part I · Exotic Options
An exchange option gives its holder the right to swap asset B for asset A at maturity. Asset A has volatility 30%, asset B has volatility 40%, and the correlation between them is 0.5. Which is the volatility that would be used in a Black-Scholes-type formula for valuing this option?
The effective volatility is about 36.1%. It is the square root of the variance of the ratio, 0.09 plus 0.16 minus 2 times 0.5 times 0.3 times 0.4, which equals 0.13. Correlation reduces the variance of the difference.
- AApproximately 36.1%Correct
- BApproximately 50.0%
- CApproximately 10.0%
- DApproximately 70.0%
Explanation
Effective variance = 0.3^2 + 0.4^2 - 2(0.5)(0.3)(0.4) = 0.09 + 0.16 - 0.12 = 0.13. The square root is about 36.1%. Option 70% adds the volatilities. Option 50% ignores correlation (sqrt(0.25)). Option 10% is the difference in volatilities.
Did you get it right without looking?
One question tells you little. A timed set on Exotic Options shows your real accuracy, how long you take and where you lose marks.
More Exotic Options questions
- A gap call on a non-dividend stock has S0 = 50, payoff strike K1 = 47 and trigger K2 = 50. The maturity is one year and the risk-free rate i…
- A bank is short a digital (cash-or-nothing) call that pays USD 100,000, with the underlying trading very close to the strike a few hours bef…
- A risk manager compares a floating-strike lookback call (strike equals the minimum asset price observed during the life) with a standard Eur…
- A risk manager hedges a short position in a down-and-out call using a static portfolio. The barrier is at 90, spot is 100, and the hedge por…
- A digital (cash-or-nothing) call on an index pays 1,000,000 USD at expiry if the index is above 4,500 and zero otherwise. At expiry the inde…
- A fund buys a variance swap with a vega notional of USD 100,000 and a volatility strike of 20. The variance notional is defined as vega noti…