FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A dealer uses Black-Scholes with a flat 8% volatility to price a one-year 25-delta out-of-the-money EUR call and put. The market shows a symmetric smile, with the implied volatility of those options at 10%. The dealer sells a strangle (call and put) priced at 8% volatility and hedges delta only. Which statement best describes the resulting exposure?
The dealer sold the strangle too cheaply, because the market prices out-of-the-money options at 10% volatility versus the dealer's 8%. The position is short convexity and exposed to large moves in either direction, which are more likely than the lognormal model implies. Delta hedging does not remove this exposure.
- AThe dealer is overhedged and profits if the exchange rate stays near the current level
- BThe dealer has sold the strangle too cheaply relative to the market and is exposed to large moves in either directionCorrect
- CThe dealer has sold the strangle too expensively and gains if tails are fat
- DThe dealer has no exposure because delta hedging eliminates all risk
Explanation
The market values the wings at 10% volatility, but the dealer charged the 8% price, which is lower. The dealer is thus underpriced on the strangle and, being short gamma, loses on large moves in either direction, which are more likely than the flat-volatility model implies. Delta hedging does not remove gamma or vega exposure.
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