FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces

A bank's Black-Scholes model uses a flat 20% volatility to price a 1-year European call with a strike far above the current spot, while the market-implied volatility for that strike is 26%. The bank sells the call at the model price and delta-hedges continuously. Assuming the market's implied volatility is the fair price of risk and realized volatility turns out to equal 20%, which statement best describes the result?

If realized volatility equals 20%, hedging replicates a 20% volatility option, so selling at the 20% model price breaks even on the hedge. The bank's only shortfall is the forgone premium relative to the 26% market price, an opportunity cost rather than a hedging loss.

1. AThe bank sold the option too cheaply relative to market, but if realized volatility is 20% the delta-hedged position earns roughly the model premium, so the shortfall versus 26% was an opportunity cost, not a hedging lossCorrect
2. BThe bank loses money on the hedge because delta hedging fails whenever realized volatility differs from implied volatility in either direction
3. CThe bank earns a profit equal to the difference between 26% and 20% volatility applied to the strike
4. DThe bank is unaffected because the position is delta neutral and delta-neutral positions have zero value