FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A trader calibrates a Merton jump-diffusion model and a pure local volatility model to the same current option surface. Both fit today's prices well. The trader then uses each to price a forward-start option and to hedge. Which statement best describes a known weakness of the local volatility model relative to a stochastic volatility or jump model?
The local volatility model fits today's surface but implies future smiles that are flatter and unlike real smile dynamics. This can misprice forward-start and other smile-dependent products and make hedges unreliable, even though current vanilla prices are matched exactly.
- AIt cannot fit any observed smile at a single maturity
- BThe smile it implies for the future tends to flatten and differ from the smile that actually evolves, so forward-start and smile-dependent products can be mispricedCorrect
- CIt requires volatility to be stochastic and independent of the asset price
- DIt always produces negative option prices for deep out-of-the-money strikes
Explanation
Local volatility can be fitted exactly to today's surface, but the future smiles it implies are typically flatter than those observed in practice, since volatility depends only on price and time. This hurts products depending on forward smiles, like forward-start options. The model does fit current smiles, so the first option is wrong.
Did you get it right without looking?
One question tells you little. A timed set on Volatility Smiles and Volatility Surfaces shows your real accuracy, how long you take and where you lose marks.
More Volatility Smiles and Volatility Surfaces questions
- A risk analyst observes that implied volatilities for one-year options on an equity index fall steadily as the strike price rises from 80% t…
- A risk manager notes that as the equity option maturity increases, the volatility smile for the index typically becomes less pronounced. Whi…
- A bank's volatility surface for a stock index shows a pronounced skew at the 1-month maturity but a nearly flat profile at the 5-year maturi…
- Implied total variance is sigma^2 times T. At-the-money implied volatility is 20% for a 1-year option and 22% for a 2-year option. Assuming …
- A trader finds that the implied volatility surface for a stock shows a much higher implied volatility for a 90-day option at one strike than…
- A one-year European call and put on a non-dividend stock share the same strike K and maturity. The put's implied volatility is 28%, and the …