FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
Which assumption of the Black-Scholes model is most directly violated when a stock price can jump suddenly following an earnings surprise, leading to a volatility smile at short maturities?
The assumption of continuous price paths with lognormally distributed returns is violated by sudden jumps. Jumps fatten the tails of the return distribution, raising prices of far out-of-the-money options relative to Black-Scholes and producing a pronounced volatility smile, especially at short maturities.
- AContinuous price paths with lognormal returnsCorrect
- BConstant risk-free interest rate
- CNo transaction costs
- DEuropean exercise only
Explanation
Jumps break the assumption of continuous diffusion with lognormal returns, creating fatter tails, especially pronounced for short maturities. Constant rates, transaction costs and exercise style do not generate smile shapes in this manner.
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 trader notes that for a given maturity, the implied volatility for a put with delta of -0.25 is 24%, the at-the-money option is 20%, and t…
- A desk holds a long position in a call option and uses a sticky-strike assumption, where each strike's implied volatility is fixed regardles…
- A trader holds a long position in a 3-month out-of-the-money index put struck at 90% of spot. The trader prices it with the at-the-money imp…
- A bank's equity options desk is short a portfolio of out-of-the-money puts and calls on a stock. Black-Scholes vega for the whole book is co…
- A risk analyst observes that implied volatilities for equity index options decline steadily as the strike price rises from well below to wel…
- A trader uses a volatility surface to price a European option with a 9-month maturity. Quoted implied volatilities at the same strike are 22…