FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
In a stochastic volatility model for an equity option, the correlation between the asset price shocks and the volatility shocks is set to a strongly negative value. Compared with zero correlation, what is the main effect on the implied volatility smile?
A strongly negative price-volatility correlation produces a downward-sloping skew with higher implied volatility at low strikes. Volatility rises as prices fall, creating a fat left tail and thin right tail, whereas zero correlation would give a roughly symmetric smile.
- AA symmetric smile with higher curvature at both wings
- BA downward-sloping skew with higher implied volatility for low strikesCorrect
- CAn upward-sloping skew with higher implied volatility for high strikes
- DA flat smile with a higher overall level only
Explanation
Negative correlation means volatility rises when the price falls, fattening the left tail and thinning the right tail of the risk-neutral distribution. This lifts implied volatility for low strikes, giving a downward skew. Zero correlation instead gives a symmetric smile driven by the volatility of volatility.
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
- Under the minimum variance delta approach, a risk manager adjusts the Black-Scholes delta for the smile. For a European call, the adjusted d…
- Which assumption of the Black-Scholes model is most directly violated when a stock price can jump suddenly following an earnings surprise, l…
- A currency option market shows a volatility smile that is symmetric around the at-the-money strike, with implied volatility rising for both …
- A risk analyst compares the implied distribution of an equity index extracted from option prices with a lognormal distribution having the sa…
- According to the standard explanation of foreign currency smiles, which two factors cause the exchange rate's risk-neutral distribution to d…
- Black-Scholes assumes the underlying asset price follows geometric Brownian motion with constant volatility. In equity markets after 1987, i…