Quiz: Implied Vol Surfaces and Smile Dynamics

1. The Breeden-Litzenberger result implies that which condition on the call price surface is equivalent to requiring the risk-neutral density to be non-negative?

2. In Dupire's local volatility formula $\sigma_L^2(K,T) = \frac{\partial_T C + (r-q)K \partial_K C + qC}{\frac{1}{2}K^2 \partial_{KK} C}$, what is the denominator $\frac{1}{2}K^2 \partial_{KK} C$ proportional to?

3. In the SABR model, which parameter primarily controls the slope of the implied vol skew (asymmetry between low-strike and high-strike implied vols)?

4. Under the local volatility model, the implied volatility smile at future dates (as seen from today) is expected to flatten relative to today's smile as the spot moves forward.

5. The Roger Lee moment formula bounds the asymptotic behaviour of the implied vol smile. For large log-moneyness $k = \ln(K/F) \to +\infty$, the upper bound on $\hat{\sigma}^2(k,T) \cdot T / |k|$ is:

6. Which of the following best describes the difference in smile dynamics between SABR and Heston?