6 problems

Stationary-variance stochastic-volatility conjecture. All stochastic-volatility models in which the variance process has a stationary distribution should exhibit similar large-matu…

Practitioners' conjecture. The large-maturity forward smile should be the same as the large-maturity spot smile.

Let $X_{\tau}^{(t)}$ denote the Heston forward log-return process over a maturity interval of length $\tau$ starting at forward date $t$, and let the Heston forward smile be the as…

Consider a process whose small-maturity forward smile is studied through the forward implied volatility $c3_{t,\tau}$, and let its quadratic variation be the accumulated quadratic…

At-the-money limit conjecture.

Levendorskii's conjecture. The asymptotic formula above holds in this greater generality.