Martin Forde (PSTAT, UCSB)

Small time and tail asymptotics for stochastic volatility models

We show how to construct a volatility-of-variance function for an uncorrelated stochastic volatility model, so as to be consistent with an observed symmetric small-maturity smile, by solving an Abel Volterra integral equation. We show how to adapt the methodolgy for implied volatility skews. We also discuss Lewis's small-time asymptotics for the derivatives of the implied volatility At the-Money, and the large-x asymptotics for his CEV(p)- volatility model. We also discuss tail asymptotics for such models, using Olver's asymptotics.