Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

The study of the implied volatility surface of stochastic volatility models and in particular it's asymptotics for small time and extreme strikes is a major topic in current research. This is not a purely academic exercise, but has practical relevance as e.g. the implied volatility of far out of the money put options contains information on trader's fear of huge crashes in the stock market. Since stochastic volatility models are in general incomplete, one has also to fix the pricing mechanism employed. In the present talk we will focus on the implied volatility surface under indifference pricing via dynamic convex risk measures given as solutions of quadratic BSDEs. We derive a characterization of the implied volatility in terms of the solution of Cauchy problem of a nonlinear PDE and provide a small time to maturity expansion. This procedure allows to choose convex risk measures in a parametrized class such that the asymptotic volatility smile under indifference pricing can be matched with the market smile. This is joint work with Ronnie Sircar.

Speaker: Stephan Sturm, Princeton University (ORFE)

Slides: (TBA)