Complete-market stochastic volatility models

OMI Seminar Series

It is an old idea that incomplete markets should be completed by adding traded options as non-redundant securities. While this is easy to show in a finite-state setting, getting a satisfactory theory in continuous time has proved highly problematic. The goal is however worth pursuing since it would provide arbitrage-free dynamic models for the whole volatility surface. In this talk we describe an approach in which all prices in the market are functions of some underlying Markov factor process. In this setting generalconditions for market completeness were given in earlier work with J. Obloj,but checking them in specific instances is not easy. We argue that Wishart processes are good candidates for modelling the factor process, combining efficient computational methods with an adequate correlation structure.

Location:
Speaker(s):

Mark Davis, Professor of Mathematics, Imperial

Date:
Tuesday, June 7, 2016 - 12:30
to 13:30