Complete-market stochastic volatility models (Joint seminar with OMI)

7 June 2016
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 general conditions 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.