Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

It is well known that the Black-Scholes model of option pricing is too simple in that the single volatility parameter cannot simultaneously match all the traded option prices seen in the market. To do this requires some concept of 'stochastic volatility', but naive approaches destroy market completeness and with it the basis for any Black-Scholes style arbitrage pricing theory. To maintain completeness, traded options must be included as autonomous (non-redundant) assets. We give conditions under which this is possible. When the market is driven by some underlying Markov process these conditions are geometric in flavor and are closely related to the Bismut formula of Malliavin calculus.

Mark Davis completed his PhD in stochastic control theory in the EECS Department at UC Berkeley and then joined the control group at Imperial College London, where he worked on stochastic analysis, nonlinear filtering and control theory. In 1995 he joined