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Probability and Computational Finance Seminar
Martin Larsson
Cornell University
Title: No Dominance in High-Dimensional Stochastic Volatility Models

Abstract: In his 1973 paper on rational option pricing, Merton introduced the No Dominance (ND) condition as a normative assumption reflecting market rationality. It was later used by Jarrow, Protter and Shimbo (2006, 2009) and Jarrow, Kchia, Larsson and Protter (2010) in the context of price bubbles. In this talk we formulate the (ND) condition for a d-dimensional semimartingale model with nonnegative prices and characterize it in terms of equivalent (true) martingale measures. We then focus on a class of high-dimensional stochastic volatility models, where we provide a sufficient condition which guarantees that (ND) is satisfied. This condition, which is given in terms of the correlation structure of the model, is also shown to be close to necessary in a certain sense.

Date: Monday, November 22, 2010
Time: 5:00 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve