Rough analysis of local stochastic volatility models
Abstract: Local stochastic volatility models are a class of (in general non-Markovian) diffusion models that have become standard in the financial industry, largely due to an efficient McKean-Vlasov particle calibration algorithm, mathematically not yet fully understood. In this talk we address the pricing problem, that is, the computation of certain expectations. We proceed by a partial conditioning that exhibits a rough semimartingale & SDE structure, topic of recent investigations with P. Zorin-Kranich, K. Lê , A. Hocquet and the speaker. In particular, we exploit partial (rough) Markovianity to compute certain conditional expectations via rough partial differential equations (RPDEs), later randomized with martingale rough paths. As far as the speaker knows, the resulting (formal) SPDE is beyond existing SPDE theory.
Joint work with P. Bank (TU Berlin), C. Bayer and L. Pelizzari (both WIAS Berlin).