Stochastic volatility is one of the main concepts widely used in mathematical finance to deal with the endemic time-varying volatility and co-dependence found in financial markets. Various extensions of stochastic volatility models (SVMs) for different purposes have been proposed in recent years with the fast-growing quantitative financial modeling in the past decade. However, a shortage of sufficient theoretical support in terms of the existence and uniqueness of a (strong) solution of the proposed models comes along. To cope with that, we consider a generalized SVM, establish its well-posedness, and conduct the stability analysis with respect to small perturbations. The model under investigation is high-dimensional and constructed hierarchically, in the way that a multi-dimensional path-dependent stochastic process is driven by another multi-dimensional path-dependent stochastic process, where both have their own subdifferential operators one of whose special cases is the general reflection operators for multi-sided barriers. This model fully covers all classical SVMs and their various newly explored variants with unknown well-posedness.

Talk based on paper: ``Well-posedness and Stability Analysis of Two Classes of Generalized Stochastic Volatility Models", SIAM Journal on Financial Mathematics, 2021.
Speaker(s): NIng Ning (UM- Stat)