Pricing in mathematical finance often involves taking expected values under different equivalent measures. Fundamentally, one needs to first ensure the existence of ELMM, which in turn requires that the stochastic exponential of the market price of risk process be a truemartingale. In general, however, this condition can be hard to validate, especially in stochastic volatility models. This had ...

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in t...

We propose a method for calibrating a volatility surface that matches option prices using an entropy-inspired framework. Starting with a stochastic volatility model for asset prices, we cast the estimation problem as a variational one and we derive a Hamilton-Jacobi-Bellman (HJB) equation for the volatility surface. We study the asymptotics of the HJB equation assuming that the stochastic volat...