Hybrid credit-equity models are developed with state-dependent jumps, local- stochastic volatility and default intensity based on time changes of Markov processes. We model the stock price process as a time changed Markov process with state-dependent local volatility and killing rate. When the time change is a Levy process in turn time changed with a time integral of an activity rate process, the stock price process has state-dependent jumps, stochastic volatility and default intensity.

SHORT BIO. Rafael Mendoza-Arriaga is an assistant professor of Information, Risk and Operations Management at the University of Texas, McCombs School of Business. Dr. Mendoza received his doctorate in Industrial Engineering and Management Sciences from Northwestern University. He also holds a Master's degree in mathematical finance from the University of Toronto and in industrial engineering and management sciences from Northwestern University. Previously, he was a financial engineer at Algorithmics Inc. and a quantitative researcher at Citadel Group. Dr. Mendoza's industry experience includes the areas of market and credit risk, asset management and distributed computing. His research interests are on the application of analytical and computational methods for derivative security pricing based on spectral expansions and integral transforms. He has developed a credit-equity modeling framework based on time-changes of state dependent Markov processes with state dependent default hazard rates.