, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility … default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein …-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS …

processes and polynomial semimartingales and by showing how efficient calibration of local stochastic volatility models is … volatility models to financial data. We show how this computationally challenging problem can be efficiently solved by applying …

effects, i.e., it is possible that the structure of the volatility surface changes without a change in the volatility level … state, I show that this superior performance is directly linked to a third volatility factor which is unrelated to the … volatility level. The second chapter studies the price of the smile, which is defined as the premia for individual option risk …

This book presents a factor-based model of the stochastic evolution of the implied volatility surface. The model allows … volatility derivatives. In the first part, the book develops a unifying theory for the analysis of contingent claims under both … the real-world measure and the risk-neutral measure in an environment of stochastic implied volatility. On the basis of …