We introduce a new class of flexible and tractable matrix a±ne jump-diffusions (AJD) to modelmultivariate sources of financial risk. We first provide a complete transform analysis of this model class,which opens a range of new potential applications to, e.g., multivariate option pricing with...

We introduce a new class of flexible and tractable matrix affine jump-diffusions (AJD) to model multivariate sources of financial risk. We first provide a complete transform analysis of this model class, which opens a range of new potential applications to, e.g., multivariate option pricing with...

We propose a local likelihood estimation for the log-transformed ARCH(1) model in the financial field. Our nonparametric estimator is constructed within the likelihood framework for non-Gaussian observations: it is different from standard kernel regression smoothing, where the innovations are...

We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive relationships between the different concepts. The relationships are of an exact analytical type if this is possible, else we use expansions to obtain approximate expressions. We close...

We recall some fundamentals on Levy processes. Then the Gamma distribution, the Variance Gamma process and option pricing for this process are considered in detail. To implement the Variance Gamma model for option pricing, we use the fast Fourier transform, time change and discuss error bounds

We study how the interaction of agents with different beliefs about a firm’s future cash flows determines the jointbehavior of credit spreads, option implied volatilities, and stock returns. Beliefs heterogeneity influences the pricing kernelin a way that supports more realistic credit spreads...

We propose a multivariate nonparametric technique for generating reliable scenarios and confidence intervals for the term structure of interest rates from historical data. The approach is based on a functional gradient descent (FGD) estimation of the conditional mean vector and the conditional...