We explore (jump) diffusion processes for risk or asset modelling that capture external influences in two specific ways. The model allows for random parameters in the stochastic process, which can be used to express uncertainty, prior beliefs or simply to enrich the process distribution, for example to obtain volatility skew in a modified Black-Scholes model. We also incorporate switching patterns that can mimic changing market conditions and can also be stochastic in nature. Such ‘randomised processes’ are highly interpretable, but their simulation is numerically expensive and problems of model consistency can arise. We address both issues of efficient simulation and model consistency by constructing a local volatility model that approximates the marginal distributions of the randomised process with arbitrary precision. Numerical examples demonstrate the differences between these two models and highlight the modelling flexibility obtained.

The presentation will be based on Wolf, Deelstra & Grzelak 2024.

Felix obtained his PhD in mathematics as part of an international research project between academia and industry dedicated to the study of modern risk management and xVAs. This took him to the Universities of Brussels and Utrecht and into close collaboration with Rabobank’s front office financial engineering department. In addition to the randomised switching model presented here, his work covers areas such as the pricing and hedging of the collateral choice option or the fast valuation of non-linear assets and interest rate sensitivities within exposure simulations.