LSV models with stochastic interest rates and correlated jumps

TL;DR

This paper extends local stochastic volatility models for exotic option pricing by incorporating stochastic interest rates and correlated jumps, and introduces a new stable, accurate finite-difference scheme.

Contribution

It presents a novel extension of existing models with stochastic interest rates and correlated jumps, along with a new implicit finite-difference scheme for improved numerical stability and accuracy.

Findings

The extended model captures more market features.

The proposed scheme is unconditionally stable and preserves positivity.

Second order accuracy in space and time achieved.

Abstract

Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be extended by adding to the model stochastic interest rates and correlated jumps in all three components. We also propose a new fully implicit modification of the popular Hundsdorfer and Verwer and Modified Craig-Sneyd finite-difference schemes which provides second order approximation in space and time, is unconditionally stable and preserves positivity of the solution, while still has a linear complexity in the number of grid nodes.