Randomised Mixture Models for Pricing Kernels

TL;DR

This paper introduces a novel approach to financial modeling using randomised mixtures of Lévy processes and filtered Esscher martingales to capture uncertainties and their impact on pricing kernels and yield curves.

Contribution

It develops a new class of pricing kernel models based on randomised mixtures and stochastic filtering, extending to heat kernel and Markov process driven models.

Findings

Choice of random mixture significantly affects yield curve dynamics

Parameter sensitivity influences model behavior and option pricing

Models can incorporate various sources of economic uncertainty

Abstract

Numerous kinds of uncertainties may affect an economy, e.g. economic, political, and environmental ones. We model the aggregate impact by the uncertainties on an economy and its associated financial market by randomised mixtures of L\'evy processes. We assume that market participants observe the randomised mixtures only through best estimates based on noisy market information. The concept of incomplete information introduces an element of stochastic filtering theory in constructing what we term "filtered Esscher martingales". We make use of this family of martingales to develop pricing kernel models. Examples of bond price models are examined, and we show that the choice of the random mixture has a significant effect on the model dynamics and the types of movements observed in the associated yield curves. Parameter sensitivity is analysed and option price processes are derived. We extend the class of pricing kernel models by considering a weighted heat kernel approach, and develop models driven by mixtures of Markov processes.