An interacting model of asset dynamics with applications to market risk

Abstract

In this thesis we explore a novel approach to understanding the dynamics of asset prices. Inspired by statistical physics models of interacting traders, we start with a simple question as to how such a model might be formulated directly at the level of the prices instead. We propose a general model class stemming from a hypothetically complete description of market dynamics in which all degrees of freedom except the price are integrated out. We argue that within this description, both interactions between asset prices and non-Markovian dynamics will be unavoidable when considering prices alone. The majority of this thesis is spent investigating a minimal variant of this model class in which we consider a system of asset with only pairwise interactions within a Markovian approximation. We refer to this model as an interacting geometric Brownian motion or the iGBM for short. This thesis involves a thorough analysis of the iGBM as well as practical attempts to calibrate the model and assess its predictive capabilities for market risk assessment.

Date of Award	1 Mar 2020
Original language	English
Awarding Institution	King's College London
Supervisor	Reimer Kuhn (Supervisor)