Measures of Model Risk in Continuous-time Finance Models

TL;DR

This paper introduces new measures for quantifying model risk in continuous-time finance models, focusing on Levy jump and affine jump-diffusion models, and assesses the impact of different risk components on model performance.

Contribution

It proposes expected shortfall type model risk measures for jump models and jointly estimates parameters under different probability measures using MCMC techniques.

Findings

Strong evidence supporting the modeling of price jumps.

Parameter estimation and model specification risks significantly affect model accuracy.

Joint estimation under multiple measures enhances understanding of model risk.

Abstract

Measuring model risk is required by regulators on financial and insurance markets. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to Levy jump models and affine jump-diffusion models. We investigate the impact of parameter estimation risk and model specification risk on the models' ability to capture the joint dynamics of stock and option prices. We estimate the parameters using Markov chain Monte Carlo techniques, under the risk-neutral probability measure and the real-world probability measure jointly. We find strong evidence supporting modeling of price jumps.