PDE-Based Bayesian Inference of CEV Dynamics for Credit Risk in Stock Prices

Abstract

This study proposes a method to infer the parameters of the constant elasticity of variance (CEV) model from the market values of stock after the extension from the asset process of the Merton model in the structural credit risk model to that of the CEV model. The state space model is used, which consists of an asset process (system equation) and the call option pricing a stock value (observation equation), for the inference. However, it is usually difficult to apply the Markov chain Monte Carlo (MCMC) method to estimate the parameters of the CEV model because the observation equation of the state space model has no analytical formula. Our method solves this parameter estimation problem by applying the MCMC combined with a finite difference method of partial differential equations, where the stock value obtained as a CEV option price is numerically solved. This study estimates the parameters from the real stock values of the US financial institutions as an empirical analysis. Furthermore, we analyze the default probability and measure the credit risk of bank portfolios.