The Dynamics of Correlated Shocks: Option Pricing and Estimation in a Regime-Switching Co-Jump Model

Abstract

This paper proposes and estimates a regime-switching stochastic volatility co-jump (RS-SVCJ) model in which the parameters governing the joint distribution of simultaneous jumps in returns and volatility are allowed to vary across macroeconomic regimes governed by a continuous-time finite-state Markov chain. Within each regime, asset prices and stochastic variance follow a generalization of the Eraker–Johannes–Polson (2003) model, while the co-jump correlation, jump intensity, and jump size distribution are all regime-dependent. We derive a semi-closed-form expression for the conditional characteristic function of the log-asset price by solving a system of coupled Riccati-type ordinary differential equations, from which European option prices are computed via the fast Fourier transform. A Bayesian MCMC estimator is developed that jointly samples model parameters, latent volatility, jump times, jump sizes, and the latent regime sequence via a combination of Gibbs sampling and forward-filtering backward-sampling. Simulation experiments confirm excellent finite-sample performance. Applied to twenty years of daily S&P 500 returns, the model identifies two well-defined regimes a tranquil bull market and a crisis bear market with markedly different co-jump correlations and jump intensities. Bayes factors strongly favour the full RS-SVCJ specification over all nested alternatives, and the model produces substantially smaller implied volatility pricing errors than single-regime benchmarks. Our results confirm that the correlation between return jumps and volatility jumps is strongly state-dependent, with important consequences for tail risk measurement and derivative pricing.

Keywords: regime-switching; co-jumps; stochastic volatility; option pricing; Bayesian MCMC; characteristic function; implied volatility