A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications

- We propose a Markov-modulated jump diffusion pricing model.
- The model has closed-form solutions in a general equilibrium framework for options and futures prices.
- The model further describes three features: leptokurtic returns, volatility smile, and volatility clustering.
- The model shows the feature of jump clustering, where high (low) jump arrivals are followed by high (low) jump arrivals.

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features, volatility smile, and volatility clustering observed empirically for the Dow Jones Industrial Average (DJIA) and its component stocks. Using 10 years of stock return data, we confirm the existence of jump intensity switching and clustering, illustrate transition probabilities, and verify superior empirical fit over competing Poisson-style models.