Option Pricing When Jump Risk Is Systematic1

This paper generalizes the Merton jump-diffusion option pricing model to the case in which jump risk cannot be eliminated in the market portfolio. the option pricing formula is obtained using a general equilibrium asset pricing model. Since jump risk is systematic, the correlation of the underlying stock's jump with the market portfolio's jump affects the option price.     

A Jump/Diffusion Consumption-Based Capital Asset Pricing Model and the Equity Premium Puzzle

This paper derives the equilibrium excess returns on risky assets in an exchange economy where the underlying exogenous uncertainty is a combination of a pure multidimensional jump process and a diffusion model. We derive closed-form solutions for the interest rate and the risk premiums on risky assets for a traditional class of separable utility indices. Our analysis demonstrates that when the underlying jumps of the aggregate consumption process are not negligible, then the traditional form of the consumption-based capital asset princing model need not hold and the asset risk premiums may be larger than predicted by the traditional CCAPM in continuous time, based on pure Itô diffusion processes. Our analysis suggests an explanation for the large estimates of the risk premiums reported in empirical tests of the single-beta CCAPM.