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This paper derives the appropriate characterization of asset market equilibrium when asset prices follow jump-diffusion processes, and develops the general methodology for pricing options on such assets. Specific restrictions on distributions and preferences are imposed, yielding a tractable option pricing model that is valid even when jump risk is systematic and non-diversifiable. The dynamic hedging strategies justifying the option pricing model are described. Comparisons are made throughout the paper to the analogous problem of pricing options under stochastic volatility.