Jump/Diffusion Option Pricing -a Reexamination from an Economic Viewpoint

Abstract

Options will usually elude arbitrage-oriented pricing if the underlying stock follows a jump/ diffusion process - one has to rely on equilibrium-based pricing approaches. However, all ex-isting pricing models under jumps have one in common weakness: they pay too less attention to the economic modeling of jumps, because they chiefly argue with constant, at best deter-ministicly changing jump probabilities. Hence, they imply a predictable pattern of jumps' oc-currences, which is not able to adequately depict the arrival of extraordinary and partly surpris-ing information jumps are intended to capture. Therefore, we need an economically more precise characterization of the jump phenomenon. To that end, we firstly distinguish between firm-specific and market jumps (scope of jumps) as well as between crashes and explosions (direction of jumps). Secondly, we use stochastic jump probabilities and density functions of jump amplitudes to take into account the uncertain arri-val of extraordinary information. Based on this - compared to literature - significantly modi-fied jump representation, we derive option pricing formulas in a jump/diffusion environment under exogenous and endogenous interest rate.