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Asymptotic Analysis of the Mixed-Exponential Jump Diffusion Model and Its Financial Applications

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  • Shi, Chao

Abstract

Transform inversion is a popular approach to pricing many types of path-dependent options under various dynamic models. However, it is usually difficult to guarantee the accuracy due to the lack of error control, which often depends heavily on the asymptotic property of the transform function. This article characterizes the asymptotic behaviors of all the complex roots of the exponent equation under the mixed-exponential jump diffusion model (MEM), by which one can output the error bounds and achieve any pre-specified error tolerance in the transform inversion algorithm when pricing various path-dependent options under the MEM. Numerical examples indicate that the resulting transform inversion algorithm with our computable error bounds are reliably accurate and efficient for pricing lookback options and barrier options, and evaluating a joint distribution under the MEM.

Suggested Citation

  • Shi, Chao, 2022. "Asymptotic Analysis of the Mixed-Exponential Jump Diffusion Model and Its Financial Applications," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:dyncon:v:143:y:2022:i:c:s0165188922002226
    DOI: 10.1016/j.jedc.2022.104518
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    References listed on IDEAS

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