Applications of the Second-Order Esscher Pricing in Risk Management

TL;DR

This paper investigates the second-order Esscher pricing model's application in option pricing and risk management, demonstrating its effectiveness in capturing complex risk factors across various jump-diffusion models.

Contribution

It introduces a comprehensive application of second-order Esscher pricing to multiple jump-diffusion models, including practical formulas and risk management strategies.

Findings

Pricing intervals effectively incorporate jump risks.

Dynamic delta hedging demonstrates risk management benefits.

Fast Fourier transform enables efficient option pricing.

Abstract

This paper explores the application and significance of the second-order Esscher pricing model in option pricing and risk management. We split the study into two main parts. First, we focus on the constant jump diffusion (CJD) case, analyzing the behavior of option prices as a function of the second-order parameter and the resulting pricing intervals. Using real data, we perform a dynamic delta hedging strategy, illustrating how risk managers can determine an interval of value-at-risks (VaR) and expected shortfalls (ES), granting flexibility in pricing based on additional information. We compare our pricing interval to other jump-diffusion models, showing its comprehensive risk factor incorporation. The second part extends the second-order Esscher pricing to more complex models, including the Merton jump-diffusion, Kou's Double Exponential jump-diffusion, and the Variance Gamma model. We derive option prices using the fast Fourier transform (FFT) method and provide practical formulas for European call and put options under these models.