Exchange options under clustered jumps dynamics
Date
2019-10-28
Authors
Yong, Ma, author
Pan, Dongtao, author
Wang, Tianyang, author
Quantitative Finance, publisher
Journal Title
Journal ISSN
Volume Title
Abstract
Exchange options are one of the most popular exotic options, and have important implications for many common financial arrangements and for implied beta as a measure of systematic risk. In this study, we extend the existing literature on exchange options to allow for clustered jump contagion dynamics in each single asset, as well as across assets, using the Hawkes jump-diffusion model. We derive the analytical pricing formulae, the Greeks, and the optimal hedging strategy via Fourier transforms. Using an illustrative numerical analysis, we present the relationship between the exchange option price and clustered jump intensities and jump sizes in the underlying assets. We discuss the managerial insights on financial arrangements with exchange option characteristics. Furthermore, we discuss the implications of incorporating clustered jumps into the estimation of implied beta with exchange options, in which the applications can be insightful and useful in finance practice.
Description
Includes bibliographical references (pages 26-28).
Published as: Quantitative Finance, January 2020, https://doi.org/10.1080/14697688.2019.1704045.
Published as: Quantitative Finance, January 2020, https://doi.org/10.1080/14697688.2019.1704045.
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Subject
exchange option
Greeks
Hawkes jump-diffusion process
optimal hedging
implied beta