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A closed-form pricing formula for catastrophe equity options

Published online by Cambridge University Press:  15 July 2021

Puneet Pasricha Open the ORCID record for Puneet Pasricha [Opens in a new window] ,
Anubha Goel Open the ORCID record for Anubha Goel [Opens in a new window]  and
Song-Ping Zhu
Puneet Pasricha
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia. E-mails: pasrichapuneet5@gmail.com, spz@uow.edu.au
Anubha Goel
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. E-mail: anubha.goel1@gmail.com
Song-Ping Zhu
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia. E-mails: pasrichapuneet5@gmail.com, spz@uow.edu.au
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Abstract

In this article, we derive a closed-form pricing formula for catastrophe equity put options under a stochastic interest rate framework. A distinguishing feature of the proposed solution is its simplified form in contrast to several recently published formulae that require evaluating several layers of infinite sums of $n$-fold convoluted distribution functions. As an application of the proposed formula, we consider two different frameworks and obtain the closed-form formula for the joint characteristic function of the asset price and the losses, which is the only required ingredient in our pricing formula. The prices obtained by the newly derived formula are compared with those obtained using Monte-Carlo simulations to show the accuracy of our formula.

Keywords

Catastrophe put optionJoint characteristic functionJump-diffusionStochastic interest rate
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 1103 - 1115
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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