Pricing and hedging catastrophe equity put optionsunder a Markov-modulated jump diffusion model

Wei Wang; Linyi Qian; Xiaonan Su

doi:10.3934/jimo.2015.11.493

Article Contents

2015, Volume 11, Issue 2: 493-514. Doi: 10.3934/jimo.2015.11.493

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Pricing and hedging catastrophe equity put options under a Markov-modulated jump diffusion model

1.
Department of Financial Engineering, Ningbo University, Ningbo, 315211
2.
School of Finance and Statistics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241
3.
School of Science, Nanjing Audit University, Nanjing, 210029

Received: December 31, 2013

Revised: March 31, 2014

Published: March 2015

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Abstract

In this paper, we consider pricing and hedging of catastrophe equity put options under a Markov-modulated jump diffusion process with a Markov switching compensator. We assume that the risk free interest rate, the appreciation rate and the volatility of the risky asset depend on a finite-state Markov chain. We investigate the pricing of catastrophe equity put options and obtain the explicit pricing formulas. A numerical analysis is provided to illustrate the effect of regime switching on the price of catastrophe equity put options. In the end, since the market which we consider is not complete, we also provide an optimal hedging strategy by using the local risk minimization method.

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Mathematics Subject Classification: Primary: 91B24, 91B30; Secondary: 60J75.

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