Catastrophe insurance derivatives pricing using a Cox process with jump diffusion CIR intensity

Jiwook Jang, Jong Jun Park, Hyun Jin Jang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We propose an analytical pricing method for stop-loss reinsurance contracts and catastrophe insurance derivatives using a Cox process with jump diffusion Cox–Ingersoll–Ross (CIR) intensity. The expected payoff of these contracts is expressed by the Laplace transform of the integration of the jump diffusion CIR process and the first moment of the aggregate loss. To confirm that the proposed analytical formula provides stable and accurate insurance derivative prices, we simulate them using a full Monte Carlo method compared to those obtained from its theoretical expectation. It shows that it is much faster way to obtain them than the full Monte Carlo method. We also conduct sensitivity analysis by changing the relevant parameters in the loss intensity providing their figures.
Original languageEnglish
Article number1850041
Number of pages20
JournalInternational Journal of Theoretical and Applied Finance
Volume21
Issue number7
Early online date2018
DOIs
Publication statusPublished - Nov 2018

Keywords

  • Cox process
  • integrated jump diffusion CIR process
  • Laplace transform
  • characteristic function
  • insurance derivatives

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