### Abstract

This paper develops a catastrophe equity put (CatEPut) option model under realistic assumptions. To reflect the phenomena of real data, we adopt the following assumptions. First, following the reasoning in Lin and Wang [12], we assume that the loss index follows a compound Poisson process with jumps of a mixture of Erlangs. Second, the volatility of stock return is assumed to be stochastic as in Heston [8]. Under the assumptions, we derives a pricing formula for CatEPut options. Numerical examples are given to insist that the pricing formula can be easily implemented numerically. We also confirm the validity and accuracy of implementation of the pricing formula by comparing the numerical results obtained by the pricing formula with those obtained by the Monte Carlo simulation.

Original language | English |
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Pages (from-to) | 41-55 |

Number of pages | 15 |

Journal | Journal of Industrial and Management Optimization |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### Keywords

- CatEPut
- Jump-diffusion process
- Moment generating transform
- Option pricing
- Stochastic volatility

### ASJC Scopus subject areas

- Business and International Management
- Strategy and Management
- Control and Optimization
- Applied Mathematics

### Cite this

*Journal of Industrial and Management Optimization*,

*10*(1), 41-55. https://doi.org/10.3934/jimo.2014.10.41

**Catastrophe equity put options under stochastic volatility and catastrophe-dependent jumps.** / Kim, Hwa Sung; Kim, Bara; Kim, Jerim.

Research output: Contribution to journal › Article

*Journal of Industrial and Management Optimization*, vol. 10, no. 1, pp. 41-55. https://doi.org/10.3934/jimo.2014.10.41

}

TY - JOUR

T1 - Catastrophe equity put options under stochastic volatility and catastrophe-dependent jumps

AU - Kim, Hwa Sung

AU - Kim, Bara

AU - Kim, Jerim

PY - 2014/1/1

Y1 - 2014/1/1

N2 - This paper develops a catastrophe equity put (CatEPut) option model under realistic assumptions. To reflect the phenomena of real data, we adopt the following assumptions. First, following the reasoning in Lin and Wang [12], we assume that the loss index follows a compound Poisson process with jumps of a mixture of Erlangs. Second, the volatility of stock return is assumed to be stochastic as in Heston [8]. Under the assumptions, we derives a pricing formula for CatEPut options. Numerical examples are given to insist that the pricing formula can be easily implemented numerically. We also confirm the validity and accuracy of implementation of the pricing formula by comparing the numerical results obtained by the pricing formula with those obtained by the Monte Carlo simulation.

AB - This paper develops a catastrophe equity put (CatEPut) option model under realistic assumptions. To reflect the phenomena of real data, we adopt the following assumptions. First, following the reasoning in Lin and Wang [12], we assume that the loss index follows a compound Poisson process with jumps of a mixture of Erlangs. Second, the volatility of stock return is assumed to be stochastic as in Heston [8]. Under the assumptions, we derives a pricing formula for CatEPut options. Numerical examples are given to insist that the pricing formula can be easily implemented numerically. We also confirm the validity and accuracy of implementation of the pricing formula by comparing the numerical results obtained by the pricing formula with those obtained by the Monte Carlo simulation.

KW - CatEPut

KW - Jump-diffusion process

KW - Moment generating transform

KW - Option pricing

KW - Stochastic volatility

UR - http://www.scopus.com/inward/record.url?scp=84886841426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886841426&partnerID=8YFLogxK

U2 - 10.3934/jimo.2014.10.41

DO - 10.3934/jimo.2014.10.41

M3 - Article

AN - SCOPUS:84886841426

VL - 10

SP - 41

EP - 55

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

SN - 1547-5816

IS - 1

ER -