Pricing Earthquake Catastrophe Options Based on the Mixed-Multinomial Tree Model

Feixing Wang; Xiaoling Gu

doi:10.20965/jdr.2015.p1110

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JDR Vol.10 No.6 pp. 1110-1116

(2015)

doi: 10.20965/jdr.2015.p1110

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Pricing Earthquake Catastrophe Options Based on the Mixed-Multinomial Tree Model

Feixing Wang and Xiaoling Gu

Schools of Mathematics and Physics, University of Science and Technology Beijing
No.30, Xueyuan Road, Haidian District, Beijing 100083, P.R. China

Received:

August 25, 2015

Accepted:

October 23, 2015

Published:

December 1, 2015

Keywords:

earthquake catastrophe option, mixed-multinomial tree model, earthquake intensity, earthquake loss ratio

Abstract

The discrete time model we propose for option pricing, called the mixed-multinomial tree model (MMTM), extends the conventional multinomial tree model by assuming that both the number of branches of node m and possible values u_i are random variables during each period. The conventional multinomial tree model cannot be used to describe the accumulated loss process in earthquakes because earthquakes occur randomly and different main shocks may have different aftershocks. We therefore apply the MMTM to build an accumulated earthquake loss model in earthquake catastrophe options. We study option pricing for such a model and obtain a call option pricing formula.

Cite this article as:

F. Wang and X. Gu, “Pricing Earthquake Catastrophe Options Based on the Mixed-Multinomial Tree Model,” J. Disaster Res., Vol.10 No.6, pp. 1110-1116, 2015.

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References

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This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] K. X. Hao and H. Fujiwara, “Recent Destructive Earthquakes and International Collaboration for Seismic Hazard Assessment,” Journal of Disaster Research, Vol.8, No.2, pp. 1001-1007, 2013.

[2] [2] S. Koshimura, S. Hayashi, and H. Gokon, “Lessons from the 2011 Tohoku earthquake tsunami disaster,” Journal of Disaster Research, Vol.8, No.4, pp. 549-560, 2013.

[3] [3] X. X. Du, et al., “Comparative Analysis of Earthquake Emergency Response in China & Japan Based on Timeline – 311 Earthquake vs 512 Earthquake,” Journal of Disaster Research, Vol.10, No.2, pp. 277, 2015.

[4] [4] E. Krausmann, A. M. Cruz, and B. Affeltranger, “The impact of the 12 May 2008 Wenchuan earthquake on industrial facilities,” Journal of Loss Prevention in the Process Industries, Vol.23, No.2, pp. 242-248, 2010.

[5] [5] L. A. Johnson, “New Orleans’ recovery following Hurricane Katrina: Observations on local catastrophic recovery management,” Journal of Disaster Research, Vol.2, No.6, pp. 517-529, 2007.

[6] [6] R. H. Litzenberger, D. R. Beaglehole, and C. E. Reynolds, “Assessing catastrophe reinsurance-linked securities as a new asset class,” Journal of Portfolio Management, Vol.23, pp. 76-86, 1996.

[7] [7] S. Borden and A. Sarkar, “Securitizing property catastrophe risk,” Current Issues in Economics and Finance, Vol.2, No.8, pp. 1-6, 1996.

[8] [8] J. C. Cox, S. A. Ross, and M. Rubinstein, “Option pricing: A simplified approach,” Journal of Financial Economics, Vol.7, No.3, pp. 229-263, 1979.

[9] [9] C. W. Chang, J. SK. Chang, and W. L. Lu, “Pricing catastrophe options with stochastic claim arrival intensity in claim time.” Journal of Banking & Finance, Vol.34, No.1, pp. 24-32, 2010.

[10] [10] S. Perrakis and A . Boloorforoosh, “Catastrophe Derivatives and Reinsurance Contracts: An Incomplete Markets Approach,” Available at SSRN 2493313, 2014.

[11] [11] D. B. Madan, F. Milne, and H. Shefrin, “The multinomial option pricing model and its Brownian and Poisson limits,” Review of Financial Studies, Vol.2, No.2, pp. 251-265, 1989.

[12] [12] N. Ganikhodjaev and K. Bayram, “Random binomial tree models and options,” Journal of Applied Sciences (Faisalabad), Vol.12, No.18, pp. 1978-1981, 2012.

[13] [13] D. B. Madan and S. H. Hartzell, “Aftershock patterns and main shock faulting,” Bulletin of the Seismological Society of America, Vol.78, No.4, pp. 1438-1449, 1988.

[14] [14] Y. Huang, J. P. Wu, T. Z. Zhang, and D. N. Zhang, “Relocation of the M8.0 Wenchuan earthquake and its aftershock sequence,” Science in China Series D: Earth Sciences, Vol.51, No.12, pp. 1703-1711, 2008.

[15] [15] C. F. Richter, “Elementary seismology,” WH Freeman and Company, San Francisco, 1958.

[16] [16] T. Utsu, “Aftershocks and Earthquake Statistics (1): Some Parameters,” Geophysics, Vol.3, No.3, pp. 129-195, 1958.

[17] [17] X. M. Ren, J. L. Tian, H. Q. Ma, and X. W. Zeng, “Statistic features of maximum aftershock of earthquake sequences with MS≥6.0 in Chinese mainland and its border region,” Earthquake Research in China, Vol.29, No.4, pp. 480-488, 2013 (in Chinese).

[18] [18] U. J. Na and M. Shinozuka, “Simulation-based seismic loss estimation of seaport transportation system,” Reliability Engineering & System Safety, Vol.94, No.3, pp. 722-731, 2009.

[19] [19] Ö. Aydan, M. Hamada, J. Itoh, and K. Ohkubo, “Damage to civil engineering structures with an emphasis on rock slope failures and tunnel damage induced by the 2008 Wenchuan earthquake,” Journal of Disaster Research, Vol.4, No.2, pp. 153-162, 2009.

[20] [20] M. Wakaura, Y. Komaru, S. Shimizu, et al., “Seismic Risk Evaluation on Building Damage of Municipalities Based on the Seismic Activity Model in National Seismic Hazard Maps for Japan,” Journal of Disaster Research, Vol.8, No.5, pp. 848-860, 2013.

[21] [21] Editor Committee of China Earthquake Yearbook, China Earthquake Yearbook (1995). Seismological Press, Beijing, 1997 (in Chinese).

[22] [22] Editor Committee of China Earthquake Yearbook, China Earthquake Yearbook (2004). Seismological Press, Beijing, 2005 (in Chinese).

[23] [23] T. Y. Zheng, J. S. Hou, and H. L. Mi, “A Review of Earthquake Disasters Loss in Mainland China in 2008,” Journal of Catastrophology, Vol.25, No.2, pp. 112-118, 2010 (in Chinese).

[24] [24] T. Y. Zheng, P. Zhao, and Z. T. Liu, “A Review of Earthquake Disasters Loss in Mainland China in 2010,” Journal of Catastrophology, Vol.20, No.4, pp. 107-113, 2011 (in Chinese).