Catastrophe Swap Price Modeling with Random Severity

Mahmoudpour, N.; Neisy, A.; Peymany, M.; Amiri, M.

doi:10.22056/ijir.2019.04.02

Document Type : Original Research Paper

Authors

¹ Department of Financial Management, School of Accounting and Management, Allameh Tabatabai University, Tehran, Iran

² Department of Mathematics, School of Statistics, Mathematics and Computers, Allameh Tabatabai University, Tehran, Iran

³ Department of Finance and Banking, School of Management and Accounting, Allameh Tabatabai University, Tehran, Iran

https://doi.org/10.22056/ijir.2019.04.02

Abstract

Objective: Presenting a model for catastrophe swap pricing based on stochastic models and numerical solution of the model.
Methodology: Descriptive, its design is retrospective, the direction of applied research and the method of collecting information is library. In this research, the "use of available information and documents" tool was used and Varans and Pilke (2009) database was used. In determining the changes in the swap price, Ito's order was followed, and Black and Schulz's generalization of the modeling method was used to reach the catastrophe swap model. A partial integral differential equation was extracted and converted to ordinary differential equations using semi-discretization and finite difference method and Euler method were used to solve the catastrophe swap pricing model. The parameters were estimated and implemented numerically based on Björk's (2009) statistical inference method, and finally, the model was implemented using MATLAB software.
Findings: A new two-factor model for damage has been presented. In other words, instead of C in Anger's model, 〖"Ce"〗^"λ" is used and Landa is considered to change randomly every moment. Therefore, from the point of view of the mathematics of probability, the intensity does not have a fixed value and follows a random geometric Brownian process, which is correlated with the damage. Also, a new model for catastrophe swap pricing has been presented, which has two integral and differential parts.

Conclusion: The catastrophe swap price has an inverse relationship with the growth of damage and the growth of damage severity. Also, the trend of the price for damage less than the threshold has a regular trend, and these changes are proportional to the changes in damage and severity.

Keywords

References

عسکری فیروز حایی، احسان، ساده وند، محمد جواد 1393 . اوراق بهادار سازی بیمه (ویرایش اول)، بورس اوراق بهادار تهران، تهران
نیسی، عبدالساده، سلمانی قرائی، کامران 1397، مهندسی مالی و مدل سازی بازارها با رویکرد نرم ابزار MATLAB ، دانشگاه علامه طباطبایی، تهران
1. Aase, K.K., 2001, "A Markov model for the pricing of catastrophe insurance futures and spreads", Journal of Risk and Insurance ,68 (1), 25–49.
2. Azizi S.M.E.P.M. , Neisy, A. ,2018, "A New Approach in Geometric Brownian Motion Model. In: Cao BY. (eds) Fuzzy Information and Engineering and Decision. Advances in Intelligent Systems and Computing", vol 646. Springer.
3. Biagini, F., Bregman, Y., & Meyer-Brandis, T., 2008, "Pricing of catastrophe insurance options written on a loss index with reestimation. Insurance", Mathematics and Economics, 43(2), 214-222.
4. Bjork, T, 2009, Arbitrage theory in continuous time, Oxford University Press, Oxford, 3^rd ed
5. Borden, S., Sarkar, A., 1996, "Securitizing property catastrophe risk", Current Issues in Economics and Finance, 2 (9), 1–6.
6. Braun, A.,2011, "Pricing catastrophe swaps: A contingent claims approach. Insurance". Mathematics and Economics, 49(3), 520-536.
7. Campbell, J.Y., Cochrane, J.H., 1999. "By force of habit: a consumption-base explanation of aggregate stock market behavior", Journal of Political Economy 107 (2), 205–251.
8. Canter, M.S., Cole, J.B., Sandor, R.L., 1997, "Insurance derivatives: a new asset class for the capital markets and a new hedging tool for the insurance industry", Applied Corporate Finance, 10 (3), 69–81.
9. Chang, C.W., Chang, J.S.K., Yu, M.-T., 1996, "Pricing catastrophe insurance futures call spreads", Risk and Insurance, Vol. 63, No. 4, pp. 599-617
10. Chang, C. W., Chang, J. S., & Lu, W., 2008, "Pricing catastrophe options in discrete operational time", Insurance: Mathematics and Economics, 43(3), 422-430.
11. Chang, C. W., Chang, J. S., & Lu, W.,2010, "Pricing catastrophe options with stochastic claim arrival intensity in claim time", Banking & Finance, 34(1), 24-32.
12. Cummins, J.D., 2008, "CAT bonds and other risk-linked securities: state of the market and recent developments", Risk Management and Insurance Review ,11 (1),23–47.
13. Cummins, J.D., Geman, H., 1994, "An Asian option approach to the valuation of insurance futures contracts", Review of Futures Markets, 13 (2), 517–557.
14. Cummins, J.D., Geman, H., 1995, "Pricing catastrophe insurance futures and call spreads: an arbitrage approach", Journal of Fixed Income, 4 (4), 46–57.
15. Cummins, J. D., & Weiss, M. A.,2009, "Convergence of insurance and financial markets: Hybrid and securitized risk‐transfer solutions", Risk and Insurance, 76(3), 493-545.
16. Dieckmann, S., 2009, "By force of nature: explaining the yield spread on catastrophe bonds Working Paper", University of Pennsylvania, finance department.
17. Egami, M., Young, V.R., 2008, "Indifference prices of structured catastrophe (CAT) bonds", Insurance: Mathematics and Economics, 42 (2), 771–778.
18. Forrester, J.P., 2008, "Insurance risk collateralized debt obligations", Structured Finance ,14 (1), 28–32.
19. Geman, H., Yor, M., 1997, "Stochastic time changes in catastrophe option pricing", Insurance: Mathematics and Economics, 21 (3), 185–193.
20. Härdle, W. K., & Cabrera, B. L., 2010, "Calibrating CAT bonds for Mexican earthquakes", Risk and Insurance, 77(3), 625-650.
21. Hirsa, Ali, 2012, Computational Methods in Finance, Chapman and Hall/CRC, Financial Mathematics Series, Taylor & Francis
22. Ionut florescu, Ruihua liu, Maria cristina mariana, 2012, " Solutions to a partial integro-differential parabolic system arising in the pricing of financial options in regime-switching jump diffusion models", Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 231, pp. 1–12.
23. Jarrow, R.A., Yu, F., 2001, Counterparty risk and the pricing of defaultable securities, The Journal of Finance 56 (5), 1765–1799.
24. Lane, M., & Mahul, O., 2008, Catastrophe risk pricing: an empirical analysis, International Bank for Reconstruction and Development, The World Bank
25. Lee, J. P., & Yu, M. T., 2007, "Valuation of catastrophe reinsurance with catastrophe bonds", Insurance: Mathematics and Economics, 41(2), 264-278.
26. Muermann, A., 2008, "Market price of insurance risk implied by catastrophe derivatives", North American Actuarial Journal, 12(3), 221-227.
27. Neisy, A, Salmani, K, 2013, "An inverse finance problem for estimation of the volatility", Computational Mathematics and Mathematical Physics, Volume 53, Issue 1, pp 63–77. Springer.
28. Pielke Jr, R. A., Gratz, J., Landsea, C. W., Collins, D., Saunders, M. A., & Musulin, R., 2008, "Normalized hurricane damage in the United States: 1900–2005", Natural Hazards Review, 9(1), 29-42.
29. Swiss Re, 2009, "The role of indices in transferring insurance risk to the capital markets. Sigma, 4, Zurich, Switzerland.
30. Unger, A.J.A., 2010, "Pricing index-based catastrophe bonds: Part 1: Formulation and discretization issues using a numerical PDE approach", Computers & Geosciences,36, 2, 2010, 139-149.
31. Vickery, P., Skerlj, P., Lin, J., Twisdale, L., Jr, Young, M., & Lavelle, F., 2006, "HAZUS-MH Hurricane model methodology. II: Damage and loss estimation", Natural Hazards Review, 7, 94–103.
32. Vranes, K., & Pielke Jr, R., 2009, "Normalized earthquake damage and fatalities in the United States: 1900–2005". Natural Hazards Review, 10(3), 84-101.
33. Wu, Y. C., & Chung, S. L., 2010, "Catastrophe risk management with counterparty risk using alternative instruments", Insurance: Mathematics and Economics, 47(2), 234-245
34. Xu, Y., 2016, "A Study of the Loss Distribution of Natural Disasters in Norway Comparing a Common Model with a Model Broken Down into Catastrophe Types", University of Oslo Library.
35. Young, V.R., 2004, "Pricing in an incomplete market with an affine term structure", Mathematical Finance, 14 (3), 359–381.
36. Zolfaghari, M.R., and Campbell, K.W., 2008, "A NEW INSURANCE LOSS MODEL TO PROMOTE CATASTROPHE INSURANCE MARKET IN INDIA AND PAKISTAN", The 14th World Conference on Earthquake Engineering October 12-17, Beijing, China.

Letters to Editor

IJIR Journal welcomes letters to the editor for the post-publication discussions and corrections which allows debate post publication on its site, through the Letters to Editor. Letters pertaining to manuscript published in IJIR should be sent to the editorial office of IJIR within three months of either online publication or before printed publication, except for critiques of original research. Following points are to be considering before sending the letters (comments) to the editor.

[1] Letters that include statements of statistics, facts, research, or theories should include appropriate references, although more than three are discouraged.

[2] Letters that are personal attacks on an author rather than thoughtful criticism of the author’s ideas will not be considered for publication.

[3] Letters can be no more than 300 words in length.

[4] Letter writers should include a statement at the beginning of the letter stating that it is being submitted either for publication or not.

[5] Anonymous letters will not be considered.

[6] Letter writers must include their city and state of residence or work.

[7] Letters will be edited for clarity and length.

Name *

Email Address *

Affiliation *

Comments *

Security Code *

Iranian Journal of Insurance Research

Catastrophe Swap Price Modeling with Random Severity

References

References

Letters to Editor

Send comment about this article

Volume 8, Issue 4 - Serial Number 30
October 2019
Pages 266-283

Catastrophe Swap Price Modeling with Random Severity

References

References

Letters to Editor

Send comment about this article

Volume 8, Issue 4 - Serial Number 30October 2019Pages 266-283

Volume 8, Issue 4 - Serial Number 30
October 2019
Pages 266-283