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Frequency Domain and Time Domain Response of the Horizontal Grounding Electrode Using the Antenna Theory Approach Read chapter Read first chapter

2016 | OriginalPaper | Chapter

17. Sensitivity Analysis of Catastrophe Bond Price Under the Hull–White Interest Rate Model

Authors : Anatoliy Malyarenko, Jan Röman, Oskar Schyberg

Published in: Engineering Mathematics I

Publisher: Springer International Publishing

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Abstract

We consider a model, where the natural risk index is described by the Merton jump-diffusion while the risk-free interest rate is governed by the Hull–White stochastic differential equation. We price a catastrophe bond with payoff depending on finitely many values of the underlying index. The sensitivities of the bond price with respect to the initial condition, volatility of the diffusion component, and jump amplitude, are calculated using the Malliavin calculus approach.

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Literature
1.
Aase, K.: An equilibrium model of catastrophe insurance futures and spreads. The GENEVA Pap. Risk and Insur. Theory 24(1), 69–96 (1999)
2.
Bichteler, K., Gravereaux, J.B., Jacod, J.: Malliavin Calculus for Processes with Jumps, Stochastics Monographs, vol. 2. Gordon and Breach Science Publishers, New York (1987)MATH
3.
4.
Burnecki, K., Kukla, G., Taylor, D.: Pricing of catastrophe bonds. In: Čížek, P., Härdle, W.K., Weron, R. (eds.) Statistical Tools for Finance and Insurance, 2nd edn, pp. 371–391. Springer, Heidelberg (2011)CrossRef
5.
Cox, S.H., Fairchild, J.R., Pedersen, H.W.: Economic aspects of securitization of risk. Astin Bull. 30(1), 157–193 (2000)MathSciNetCrossRef
6.
7.
Cox, S.H., Schwebach, R.G.: Insurance futures and hedging insurance price risk. The J. of Risk and Insur. 59(4), 628–644 (1992)CrossRef
8.
Cummins, J.D., Geman, H.: Pricing catastrophe insurance futures and call spreads: An arbitrage approach. The J. of Fixed Income 4(4), 46–57 (1995)CrossRef
9.
Dassios, A., Jang, J.W.: Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity. Financ. Stoch. 7(1), 73–95 (2003)MathSciNetCrossRefMATH
10.
Di Nunno, G., Øksendal, B., Proske, F.: Malliavin Calculus for Lévy Processes with Applications to Finance. Springer, Berlin (2009)CrossRef
11.
Fournié, E., Lasry, J.M., Lebuchoux, J., Lions, P.L.: Applications of Malliavin calculus to Monte-Carlo methods in finance. II. Financ. Stoch. 5(2), 201–236 (2001)MathSciNetCrossRefMATH
12.
Fournié, E., Lasry, J.M., Lebuchoux, J., Lions, P.L., Touzi, N.: Applications of Malliavin calculus to Monte Carlo methods in finance. Financ. Stoch. 3(4), 391–412 (1999)MathSciNetCrossRefMATH
13.
14.
Girsanov, I.: On transforming a certain class of stochastic processes by absolutely continuous substitution of measures. Theory Probab. Appl. 5(3), 285–301 (1960)MathSciNetCrossRefMATH
15.
Glynn, P.: Optimization of stochastic systems via simulation. In: Proceedings of the 1989 Winter simulation Conference, pp. 90–105. (1989)
16.
Hull, J., Sokol, A., White, A.: Short-rate joint-measure models. Risk 10, 59–63 (2014)
17.
Hull, J., White, A.: Pricing interest-rate-derivative securities. Rev. of Financ. Stud. 3(4), 573–592 (1990)CrossRef
18.
Hull, J., White, A.: Bond option pricing based on a model for the evolution of bond prices. Adv. in Futures and Options Res. 3, 1–13 (1993)
19.
Loubergé, H., Kellezi, E., Gilli, M.: Using catastrophe-linked securities to diversity insurance risk: A financial analysis of cat bonds. J. of Insur. Issues 22(2), 125–146 (1999)
20.
21.
Merton, R.C.: Option pricing when underlying stock returns are discontinuous. J. of Financ. Econ. 3(1), 125–144 (1976)CrossRefMATH
22.
23.
Øksendal, B., Sulem, A.: Applied Stochastic Control of Jump Diffusions, 2nd edn. Springer, Berlin (2007)CrossRefMATH
24.
25.
Privault, N., Wei, X.: A Malliavin calculus approach to sensitivity analysis in insurance. Insur. Math. Econ. 35(3), 679–690 (2004)MathSciNetCrossRefMATH
26.
Romaniuk, M.: Pricing the risk-transfer financial instruments via Monte Carlo methods. Syst. Anal. Model. Simul. 43(8), 1043–1064 (2003)MathSciNetMATH
27.
Roumelioti, E.E., Zazanis, M.A., Frangos, N.E.: Sensitivity of the joint survival probability for reinsurance schemes. Math. Methods Appl. Sci. 37(2), 289–295 (2014)MathSciNetCrossRefMATH
28.
29.
Unger, A.J.: Pricing index-based catastrophe bonds: Part 1: Formulation and discretization issues using a numerical PDE approach. Comput. Geosci. 36(2), 139–149 (2010)CrossRef
30.
Unger, A.J.: Pricing index-based catastrophe bonds: Part 2: Object-oriented design issues and sensitivity analysis. Comput. Geosci. 36(2), 150–160 (2010)CrossRef
31.
Vaugirard, V.E.: Pricing catastrophe bonds by an arbitrage approach. The Q. Rev. of Econ. Financ. 43(1), 119–132 (2003)CrossRef
32.
Vaugirard, V.E.: Valuing catastrophe bonds by Monte Carlo simulations. Appl. Math. Financ. 10(1), 75–90 (2003)CrossRefMATH
Metadata
Title
Sensitivity Analysis of Catastrophe Bond Price Under the Hull–White Interest Rate Model
Authors
Anatoliy Malyarenko
Jan Röman
Oskar Schyberg
Copyright Year
2016
Book
Engineering Mathematics I

Print ISBN: 978-3-319-42081-3

Electronic ISBN: 978-3-319-42082-0

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-42082-0_17

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