Soft Computing

, Volume 21, Issue 5, pp 1181–1192 | Cite as

Relevant applications of Monte Carlo simulation in Solvency II

  • Giuseppe Casarano
  • Gilberto Castellani
  • Luca Passalacqua
  • Francesca Perla
  • Paolo Zanetti
Methodologies and Application

Abstract

The definition of solvency for insurance companies, within the European Union, is currently being revised as part of Solvency II Directive. The new definition induces revolutionary changes in the logic of control and expands the responsibilities in business management. The rationale of the fundamental measures of the Directive cannot be understood without reference to probability distribution functions. Many insurers are struggling with the realisation of a so-called “internal model” to assess risks and determine the overall solvency needs, as requested by the Directive. The quantitative assessment of the solvency position of an insurer relies on Monte Carlo simulation, in particular on nested Monte Carlo simulation that produces very hard computational and technological problems to deal with. In this paper, we address methodological and computational issues of an “internal model” designing a tractable formulation of the very complex expectations resulting from the “market-consistent” valuation of fundamental measures, such as Technical Provisions, Solvency Capital Requirement and Probability Distribution Forecast, in the solvency assessment of life insurance companies. We illustrate the software and technological solutions adopted to integrate the Disar system—an asset–liability computational system for monitoring life insurance policies—in advanced computing environments, thus meeting the demand for high computing performance that makes feasible the calculation process of the solvency measures covered by the Directive.

Keywords

Life insurance policies Monte carlo simulation Nested simulation Modelling uncertainty Stochastic models  Risk assessment Asset–liability management 

References

  1. Bauer D, Bergmann D, Kiesel R (2010a) On the risk-neutral valuation of life insurance contracts with numerical methods in view. Astin Bull 40(1):65–95Google Scholar
  2. Bauer D, Bergmann D, Reuss A (2010b) Solvency II and Nested Simulations—a Least- Squares Monte Carlo Approach, Working paper, Georgia State University and Ulm UniversityGoogle Scholar
  3. Bauer D, Reuss A, Singer D (2012) On the calculation of the Solvency II Capital requirement based on Nested simulations. Astin Bull 42(2):453–501MathSciNetMATHGoogle Scholar
  4. Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Political Econ 81(3):637–654MathSciNetCrossRefMATHGoogle Scholar
  5. Broadie M, Du Y, Moallemi CC (2011) Efficient risk estimation via nested sequential simulation. Manag Sci 57:1172–1194CrossRefMATHGoogle Scholar
  6. Broadie M, Glasserman P (2007) Pricing American-style securities using simulation. J Econ Dyn Control 21:1323–1352MathSciNetCrossRefMATHGoogle Scholar
  7. Castellani G, De Felice M, Moriconi F, Pacati C (2005) Embedded Value in Life Insurance, Working PaperGoogle Scholar
  8. Castellani G, Passalacqua L (2011) Applications of Distributed and Parallel Computing in the Solvency II Framework: the DISAR System. In: Guarracino MR et al (eds) Euro-Par 2010 Parallel Processing Workshops., Lect Notes Comp Sci 6586, 413–421 Springer-Verlag, BerlinGoogle Scholar
  9. Corsaro S, De Angelis PL, Marino Z, Perla F, Zanetti P (2009) Computational issues in internal models: the case of profit-sharing life insurance policies. G dell’Istituto Ital degli Attuari LXXII:237–256Google Scholar
  10. Corsaro S, Marino Z, Perla F, Zanetti P (2011) Measuring default risk in a parallel ALM software for life insurance portfolios. In: Guarracino MR et al (eds) Euro-Par 2010 Parallel Processing Workshops., Lect Notes Comp Sci 6586, 471–478 Springer-Verlag, BerlinGoogle Scholar
  11. Cox JC, Ingersoll JE, Ross SA (1985) A theory of the term structure of interest rates. Econometrica 53:385–407MathSciNetCrossRefMATHGoogle Scholar
  12. de Andrés-Sánchez J (2012) Claim reserving with fuzzy regression and the two ways of ANOVA. Appl Soft Comput 12(8):2435–2441CrossRefGoogle Scholar
  13. De Angelis PL, Perla F, Zanetti P (2013) Hybrid MPI/OpenMP application on multicore architectures: the case of profit-sharing life insurance policies valuation. Appl Math Sci 7(102):5051–5070CrossRefGoogle Scholar
  14. De Felice M, Moriconi F (2004) Market consistent valuation in life insurance. Measuring fair value and embedded options. G dell’Istituto Ital degli Attuari LXVII:95–117Google Scholar
  15. De Felice M, Moriconi F (2005) Market based tools for managing the life insurance company. Astin Bull 35(1):79MathSciNetCrossRefMATHGoogle Scholar
  16. Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II), Official Journal of the European Union, L335/1, 17.12.2009Google Scholar
  17. Duffie D, Singleton K (1999) Modeling term structures of defaultable bonds. Rev Financ Stud 12(4):687–720CrossRefGoogle Scholar
  18. EIOPA (2012) Final Report on Public Consultation No. 11/008. On the Proposal for Guidelines on ORSA, 9 July 2012Google Scholar
  19. EIOPA (2013) Final Report on Public Consultation No. 13/009. On the Proposal for Guidelines on Forward Looking Assessment of Own Risks (based on the ORSA principles), 23 Sept 2013Google Scholar
  20. Glasserman P (2004) Monte Carlo methods in financial engineering. Springer, New YorkMATHGoogle Scholar
  21. Gordy MB, Juneja S (2010) Nested simulation in portfolio risk management. Manag Sci 56(10):1833–1848CrossRefMATHGoogle Scholar
  22. Haromoto H, Matsumoto M, Nishimura T, Panneton F, L’Ecuyer P (2008) Efficient jump ahead for \(\mathbb{F}_2\)-linear random number generators. INFORMS J Comput 20(3):385–390MathSciNetCrossRefMATHGoogle Scholar
  23. Hull JC (2012) Options, futures, and other derivatives, 8th Edition, Prentice Hall, USAGoogle Scholar
  24. Lesnevski V, Nelson BL, Staum J (2008) An adaptive procedure for simulating coherent risk measures based on generalized scenarios. J Comput Finance 11:1–31CrossRefGoogle Scholar
  25. Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: a simple least-squares approach. Rev Financ Stud 14:113–147Google Scholar
  26. Luckner WR, Abbott MC, Backus JE, Benedetti S, Bergman D, Cox SH, Feldblum S, Gilbert CL, Liu XL, Lui VY, Mohrenweiser JA, Overgard WH, Pedersen HW, Rudolph MJ, Shiu ES, Smith PL (2002) Professional actuarial speciality guide—asset–liability management, Society of ActuariesGoogle Scholar
  27. Matsumoto M, Nishimura T (1998) Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Trans. on Modeling and Computer. Simulation 8(1):3–30MATHGoogle Scholar
  28. Matsumoto M, Nishimura T (2000) Dynamic creation of pseudorandom number generators. In: Niederreiter H, Spanier J (eds) Monte Carlo and Quasi-Monte Carlo methods. Springer, Berlin, pp 56–69Google Scholar
  29. McNeil A, Frey R, Embrechts P (2006) Quantitative risk management: concepts, techniques, and tools. Princeton University Press, Princeton, New JerseyMATHGoogle Scholar
  30. Official Journal of the European Union, Commission Delegated Regulation (EU) 2015/35 of 10 October 2014 supplementing Directive 2009/138/EC of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II) Text with EEA relevance, 17.1.2015Google Scholar
  31. Oyanagi S (2014) MPICH ABI Compatibility Status, CRAYDOC S-2544-70, Jun (2014)Google Scholar
  32. Salzmann R, Wüthrich MW (2010) Cost-of-capital margin for a general insurance liability runoff. ASTIN Bull 40(2):415–451MathSciNetMATHGoogle Scholar
  33. Shapiro AF (2002) The merging of neural networks, fuzzy logic, and genetic algorithms. Insur: Math Econ 31(1):115–131MathSciNetGoogle Scholar
  34. Shapiro AF (2004) Fuzzy logic in insurance. Insur: Math Econ 35(2):399–424MathSciNetMATHGoogle Scholar
  35. Yoshida Y (2009) An estimation model of value-at-risk portfolio under uncertainty. Fuzzy Sets Syst 160(22):3250–3262MathSciNetCrossRefMATHGoogle Scholar
  36. Zmeškal Z (2005) Value at risk methodology under soft conditions approach (fuzzy-stochastic approach). Eur J Oper Res 161(2):337–347MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Giuseppe Casarano
    • 1
  • Gilberto Castellani
    • 2
  • Luca Passalacqua
    • 2
  • Francesca Perla
    • 3
  • Paolo Zanetti
    • 3
  1. 1.Alef Avanced Laboratory Economics and FinanceRomeItaly
  2. 2.Department of Statistical SciencesSapienza, University of RomeRomeItaly
  3. 3.Department of Management and Quantitative StudiesUniversity of Naples “Parthenope”NaplesItaly

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