Financial Evaluation of Life Insurance Policies in High Performance Computing Environments

  • Stefania Corsaro
  • Pasquale Luigi De Angelis
  • Zelda Marino
  • Paolo Zanetti
Part of the Springer Optimization and Its Applications book series (SOIA, volume 70)


The European Directive Solvency II has increased the request of stochastic asset–liability management models for insurance undertakings. The Directive has established that insurance undertakings can develop their own “internal models” for the evaluation of values and risks in the contracts. In this chapter, we give an overview on some computational issues related to internal models. The analysis is carried out on “Italian style” profit-sharing life insurance policies (PS policy) with minimum guaranteed return. We describe some approaches for the development of accurate and efficient algorithms for their simulation. In particular, we discuss the development of parallel software procedures. Main computational kernels arising in models employed in this framework are stochastic differential equations (SDEs) and high-dimensional integrals. We show how one can develop accurate and efficient procedures for PS policies simulation applying different numerical methods for SDEs and techniques for accelerating Monte Carlo simulations for the evaluation of the integrals. Moreover, we show that the choice of an appropriate probability measure provides a significative gain in terms of accuracy.


Monte Carlo Credit Spread Short Rate Risk Source Defaultable Bond 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    G. Barone-Adesi, E. Barone, G. Castagna, Pricing bonds and bond options with default risk. Eur. Financ. Manag. 4, 231–282 (1998)CrossRefGoogle Scholar
  2. 2.
    F. Black, M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–654 (1973)CrossRefGoogle Scholar
  3. 3.
    D. Brigo, A. Alfonsi, Credit default swaps calibration and option pricing with the SSRD stochastic intensity and interest-rate model. Finance Stochast. 9(1), 29–42 (2005)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    D. Brigo, F. Mercurio, Interest Rate Models: Theory and Practice (Springer, New York, 2006)MATHGoogle Scholar
  5. 5.
    S.J. Brown, P.H. Dybvig, The empirical implications of the Cox, Ingersoll, Ross theory of the term structure of interest rates. J. Finance 41(3), 617–630 (1986)Google Scholar
  6. 6.
    H. Bulhmann, New math for life insurance. Astin Bull. 32(2), 209–211 (2002)CrossRefGoogle Scholar
  7. 7.
    R. Caflisch, W. Morokoff, A. Owen, Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance 1, 27–46 (1998)Google Scholar
  8. 8.
    G. Castellani, L. Passalacqua, Applications of distributed and parallel computing in the solvency II framework: the DISAR system, in Euro-Par 2010 Parallel Processing Workshops, ed. by M.R. Guarracino, F. Vivien, J.L. Träff, M. Cannataro, M. Danelutto, A. Hast, F. Perla, A. Knüpfer, B. Di Martino, M. Alexander. Lecture Notes in Computer Science, vol. 6586 (Springer, Berlin, 2011), pp. 413–421Google Scholar
  9. 9.
    G. Castellani, M. De Felice, F. Moriconi, C. Pacati, Embedded Value in Life Insurance. Working paper (2005)Google Scholar
  10. 10.
    G. Castellani, M. De Felice, F. Moriconi, Manuale di Finanza, vol. III. Modelli Stocastici e Contratti Derivati (Società editrice il Mulino, Bologna, 2006)Google Scholar
  11. 11.
    S. Corsaro, P.L. De Angelis, Z. Marino, F. Perla, P. Zanetti, On high performance software development for the numerical simulation of life insurance policies, in Numerical Methods for Finance, ed. by J. Miller, I.D. Edelman, J. Appleby (Chapman and Hall/CRC, Dublin, 2007), pp. 87–111Google Scholar
  12. 12.
    S. Corsaro, P.L. De Angelis, Z. Marino, F. Perla, P. Zanetti, On parallel asset-liability management in life insurance: A forward risk-neutral approach. Parallel Comput. 36(7), 390–402 (2010)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    S. Corsaro, Z. Marino, F. Perla, P. Zanetti, Measuring default risk in a parallel ALM software for life insurance portfolios, in Euro-Par 2010 Parallel Processing Workshops, ed. by M.R. Guarracino, F. Vivien, J.L. Träff, M. Cannataro, M. Danelutto, A. Hast, F. Perla, A. Knüpfer, B. Di Martino, M. Alexander. Lecture Notes in Computer Science, vol. 6586 (Springer, Berlin, 2011), pp. 471–478Google Scholar
  14. 14.
    S. Corsaro, P.L. De Angelis, Z. Marino, F. Perla, Participating life insurance policies: An accurate and efficient parallel software for COTS clusters. Comput. Manag. Sci. 8(3), 219–236 (2011)MathSciNetCrossRefGoogle Scholar
  15. 15.
    J.C. Cox, J.E. Ingersoll, S.A Ross. A theory of the term structure of interest rates. Econometrica 53, 385–407 (1985)Google Scholar
  16. 16.
    G. Deelstra, F. Delbaen, Convergence of discretized stochastic (interest rate) processes with stochastic drift term. Appl. Stochast. Model Data Anal. 14(1), 77–84 (1998)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    M. De Felice, F. Moriconi, Market consistent valuation in life insurance: Measuring fair value and embedded options. Giornale dell’Istituto Italiano degli Attuari 67, 95–117 (2004)Google Scholar
  18. 18.
    M. De Felice, F. Moriconi, Market based tools for managing the life insurance company. Astin Bull. 35(1), 79–111 (2005)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    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. Official Journal of the European Union 335(52), 1–155 (2009)Google Scholar
  20. 20.
    D. Duffie, Credit risk modeling with affine processes. J. Bank. Finance 29, 2751–2802 (2005)CrossRefGoogle Scholar
  21. 21.
    D. Duffie, K.J. Singleton, Modeling term structures of defaultable bonds. Rev. Financ. Stud. 12(4), 686–720 (1999)CrossRefGoogle Scholar
  22. 22.
    D. Duffie, K.J. Singleton, Credit Risk: Pricing, Measurement, and Management (Princeton University Press, Princeton, 2003)Google Scholar
  23. 23.
    H. Geman, N. El Karoui, J.C. Rochet. Changes of numéraire, changes of probability measure and option pricing. J. Appl. Probab. 32(2), 443–458 (1995)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    P. Glasserman, Monte Carlo Methods in Financial Engineering (Springer, New York, 2004)MATHGoogle Scholar
  25. 25.
    D. Higham, X. Mao, Convergence of Monte Carlo simulations involving the mean-reverting square root process. J. Comput. Finance 8(3), 35–62 (2005)Google Scholar
  26. 26.
    J. Hull, A. White, One-factor interest rate models and the valuation of interest rate derivative securities. J. Financ. Quant. Anal. 28, 235–254 (1993)CrossRefGoogle Scholar
  27. 27.
    IAIS, Guidance Paper on the Use of Internal Models for Regulatory Capital Purpose, International Association of Insurance Supervisors, Basel, Guidance paper no. 2.6 (2008)Google Scholar
  28. 28.
    J. Jamshidian, An exact bond option formula. J. Finance 44(1), 205–209 (1989)CrossRefGoogle Scholar
  29. 29.
    R.A. Jarrow, D. Lando, S.M. Turnbull, A Markov model for the term structure of credit risk spreads. Rev. Finan. Stud. 10(2), 481–523 (1997)CrossRefGoogle Scholar
  30. 30.
    P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, Berlin, 1992)MATHGoogle Scholar
  31. 31.
    D. Lando, On Cox processes and credit risky securities. Rev. Derivatives Res. 2(2–3), 99–120 (1998)Google Scholar
  32. 32.
    D. Lando, Credit Risk Modeling, Theory and Applications (Princeton University Press, Princeton, 2004)Google Scholar
  33. 33.
    R. Lord, R. Koekkoek, D. van Dijk, A comparison of biased simulation schemes for stochastic volatility models. Quant. Finance 10(2), 177–194 (2010)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    M. Mascagni, A. Srinivasan, Algorithm 806: SPRNG: A scalable library for pseudorandom number generation. ACM Trans. Math. Software 26, 436–461 (2000)CrossRefGoogle Scholar
  35. 35.
    M. Mascagni, S.A. Cuccaro, D.V. Pryor, M.L. Robinson, A fast, high-quality, and reproducible lagged-Fibonacci pseudorandom number generator. J. Comput. Phys. 15, 211–219 (1995)MathSciNetCrossRefGoogle Scholar
  36. 36.
    G.N. Milstein, A method of second-order accuracy integration of stochastic differential equations. Theor. Probab. Appl. 23, 396–401 (1978)CrossRefGoogle Scholar
  37. 37.
    G.N. Milstein, E. Platen, H. Schurz, Balanced implicit methods for stiff stochastic systems. SIAM J. Numer. Anal. 35(3), 1010–1019 (1998)MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    C. Pacati, Estimating the Euro term structure of interest rates. Research Group on “Models for Mathematical Finance”, Working Paper 32 (1999)Google Scholar
  39. 39.
    S. Paskov, J. Traub, Faster valuation of financial derivatives. J. Portfolio Manag. 22(1), 113–123 (1995)CrossRefGoogle Scholar
  40. 40.
    P.J. Schonbucher, Credit Derivatives Pricing Models – Models, Pricing and Implementation (Wiley, New York, 2005)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Stefania Corsaro
    • 1
  • Pasquale Luigi De Angelis
    • 1
  • Zelda Marino
    • 1
  • Paolo Zanetti
    • 1
  1. 1.Dipartimento di Statistica e Matematica per la Ricerca EconomicaUniversità degli Studi di Napoli “Parthenope”NapoliItaly

Personalised recommendations