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VALUATION OF CONTINGENT GUARANTEES USING LEAST-SQUARES MONTE CARLO

Part of: Mathematical finance

Published online by Cambridge University Press:  01 March 2019

T. Bienek Open the ORCID record for T. Bienek [Opens in a new window]  and
M. Scherer
T. Bienek*
Affiliation:
Lehrstuhl für Finanzmathematik, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany E-Mail: [email protected]
M. Scherer
Affiliation:
Lehrstuhl für Finanzmathematik, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
*
E-Mail: [email protected]
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Abstract

We consider the problem of pricing modern guarantee concepts in unit-linked life insurance, where the guaranteed amount grows contingent on the performance of an investment fund that acts simultaneously as the underlying security and the replicating portfolio. Using the Martingale Method, this nonstandard pricing problem can be transformed into a fixed-point problem, whose solution requires the evaluation of conditional expectations of highly path-dependent payoffs. By adapting the least-squares Monte Carlo method for American option pricing problems, we develop a new numerical approach to approximate the value of contingent guarantees and prove its convergence. Our valuation procedure can be applied to large-scale pricing problems, for which existing methods are infeasible, and leads to significant improvements in performance.

Keywords

Fixed-point problemcontingent guaranteeleast-squares Monte Carlo

MSC classification

Primary: 91G20: Derivative securities
Secondary: 91G60: Numerical methods (including Monte Carlo methods) 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 31 - 56
Copyright
Copyright © Astin Bulletin 2019 

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References

Bauer, D., Kiesel, R., Kling, A. and Russ, J. (2006) Risk-neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics, 39(2), 171–183.Google Scholar
Bienek, T. and Scherer, M. (2018) Hedging and valuation of contingent guarantees. Working paper.Google Scholar
Brigo, D. and Mercurio, F. (2006) Interest Rate Models: Theory and Practice. Berlin, Heidelberg: Springer.Google Scholar
Clément, E., Lamberton, D. and Protter, P. (2002) An analysis of a least squares regression method for American option pricing. Finance and Stochastics, 6(4), 449–471.CrossRefGoogle Scholar
Consiglio, A., Cocco, F. and Zenios, S.A. (2008) Asset and liability modelling for participating policies with guarantees. European Journal of Operational Research, 186(1), 380–404.CrossRefGoogle Scholar
Consiglio, A., Tumminello, M. and Zenios, S.A. (2015) Designing and pricing guarantee options in defined contribution pension plans. Insurance: Mathematics and Economics, 65, 267–279.Google Scholar
Delong, L. (2012) Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance. Applicationes Mathematicae, 39, 463–488.CrossRefGoogle Scholar
European Union. (2015) Commission delegated regulation (EU) 2015/35. Official Journal of the European Union, 58(L012), 1–797.Google Scholar
Grosen, A. and Jørgensen, P.L. (2000). Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics, 26(1), 37–57.Google Scholar
Hansen, M. and Miltersen, K.R. (2002) Minimum rate of return guarantees: The Danish case. Scandinavian Actuarial Journal, 2002(4), 280–318.CrossRefGoogle Scholar
Hull, J. and White, A. (1990) Pricing interest-rate-derivative securities. The Review of Financial Studies, 3(4), 573–592.CrossRefGoogle Scholar
Hull, J. and White, A. (1993) One-factor interest-rate models and the valuation of interest rate derivative securities. The Journal of Financial and Quantitative Analysis, 28(2), 235–254.CrossRefGoogle Scholar
International Accounting Standards Board. (2017) IFRS 17: Insurance Contracts.Google Scholar
Johnson, L.L. (1960) The theory of hedging and speculation in commodity futures. The Review of Economic Studies, 27(3), 139–151.CrossRefGoogle Scholar
Kleinow, T. (2009) Valuation and hedging of participating life-insurance policies under management discretion. Insurance: Mathematics and Economics, 44(1), 78–87.Google Scholar
Kleinow, T. and Willder, M. (2007) The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees. Insurance: Mathematics and Economics, 40(3), 445–458.Google Scholar
Longstaff, F.A. and Schwartz, E.S.. (2001) Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14(1), 113–147.CrossRefGoogle Scholar
Pelsser, A. and Schweizer, J. (2016) The difference between LSMC and replicating portfolio in insurance liability modeling. European Actuarial Journal, 6(2), 441–494.CrossRefGoogle ScholarPubMed
Smart, D.R. (1980) Fixed Point Theorems. Cambridge: Cambridge University Press.Google Scholar