Stochastic evaluation of life insurance contracts: Model point on asset trajectories and measurement of the error related to aggregation
In this paper,11Version of 2012/07/08. we are interested in the optimization of computing time when using Monte-Carlo simulations for the pricing of the embedded options in life insurance contracts. We propose a very simple method which consists in grouping the trajectories of the initial process of the asset according to a quantile. The measurement of the distance between the initial process and the discretized process is realized by the L2-norm. L2 distance decreases according to the number of trajectories of the discretized process. The discretized process is then used in the valuation of the life insurance contracts. We note that a wise choice of the discretized process enables us to correctly estimate the price of a European option. Finally, the error due to the valuation of a contract in Euro using the discretized process can be reduced to less than 5%.
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- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Michael B. Gordy & Sandeep Juneja, 2010.
"Nested Simulation in Portfolio Risk Measurement,"
INFORMS, vol. 56(10), pages 1833-1848, October.
- Laurent Devineau & Stéphane Loisel, 2009. "Construction d'un algorithme d'accélération de la méthode des «simulations dans les simulations» pour le calcul du capital économique Solvabilité II," Post-Print hal-00365363, HAL.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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