Analytical Approximations for Prices of Swap Rate Dependent Embedded Options in Insurance Products

26 Pages Posted: 17 Feb 2008 Last revised: 9 May 2011

See all articles by Richard Plat

Richard Plat

Richard Plat Consultancy

Antoon Pelsser

Maastricht University; Netspar

Date Written: February 15, 2008

Abstract

Life insurance products have profit sharing features in combination with guarantees. These so-called embedded options are often dependent on or approximated by forward swap rates. In practice, these kinds of options are mostly valued by Monte Carlo simulations. However, for risk management calculations and reporting processes, lots of valuations are needed. Therefore a more efficient method to value these options would be helpful. In this paper analytical approximations are derived for these kinds of options, based on an underlying multi-factor Gaussian interest rate model. The analytical approximation for options with direct payment is almost exact while the approximation for compounding options is also satisfactory. In addition, the proposed analytical approximation can be used as a control variate in Monte Carlo valuation of options for which no analytical approximation is available, such as similar options with management actions. Furthermore, it's also possible to construct analytical approximations when returns on additional assets (such as equities) are part of the profit sharing rate.

Keywords: Embedded options, insurance products, analytical approximation, Gaussian interest rate model, Fair Value of Liabilities, IFRS 4 Phase 2, Solvency 2, Monte Carlo simulation, Control Variate technique

Suggested Citation

Plat, Richard and Pelsser, Antoon A. J., Analytical Approximations for Prices of Swap Rate Dependent Embedded Options in Insurance Products (February 15, 2008). Insurance: Mathematics and Economics, Vol. 44, No. 1, 2009, Available at SSRN: https://ssrn.com/abstract=1093710

Richard Plat (Contact Author)

Richard Plat Consultancy ( email )

Volendam
Netherlands

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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