Pricing life insurance contracts with early exercise features

Abstract

a b s t r a c tIn this paper we describe an algorithm based on the Least Squares Monte Carlo method to price life insurance contracts embedding American options. We focus on equity-linked contracts with surrender options and terminal guarantees on benefits payable upon death, survival and surrender. The framework allows for randomness in mortality as well as stochastic volatility and jumps in financial risk factors. We provide numerical experiments demonstrating the performance of the algorithm in the context of multiple risk factors and exercise dates.

Variable annuities: A unifying valuation approach

“…This method combines Monte Carlo simulation with least squares regression within the dynamic programming principle used to find an optimal exercise strategy. In the life insurance field, the LSMC has recently been explored by Bacinello et al (2009Bacinello et al ( , 2010a. We provide now a concise, yet self contained, description of the algorithm and refer to Bacinello et al (2010a) for further details and related literature.…”

“…We do not deal with the calibration of this model to real market data, as our purpose is just to illustrate the flexibility of the valuation approach. We adopt a slightly simplified version of the framework presented in Bacinello et al (2009); all processes are specified under the selected risk-adjusted probability measure. The instantaneous risk-free rate r and the variance K of the reference fund follow square root processes:…”

The Difference between LSMC and Replicating Portfolio in Insurance Liability Modeling

“…Consequently, the righthand side of Eq. (2.9) is truncated to a finite number K; Pricing function at t ¼ 1 for call with maturity T ¼ 2 2 We remark again that in the case where the basis includes a constant EP½a…”

“…Examples for LSMC in the context of American option pricing can be found in [5, 12, 15, 19-21, 30, 39, 41, 42]. Andreatta and Corradin [1] and Bacinello et al [2,3] apply the LSMC approach to the valuation of life insurance policies with surrender options. Devineau and Chauvigny [18] show how the LSMC method can be extended to obtain a portfolio of replicating assets consisting of standard financial instruments.…”

The Cost of Counterparty Risk and Collateralization in Longevity Swaps

“…12 A similar approach is used by Bacinello et al (2009Bacinello et al ( , 2010 for surrender guarantees in life policies and by Bauer et al (2009) for the computation of capital requirements within the Solvency II framework. The term American Monte Carlo is often used in financial engineering to refer to this approach.…”