Valuation of the Reset Options Embedded in Some Equity-Linked Insurance Products

Abstract

This paper proposes a method for valuing American options using a Monte Carlo simulation approach. Our approach can be used to price the reset feature found in some equity-linked insurance contracts. We model this feature as a multiple shout option and give examples based on certain equity-linked insurance products that are very popular in Canada. These contracts are known as segregated fund contracts and the valuation of the embedded options in these contracts has posed serious challenges for actuaries. One of the advantages of the Monte Carlo approach in this connection is that it can be extended to handle different investment assumptions as well as multiple assets. We show how to modify the stochastic mesh model of Broadie and Glasserman (1997b) to incorporate quasi-Monte Carlo in the simulation and thus improve the efficiency. We benchmark the efficiency gains in our method using standard American options and multiple shout options.

Real World Pricing of Long Term Contracts

“…After more than 35 years of development no-arbitrage remains the dominant pricing paradigm for variable annuities linked to financial assets. Other papers worth mentioning in this regard include Delbaen (1986), Bacinello & Ortu (1993, 1994, Briys & Varenne (1997), Pennachi (1999), Boyle, Kolkiewicz & Tan (2001), Jorgensen (2001Jorgensen ( , 2004, Milevsky & Posner (2001), Milevsky & Salisbury (2001, 2006, Melnikov, Volkov & Nechaev (2002), Melnikov (2003Melnikov ( , 2004c, Pelsser (2003), Tanskanen & Lukkarinen (2003), Hürlimann (2004), De Felice & Moriconi (2005, Siu (2005), Biffis & Millosovich (2006), Milevsky, Moore & Young (2006), Chu & Kwok (2006, Bauer, Kling & Russ (2007) and Kling, Richter & Russ (2007) for European style payoffs; and Grosen & Jorgensen (1997, Bacinello (2001Bacinello ( , 2005, Ballotta, Haberman & Wang (2003), Vannucci (2003), Ballotta (2004) and Costabile, Massabo & Russo (2007) for Americantype contracts. The effect of stochastic interest rates on the risk neutral value of a guarantee has been discussed, for instance, in Bacinello & Ortu (1993, Aase & Persson (1994), Albizzati & Geman (1994), Nielsen & Sandmann, (1995,…”

We Are All “Actuaries Of The Third Kind” Now

“…Also, ten of the eleven annual ''best paper'' prizes awarded since the inception of the NAAJ in 1997 have been for papers related to financial economics or financial engineering. Prize-winning contributions have appeared from: Boyle and Lin (1997); Pafumi (1998, 2000); Yao (1998); Artzner (1998); Boyle, Kolkiewicz, and Tan (2001);Hardy (2001); Girard (2002); Babbel, Gold, and Merrill (2002); Lin and Tan (2003).…”

The Project Valuation with Abandonment and Reset Investment Proportion Applying Real Option Method

“…Cheng and Zhang [6] proposed closed form solutions of the discrete multi-stage reset option represented as a multiple variables normal distribution. Boyle, Kolkiewicz and Tan [7] used Monte Carlo Simulation to price reset options. Kimura and Shinohara [8] discovered that convertible bonds generally have reset conditions additionally.…”