Insurance Mathematics and Economics 39 (2006) 135–149 www.elsevier.com/locate/ime Pricing of multi-period rate of return guarantees: The Monte Carlo approach ✩ Henrik Bakken a,1 , Snorre Lindset b,∗,2 , Lars Hesstvedt Olson c a The Boston Consulting Group, Karl Johans Gate 45, 0162 Oslo, Norway b Trondheim Business School, HIST avdeling TOH, 7004 Trondheim, Norway c First Securities, Fjordall´ een 16, 0250 Oslo, Norway Received August 2005; received in revised form January 2006; accepted 2 February 2006 Abstract The uncertain yearly returns on both life and pension insurance policies are often bounded from below by a minimum guaranteed rate of return. It turns out that this yearly, or multi-period guarantee can have a very high economic value. However, because determining this value is a problem of high dimension, obtaining an estimate of it can be rather difficult and time-consuming. In this paper we present a numerical valuation method for estimating the market value of the multi-period guarantee when the uncertainty in the interest rates is modeled in a Heath, Jarrow, and Morton framework with an exponential volatility structure. c  2006 Elsevier B.V. All rights reserved. JEL classification: C15; C63; G12; G13; G22 Subject categories: IM20; IE51; IB10 Keywords: Multi-period rate of return guarantee; Stochastic interest rates; Heath, Jarrow, and Morton term structure model; Monte Carlo simulation 1. Introduction A common way to reduce the financial risk in life and pension insurance policies is to embed the policies with minimum rate of return guarantees to bind the return from below. In several countries these guarantees work on an annual basis in the sense that the yearly return on the policy is guaranteed to not be below a guaranteed minimum return. Such guarantees are named annual guarantees or sometimes multi-period guarantees. One of the first analyses of these kinds of guarantees is made by Hipp (1996). Assuming a standard Black and Scholes (1973) framework with deterministic interest rates, he is able to obtain a closed form solution for the market value of the guarantee. The ✩ The authors would like to thank H˚ avard Rue, Sjur Westgaard, and an anonymous referee for useful discussions and comments. All authors were associated with the Norwegian University of Science and Technology, Department of Industrial Economics, Alfred Getzvei 1, 7491 Trondheim, Norway, at the time the paper was written. ∗ Corresponding author. Tel.: +47 73 55 99 78; fax: +47 73 55 99 51. E-mail addresses: bakken.henrik@bcg.com (H. Bakken), snorre.lindset@toh.hist.no (S. Lindset), lho@first.no (L.H. Olson). 1 He was a visitor at the Norwegian Computing Center when the paper was written. 2 He was a visiting scholar at the Insurance and Risk Management Department at the Wharton School, University of Pennsylvania, when the paper was written. 0167-6687/$ - see front matter c  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.insmatheco.2006.02.001