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Risks 2015, 3(3), 338-364; doi:10.3390/risks3030338

Valuation of Index-Linked Cash Flows in a Heath–Jarrow–Morton Framework

1
Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg 412 96, Sweden
2
Department of Mathematics, Stockholm University, Stockholm 106 91, Sweden
*
Author to whom correspondence should be addressed.
Academic Editor: Montserrat Guillén
Received: 1 June 2015 / Accepted: 1 September 2015 / Published: 10 September 2015
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Abstract

In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath–Jarrow–Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation. View Full-Text
Keywords: state price deflators; insurance pricing; Heath–Jarrow–Morton state price deflators; insurance pricing; Heath–Jarrow–Morton
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Alm, J.; Lindskog, F. Valuation of Index-Linked Cash Flows in a Heath–Jarrow–Morton Framework. Risks 2015, 3, 338-364.

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