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

Author

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  • Jonas Alm

    () (Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg 412 96, Sweden)

  • Filip Lindskog

    () (Department of Mathematics, Stockholm University, Stockholm 106 91, Sweden)

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.

Suggested Citation

  • Jonas Alm & Filip Lindskog, 2015. "Valuation of Index-Linked Cash Flows in a Heath–Jarrow–Morton Framework," Risks, MDPI, Open Access Journal, vol. 3(3), pages 1-27, September.
  • Handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:338-364:d:55583
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    References listed on IDEAS

    as
    1. Dorothea Diers & Martin Eling & Christian Kraus & Andreas Reuß, 2012. "Market-consistent embedded value in non-life insurance: how to measure it and why," Journal of Risk Finance, Emerald Group Publishing, vol. 13(4), pages 320-346, August.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    3. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    4. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, December.
    5. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    6. repec:dau:papers:123456789/11497 is not listed on IDEAS
    7. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    8. Tanskanen, Antti Juho & Lukkarinen, Jani, 2003. "Fair valuation of path-dependent participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 595-609, December.
    9. Robert Jarrow & Yildiray Yildirim, 2008. "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 16, pages 349-370 World Scientific Publishing Co. Pte. Ltd..
    10. Felice, Massimo De & Moriconi, Franco, 2005. "Market Based Tools for Managing the Life Insurance Company," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 35(01), pages 79-111, May.
    11. Knut Aase & Svein-Arne Persson, 1996. "Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products," Center for Financial Institutions Working Papers 96-20, Wharton School Center for Financial Institutions, University of Pennsylvania.
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    More about this item

    Keywords

    state price deflators; insurance pricing; Heath–Jarrow–Morton;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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