Pricing and Hedging Guaranteed Returns on Mix Funds

M.H. Vellekoop, A.A. van de Kamp, B.A. Post

    Research output: Contribution to journalArticleAcademicpeer-review

    1 Citation (Scopus)
    64 Downloads (Pure)

    Abstract

    Abstract In this paper we propose a valuation and hedging strategy for a guaranteed minimal rate of return on a mix fund, which participates in both bonds and stocks. For the case where a fixed amount of money is invested, we show that a European put option on the mix fund replicates the cash flows of this guarantee at all times and using the arbitrage-free pricing methodology, the market value of the guarantee can be obtained explicitly. Using historical data, we show that modeling the correlation between equity and bond returns is of fundamental importance when the stochastic nature of the term structure of interest rates is taken into account. For this model we define a hedging strategy which shows how the dependency of the option on the changing yield of the bond fund can be hedged away using mix fund contracts. We also show how Monte Carlo methods can be used to analyze the case where the guarantee is given on periodically invested fixed amounts of money instead of one single payment.
    Original languageUndefined
    Article number10.1016/j.insmatheco.2005.12.003
    Pages (from-to)585-598
    Number of pages14
    JournalInsurance: mathematics & economics
    Volume38
    Issue number06EX1521/3
    DOIs
    Publication statusPublished - 2006

    Keywords

    • EWI-8114
    • JEL-C15
    • IR-66592
    • METIS-237597
    • JEL-G13

    Cite this

    Vellekoop, M. H., van de Kamp, A. A., & Post, B. A. (2006). Pricing and Hedging Guaranteed Returns on Mix Funds. Insurance: mathematics & economics, 38(06EX1521/3), 585-598. [10.1016/j.insmatheco.2005.12.003]. https://doi.org/10.1016/j.insmatheco.2005.12.003
    Vellekoop, M.H. ; van de Kamp, A.A. ; Post, B.A. / Pricing and Hedging Guaranteed Returns on Mix Funds. In: Insurance: mathematics & economics. 2006 ; Vol. 38, No. 06EX1521/3. pp. 585-598.
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    abstract = "Abstract In this paper we propose a valuation and hedging strategy for a guaranteed minimal rate of return on a mix fund, which participates in both bonds and stocks. For the case where a fixed amount of money is invested, we show that a European put option on the mix fund replicates the cash flows of this guarantee at all times and using the arbitrage-free pricing methodology, the market value of the guarantee can be obtained explicitly. Using historical data, we show that modeling the correlation between equity and bond returns is of fundamental importance when the stochastic nature of the term structure of interest rates is taken into account. For this model we define a hedging strategy which shows how the dependency of the option on the changing yield of the bond fund can be hedged away using mix fund contracts. We also show how Monte Carlo methods can be used to analyze the case where the guarantee is given on periodically invested fixed amounts of money instead of one single payment.",
    keywords = "EWI-8114, JEL-C15, IR-66592, METIS-237597, JEL-G13",
    author = "M.H. Vellekoop and {van de Kamp}, A.A. and B.A. Post",
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    volume = "38",
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    Vellekoop, MH, van de Kamp, AA & Post, BA 2006, 'Pricing and Hedging Guaranteed Returns on Mix Funds', Insurance: mathematics & economics, vol. 38, no. 06EX1521/3, 10.1016/j.insmatheco.2005.12.003, pp. 585-598. https://doi.org/10.1016/j.insmatheco.2005.12.003

    Pricing and Hedging Guaranteed Returns on Mix Funds. / Vellekoop, M.H.; van de Kamp, A.A.; Post, B.A.

    In: Insurance: mathematics & economics, Vol. 38, No. 06EX1521/3, 10.1016/j.insmatheco.2005.12.003, 2006, p. 585-598.

    Research output: Contribution to journalArticleAcademicpeer-review

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    T1 - Pricing and Hedging Guaranteed Returns on Mix Funds

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    AB - Abstract In this paper we propose a valuation and hedging strategy for a guaranteed minimal rate of return on a mix fund, which participates in both bonds and stocks. For the case where a fixed amount of money is invested, we show that a European put option on the mix fund replicates the cash flows of this guarantee at all times and using the arbitrage-free pricing methodology, the market value of the guarantee can be obtained explicitly. Using historical data, we show that modeling the correlation between equity and bond returns is of fundamental importance when the stochastic nature of the term structure of interest rates is taken into account. For this model we define a hedging strategy which shows how the dependency of the option on the changing yield of the bond fund can be hedged away using mix fund contracts. We also show how Monte Carlo methods can be used to analyze the case where the guarantee is given on periodically invested fixed amounts of money instead of one single payment.

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    KW - METIS-237597

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    Vellekoop MH, van de Kamp AA, Post BA. Pricing and Hedging Guaranteed Returns on Mix Funds. Insurance: mathematics & economics. 2006;38(06EX1521/3):585-598. 10.1016/j.insmatheco.2005.12.003. https://doi.org/10.1016/j.insmatheco.2005.12.003