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Less Expensive Pricing and Hedging of Long-Dated Equity Index Options When Interest Rates are Stochastic

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Abstract

Many providers of variable annuities such as pension funds and life insurers seek to hedge their exposure to embedded guarantees using longdated derivatives. This paper extends the benchmark approach to price and hedge long-dated equity index options using a combination of cash, bonds and equities under a variety of market models. The results show that when the discounted index is modelled as a squared Bessel process, as in Platen's minimal market model, less expensive hedging is achieved irrespective of the short rate model.

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  • Kevin Fergusson & Eckhard Platen, 2015. "Less Expensive Pricing and Hedging of Long-Dated Equity Index Options When Interest Rates are Stochastic," Research Paper Series 357, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:357
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp357.pdf
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Kevin Fergusson & Eckhard Platen, 2014. "Hedging long-dated interest rate derivatives for Australian pension funds and life insurers," Published Paper Series 2014-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    Cited by:

    1. Benjamin Tin Chun Cheng, 2017. "Pricing and Hedging of Long-Dated Commodity Derivatives," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2017.
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    3. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.

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