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Hedging Futures Options with Stochastic Interest Rates

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Abstract

This paper presents a simulation study of hedging long-dated futures options, in the Rabinovitch (1989) model which assumes correlated dynamics between spot asset prices and interest rates. Under this model and when the maturity of the hedging instruments match the maturity of the option, forward contracts and futures contracts can hedge both the market risk and the interest rate risk of the options positions. When the hedge is rolled forward with shorter maturity hedging instruments, then bond contracts are additionally required to hedge the interest rate risk. This requirement becomes more pronounced for longer maturity contracts and amplifies as the interest rate volatility increases. Factor hedging ratios are also considered, which are suited for multi-dimensional models, and their numerical efficiency is validated.

Suggested Citation

  • Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Hedging Futures Options with Stochastic Interest Rates," Research Paper Series 375, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:375
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    1. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Empirical Hedging Performance on Long-Dated Crude Oil Derivatives," Research Paper Series 376, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Empirical Pricing Performance in Long-Dated Crude Oil Derivatives: Do Models with Stochastic Interest Rates Matter?," Research Paper Series 367, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Louis O. Scott, 1997. "Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 413-426, October.
    4. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    6. Yong-Jin Kim & Naoto Kunitomo, 1999. "Pricing Options under Stochastic Interest Rates: A New Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 49-70, January.
    7. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    8. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    9. 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.
    10. Rabinovitch, Ramon, 1989. "Pricing Stock and Bond Options when the Default-Free Rate is Stochastic," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(4), pages 447-457, December.
    11. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    12. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    13. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing and hedging of long-term futures and forward contracts by a three-factor model," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1811-1826, December.
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    Cited by:

    1. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Empirical Hedging Performance on Long-Dated Crude Oil Derivatives," Research Paper Series 376, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. 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.
    3. repec:uts:finphd:37 is not listed on IDEAS
    4. P. Karlsson & K. F. Pilz & E. Schlögl, 2017. "Calibrating a market model with stochastic volatility to commodity and interest rate risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 907-925, June.

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    More about this item

    Keywords

    Futures options; Stochastic interest rates; Delta hedging; Interest rate hedging;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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