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Efficient Solutions for Pricing and Hedging Interest Rate Asian Options

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  • Allan Jonathan da Silva
  • Jack Baczynski
  • José Valentim Machado Vicente

Abstract

We develop analytical solutions for the characteristic function of the integrated short-term rate process using the Fourier-cosine series. The method allows us to study the pricing of Asian interest rate options for a broad class of affine jump-diffusion models. In particular, we provide closed-form Fourier-cosine series representations for the price and the delta-hedge of Asian interest rate options under the augmented Vasicek model. In a numerical study, we show that Asian interest rate option prices can be accurately and efficiently approximated by truncating their series representations. The proposed procedure is calculated fast and is superior in accuracy when compared to the existing numerical methods used to price Asian interest rate options.

Suggested Citation

  • Allan Jonathan da Silva & Jack Baczynski & José Valentim Machado Vicente, 2020. "Efficient Solutions for Pricing and Hedging Interest Rate Asian Options," Working Papers Series 513, Central Bank of Brazil, Research Department.
    • Handle: RePEc:bcb:wpaper:513
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    References listed on IDEAS

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    1. Caio Almeida & Jos� Vicente, 2012. "Term structure movements implicit in Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 119-134, February.
    2. Caio Ibsen R. Almeida & José Valentim M. Vicente, 2006. "Term Structure Movements Implicit in Option Prices," Working Papers Series 128, Central Bank of Brazil, Research Department.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    5. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    6. Alan De Genaro & Marco Avellaneda, 2018. "Pricing Interest Rate Derivatives Under Monetary Changes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-28, September.
    7. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    9. Claudio Henrique Barbedo & Octávio Bessada Lion & Jose Valentim Machado Vicente, 2010. "Pricing Asian Interest Rate Options with a Three-Factor HJM Model," Brazilian Review of Finance, Brazilian Society of Finance, vol. 8(1), pages 9-23.
    10. Sumei Zhang & Junhao Geng, 2017. "Fourier-cosine method for pricing forward starting options with stochastic volatility and jumps," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 9995-10004, October.
    11. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    12. S. M. Zhang & Y. Feng, 2019. "American option pricing under the double Heston model based on asymptotic expansion," Quantitative Finance, Taylor & Francis Journals, vol. 19(2), pages 211-226, February.
    13. G. Tour & N. Thakoor & A. Q. M. Khaliq & D. Y. Tangman, 2018. "COS method for option pricing under a regime-switching model with time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 673-692, April.
    14. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    15. Ballotta, Laura & Fusai, Gianluca & Marazzina, Daniele, 2019. "Integrated structural approach to Credit Value Adjustment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1143-1157.
    16. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
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