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Pricing of Asian options on interest rates in the CIR model

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  • Dassios, Angelos
  • Nagaradjasarma, Jayalaxshmi

Abstract

In this paper, we study the integral over time of the instantaneous rate, i.e. the interest rate accrual, in the Cox Ingersoll Ross model. We derive distributional results for this process, including series representations for the density and probability distribution function. Applications to the valuation of derivatives, including Asian options prices in closed form, are presented here. Numerical examples are included to demonstrate the speed of convergence of the series. We also find that the series provide a more robust tool than numerical Laplace transform inversion for regions of high maturity and volatility. Given the versatility of the square-root process, the results derived in this paper are also of value for various others areas of finance, among which stochastic volatility and credit derivatives.

Suggested Citation

  • Dassios, Angelos & Nagaradjasarma, Jayalaxshmi, 2011. "Pricing of Asian options on interest rates in the CIR model," LSE Research Online Documents on Economics 32084, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:32084
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    File URL: http://eprints.lse.ac.uk/32084/
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    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    3. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    4. 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..
    5. Olivier Scaillet & Boris Leblanc, 1998. "Path dependent options on yields in the affine term structure model," Finance and Stochastics, Springer, vol. 2(4), pages 349-367.
    6. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    7. 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.
    8. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109, January.
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    Cited by:

    1. Adrian Prayoga & Nicolas Privault, 2017. "Pricing CIR Yield Options by Conditional Moment Matching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(1), pages 19-38, March.

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    More about this item

    Keywords

    derivatives; valuation; square-root process; average-rate claims;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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