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Pricing of Asian exchange rate options under stochastic interest rates as a sum of options

Author

Listed:
  • Klaus Sandmann

    (Department of Banking, University of Mainz, Jakob-Welder-Weg 9, D-55128 Mainz, Germany Manuscript)

  • J. Aase Nielsen

    (Department of Operations Research, University of Aarhus, Bldg. 530, Ny Munkegade, DK-8000 Aarhus C, Denmark)

Abstract

The aim of the paper is to develop pricing formulas for long term European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. The emphasis is devoted to the discretely sampled Asian option. It is shown how the value of this option can be approximated as the sum of Black-Scholes options. The formula is obtained under the extension of results developed by Rogers and Shi (1995) and Jamshidian (1991). In addition bounds for the pricing error are determined. Comparing with Monte Carlo simulation the pricing is found to be very precise.

Suggested Citation

  • Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
    • Handle: RePEc:spr:finsto:v:6:y:2002:i:3:p:355-370
    Note: received: November 2000; final version received: October 2001
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    Citations

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    Cited by:

    1. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    2. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian Options," Working Papers 28, Barcelona School of Economics.
    3. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-24.
    4. Keng‐Hsin Lo & Kehluh Wang & Ming‐Feng Hsu, 2008. "Pricing European Asian options with skewness and kurtosis in the underlying distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(6), pages 598-616, June.
    5. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 449-473, June.
    6. Yanhong Zhong & Guohe Deng, 2019. "Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate," Complexity, Hindawi, vol. 2019, pages 1-13, January.
    7. Eberlein, Ernst & Papapantoleon, Antonis, 2005. "Equivalence of floating and fixed strike Asian and lookback options," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 31-40, January.
    8. Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 301-314.
    9. Tasadduq Imam & Kevin Tickle & Abdullahi Ahmed & William Guo, 2012. "Linear Relationship Between The Aud/Usd Exchange Rate And The Respective Stock Market Indices: A Computational Finance Perspective," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 19(1), pages 19-42, January.
    10. João Pedro Vidal Nunes & Pedro Miguel Silva Prazeres, 2014. "Pricing Swaptions Under Multifactor Gaussian Hjm Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 762-789, October.
    11. Schrager, David F. & Pelsser, Antoon A.J., 2004. "Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 369-398, October.
    12. Vellekoop, M.H. & Vd Kamp, A.A. & Post, B.A., 2006. "Pricing and hedging guaranteed returns on mix funds," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 585-598, June.
    13. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    14. João Pedro Vidal Nunes & Luís Alberto Ferreira De Oliveira, 2007. "Multifactor and analytical valuation of treasury bond futures with an embedded quality option," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(3), pages 275-303, March.

    More about this item

    Keywords

    Asian exchange rate option; forward risk adjusted measure; stochastic interest rates.;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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