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Equivalence of floating and fixed strike Asian and lookback options

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  • Eberlein, Ernst
  • Papapantoleon, Antonis

Abstract

We prove a symmetry relationship between floating strike and fixed strike Asian options for assets driven by general Lévy processes using a change of numéraire and the characteristic triplet of the dual process. We apply the same technique to prove a similar relationship between floating strike and fixed strike lookback options.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:1:p:31-40
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    References listed on IDEAS

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    1. Vicky Henderson & Rafal Wojakowski, 2001. "On the Equivalence of Floating and Fixed-Strike Asian Options," OFRC Working Papers Series 2001mf08, Oxford Financial Research Centre.
    2. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    3. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    4. Jiri Hoogland & Dimitri Neumann, 2001. "Asians and cash dividends: Exploiting symmetries in pricing theory," Finance 0105002, University Library of Munich, Germany.
    5. Jiri Hoogland & Dimitri Neumann, 2000. "Asians and cash dividends: Exploiting symmetries in pricing theory," Papers cond-mat/0006133, arXiv.org.
    6. 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.
    7. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
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    Citations

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    Cited by:

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    2. Renault, Eric & Werker, Bas J.M., 2011. "Causality effects in return volatility measures with random times," Journal of Econometrics, Elsevier, vol. 160(1), pages 272-279, January.
    3. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    4. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing Asian options with regime switching," Papers 1407.5091, arXiv.org.
    5. Ning Cai & Yingda Song & Steven Kou, 2015. "A General Framework for Pricing Asian Options Under Markov Processes," Operations Research, INFORMS, vol. 63(3), pages 540-554, June.
    6. Yingda Song & Ning Cai & Steven Kou, 2018. "Computable Error Bounds of Laplace Inversion for Pricing Asian Options," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 634-645, January.
    7. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2009. "Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models," Papers 0911.0373, arXiv.org, revised Oct 2010.
    8. San‐Lin Chung & Yi‐Ta Huang & Pai‐Ta Shih & Jr‐Yan Wang, 2019. "Semistatic hedging and pricing American floating strike lookback options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 418-434, April.
    9. Sun-Yong Choi & Ji-Hun Yoon & Junkee Jeon, 2019. "Pricing of Fixed-Strike Lookback Options on Assets with Default Risk," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    10. Jan Vecer, 2013. "Asian options on the harmonic average," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1315-1322, September.
    11. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    12. Nomikos, Nikos K. & Kyriakou, Ioannis & Papapostolou, Nikos C. & Pouliasis, Panos K., 2013. "Freight options: Price modelling and empirical analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 82-94.
    13. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    14. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.

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