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Pricing Asian options in a semimartingale model

Author

Listed:
  • Jan Vecer
  • Mingxin Xu

Abstract

In this paper we studyy arithmetic Asian options when the underlying stock is driven by special semimartingale processes. We show that the inherently path dependent problem of pricing Asian options can be transformed into a problem without path dependence in the payoff function. We also show that the price is driven by a process with independent increments, Levy processes being a special case. This approach applies for both discretely or continuously options.

Suggested Citation

  • Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
  • Handle: RePEc:taf:quantf:v:4:y:2004:i:2:p:170-175
    DOI: 10.1080/14697680400000021
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    References listed on IDEAS

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    1. Jiri Hoogland & Dimitri Neumann, 2001. "Asians and cash dividends: Exploiting symmetries in pricing theory," Finance 0105002, University Library of Munich, Germany.
    2. Jiri Hoogland & Dimitri Neumann, 2000. "Asians and cash dividends: Exploiting symmetries in pricing theory," Papers cond-mat/0006133, arXiv.org.
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    1. repec:kap:annfin:v:14:y:2018:i:2:d:10.1007_s10436-017-0315-y is not listed on IDEAS
    2. repec:kap:annfin:v:13:y:2017:i:4:d:10.1007_s10436-017-0302-3 is not listed on IDEAS
    3. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
    4. Michael Schröder, 2005. "Laguerre Series In Contingent Claim Valuation, With Applications To Asian Options," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 491-531.
    5. Giacomo Bormetti & Giorgia Callegaro & Giulia Livieri & Andrea Pallavicini, 2015. "A backward Monte Carlo approach to exotic option pricing," Papers 1511.00848, arXiv.org.
    6. Kyungsub Lee, 2013. "Recursive formula for arithmetic Asian option prices," Papers 1311.4969, arXiv.org.
    7. Bara Kim & In-Suk Wee, 2014. "Pricing of geometric Asian options under Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1795-1809, October.
    8. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    9. D. Hackmann & A. Kuznetsov, 2014. "Asian options and meromorphic Lévy processes," Finance and Stochastics, Springer, vol. 18(4), pages 825-844, October.
    10. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    11. Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.
    12. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    13. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    14. 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.
    15. Alexander Novikov & Nino Kordzakhia, 2013. "On lower and upper bounds for Asian-type options: a unified approach," Papers 1309.2383, arXiv.org.
    16. repec:kap:revdev:v:20:y:2017:i:3:d:10.1007_s11147-017-9128-4 is not listed on IDEAS
    17. 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.
    18. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    19. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.
    20. Dassios, Angelos & Nagaradjasarma, Jayalaxshmi, 2006. "The square-root process and Asian options," LSE Research Online Documents on Economics 2851, London School of Economics and Political Science, LSE Library.
    21. repec:eee:apmaco:v:252:y:2015:i:c:p:418-437 is not listed on IDEAS
    22. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.

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