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The square-root process and Asian options

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  • Angelos Dassios
  • Jayalaxshmi Nagaradjasarma

Abstract

Although the square-root process has long been used as an alternative to the Black-Scholes geometric Brownian motion model for option valuation, the pricing of Asian options on this diffusion model has never been studied analytically. However, the additivity property of the square-root process makes it a very suitable model for the analysis of Asian options. In this paper, we develop explicit prices for digital and regular Asian options. We also obtain distributional results concerning the square-root process and its average over time, including analytic formulae for their joint density and moments. We also show that the distribution is actually determined by those moments.

Suggested Citation

  • Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:4:p:337-347
    DOI: 10.1080/14697680600724775
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    References listed on IDEAS

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    Cited by:

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    2. Angelos Dassios & Luting Li, 2018. "An Economic Bubble Model and Its First Passage Time," Papers 1803.08160, arXiv.org.
    3. Fusai, Gianluca & Marena, Marina & Roncoroni, Andrea, 2008. "Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2033-2045, October.
    4. 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.
    5. Plat, Richard & Pelsser, Antoon, 2009. "Analytical approximations for prices of swap rate dependent embedded options in insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 124-134, February.
    6. Angelos Dassios & Hongbiao Zhao, 2017. "Efficient Simulation of Clustering Jumps with CIR Intensity," Operations Research, INFORMS, vol. 65(6), pages 1494-1515, December.
    7. Dan Pirjol & Lingjiong Zhu, 2024. "Short-maturity asymptotics for option prices with interest rates effects," Papers 2402.14161, arXiv.org.
    8. Park, Jong Jun & Jang, Hyun Jin & Jang, Jiwook, 2020. "Pricing arithmetic Asian options under jump diffusion CIR processes," Finance Research Letters, Elsevier, vol. 34(C).
    9. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    10. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.
    11. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    12. Jang, Jiwook & Qu, Yan & Zhao, Hongbiao & Dassios, Angelos, 2023. "A Cox model for gradually disappearing events," LSE Research Online Documents on Economics 112754, London School of Economics and Political Science, LSE Library.
    13. Wugan Cai & Jiafeng Pan, 2017. "Stochastic Differential Equation Models for the Price of European CO 2 Emissions Allowances," Sustainability, MDPI, vol. 9(2), pages 1-12, February.
    14. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.

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