IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2403.17187.html
   My bibliography  Save this paper

Alternatives to classical option pricing

Author

Listed:
  • W. Brent Lindquist
  • Svetlozar T. Rachev

Abstract

We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The second approach does use a riskless asset. However, by ensuring equality between real-world and risk-neutral price-change probabilities, the second approach enables the computation of risk-neutral option prices utilizing expectations under the natural world probability P. This produces the same option prices as the classical approach in which prices are computed under the risk neutral measure Q. The second approach and the two specific examples of the first approach require the introduction of new, marketable asset types, specifically perpetual derivatives of a stock, and a stock whose cumulative return (rather than price) is deflated.

Suggested Citation

  • W. Brent Lindquist & Svetlozar T. Rachev, 2024. "Alternatives to classical option pricing," Papers 2403.17187, arXiv.org.
    • Handle: RePEc:arx:papers:2403.17187
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2403.17187
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aoki, Kosuke & Nakajima, Tomoyuki & Nikolov, Kalin, 2014. "Safe asset shortages and asset price bubbles," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 164-174.
    2. Svetlozar T. Rachev & Stoyan V. Stoyanov & Frank J. Fabozzi, 2017. "Financial Markets With No Riskless (Safe) Asset," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-24, December.
    3. Hiroshi Konno & Hiroshi Shirakawa, 1995. "Existence Of A Nonnegative Equilibrium Price Vector In The Mean‐Variance Capital Market," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 233-246, July.
    4. Yuan Hu & Abootaleb Shirvani & Stoyan Stoyanov & Young Shin Kim & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing in Markets with Informed Traders," Papers 2006.02596, arXiv.org, revised Aug 2020.
    5. Lars Tyge Nielsen, 1990. "Equilibrium in CAPM Without a Riskless Asset," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 315-324.
    6. Ricardo J. Caballero & Emmanuel Farhi, 2013. "A Model of the Safe Asset Mechanism (SAM): Safety Traps and Economic Policy," Working Paper 70936, Harvard University OpenScholar.
    7. Yuan Hu & Abootaleb Shirvani & Stoyan Stoyanov & Young Shin Kim & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing In Markets With Informed Traders," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-32, September.
    8. Kim, Y.S. & Stoyanov, S. & Rachev, S. & Fabozzi, F., 2016. "Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion," Economics Letters, Elsevier, vol. 145(C), pages 225-229.
    9. Ning Sun & Zaifu Yang, 2003. "Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 51-71, May.
    10. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    11. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. W. Brent Lindquist & Svetlozar T. Rachev & Jagdish Gnawali & Frank J. Fabozzi, 2024. "Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model," Papers 2405.12479, arXiv.org, revised Jun 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Svetlozar T. Rachev & Stoyan V. Stoyanov & Frank J. Fabozzi, 2017. "Financial Markets With No Riskless (Safe) Asset," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-24, December.
    2. Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2023. "Unifying Market Microstructure and Dynamic Asset Pricing," Papers 2304.02356, arXiv.org, revised Feb 2024.
    3. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    4. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    5. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    6. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," Papers 2011.08343, arXiv.org.
    7. Ning Sun & Zaifu Yang, 2003. "Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 51-71, May.
    8. Svetlozar Rachev & Nancy Asare Nyarko & Blessing Omotade & Peter Yegon, 2023. "Bachelier's Market Model for ESG Asset Pricing," Papers 2306.04158, arXiv.org.
    9. Pınar, Mustafa Ç., 2014. "Equilibrium in an ambiguity-averse mean–variance investors market," European Journal of Operational Research, Elsevier, vol. 237(3), pages 957-965.
    10. W. Brent Lindquist & Svetlozar T. Rachev & Jagdish Gnawali & Frank J. Fabozzi, 2024. "Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model," Papers 2405.12479, arXiv.org, revised Jun 2024.
    11. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, vol. 4(2), pages 183-195, March.
    12. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    13. repec:dau:papers:123456789/5374 is not listed on IDEAS
    14. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 9, July-Dece.
    15. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2010, January-A.
    16. Xue-Zhong He & Lei Shi, 2009. "Portfolio Analysis and Zero-Beta CAPM with Heterogeneous Beliefs," Research Paper Series 244, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Phelim P. Boyle & Chenghu Ma, 2013. "Mean-Preserving-Spread Risk Aversion and The CAPM," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    18. Davide Lauria & W. Brent Lindquist & Stefan Mittnik & Svetlozar T. Rachev, 2022. "ESG-Valued Portfolio Optimization and Dynamic Asset Pricing," Papers 2206.02854, arXiv.org.
    19. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    20. Abootaleb Shirvani & Frank J. Fabozzi & Stoyan V. Stoyanov, 2020. "Option Pricing in an Investment Risk-Return Setting," Papers 2001.00737, arXiv.org.
    21. Jiexin Dai & Abootaleb Shirvani & Frank J. Fabozzi, 2020. "Rational Finance Approach to Behavioral Option Pricing," Papers 2005.05310, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2403.17187. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.