IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v20y2020i4p531-542.html
   My bibliography  Save this article

Conic quantization: stochastic volatility and market implied liquidity

Author

Listed:
  • Lucio Fiorin
  • Wim Schoutens

Abstract

Market implied liquidity links the pricing of European options under stochastic volatility with the Conic Finance theory of two prices

Suggested Citation

  • Lucio Fiorin & Wim Schoutens, 2020. "Conic quantization: stochastic volatility and market implied liquidity," Quantitative Finance, Taylor & Francis Journals, vol. 20(4), pages 531-542, April.
  • Handle: RePEc:taf:quantf:v:20:y:2020:i:4:p:531-542
    DOI: 10.1080/14697688.2019.1687928
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2019.1687928
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/14697688.2019.1687928?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    3. Giorgia Callegaro & Lucio Fiorin & Martino Grasselli, 2019. "Quantization meets Fourier: a new technology for pricing options," Annals of Operations Research, Springer, vol. 282(1), pages 59-86, November.
    4. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    5. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    6. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    7. Gilles Pagès & Abass Sagna, 2015. "Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(5), pages 463-498, November.
    8. Albrecher, Hansjoerg & Guillaume, Florence & Schoutens, Wim, 2013. "Implied liquidity: Model sensitivity," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 48-67.
    9. T. A. McWalter & R. Rudd & J. Kienitz & E. Platen, 2018. "Recursive marginal quantization of higher-order schemes," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 693-706, April.
    10. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697.
    11. 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.
    12. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    13. Küchler, Uwe & Tappe, Stefan, 2008. "Bilateral gamma distributions and processes in financial mathematics," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 261-283, February.
    14. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    15. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    16. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    17. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    18. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    19. Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(4), pages 519-529, December.
    20. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    21. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    22. Martino Grasselli, 2017. "The 4/2 Stochastic Volatility Model: A Unified Approach For The Heston And The 3/2 Model," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1013-1034, October.
    Full references (including those not matched with items on IDEAS)

    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. Giorgia Callegaro & Lucio Fiorin & Martino Grasselli, 2019. "Quantization meets Fourier: a new technology for pricing options," Annals of Operations Research, Springer, vol. 282(1), pages 59-86, November.
    2. Kim, Hyun-Gyoon & Kim, Jeong-Hoon, 2023. "A stochastic-local volatility model with Le´vy jumps for pricing derivatives," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    4. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    5. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    6. Li, Zhe & Zhang, Weiguo & Zhang, Yue & Yi, Zhigao, 2019. "An analytical approximation approach for pricing European options in a two-price economy," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    7. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.
    8. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12, July-Dece.
    9. Wenli Zhu & Xinfeng Ruan, 2019. "Pricing Swaps on Discrete Realized Higher Moments Under the Lévy Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 507-532, February.
    10. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.
    11. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    12. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany.
    15. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    16. Sha Lin & Xin-Jiang He, 2022. "Analytically Pricing European Options under a New Two-Factor Heston Model with Regime Switching," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1069-1085, March.
    17. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    18. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Sun, Xianming & Gan, Siqing & Vanmaele, Michèle, 2015. "Analytical approximation for distorted expectations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 246-252.
    20. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.

    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:taf:quantf:v:20:y:2020:i:4:p:531-542. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.