IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1409.6042.html
   My bibliography  Save this paper

Option pricing in constant elasticity of variance model with liquidity costs

Author

Listed:
  • Krzysztof Turek

Abstract

Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The Goal of this article is to find optimal hedging strategy of European call/put option in illiquid environment. We understand illiquidity as a non linear transaction cost function depending only on rate of change of our portfolio. In case this function is quadratic, optimal policy is given by system of 3 PDE. In addition we show, that for small $\epsilon$ costs of selling portfolio in time $T$ be important ($O(\epsilon)$) and shouldn't be neglected in Value function ($o(\epsilon^k)$- our result).

Suggested Citation

  • Krzysztof Turek, 2014. "Option pricing in constant elasticity of variance model with liquidity costs," Papers 1409.6042, arXiv.org.
    • Handle: RePEc:arx:papers:1409.6042
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1409.6042
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Menachem Brenner & Rafi Eldor & Shmuel Hauser, 2001. "The Price of Options Illiquidity," Journal of Finance, American Finance Association, vol. 56(2), pages 789-805, April.
    2. Hsu, Y.L. & Lin, T.I. & Lee, C.F., 2008. "Constant elasticity of variance (CEV) option pricing model: Integration and detailed derivation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 60-71.
    3. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221, World Scientific Publishing Co. Pte. Ltd..
    4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    5. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
    6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    7. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    8. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    9. Liu, Hong & Yong, Jiongmin, 2005. "Option pricing with an illiquid underlying asset market," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2125-2156, December.
    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. 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).
    2. Shih-Ping Feng, 2011. "The Liquidity Effect In Option Pricing: An Empirical Analysis," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 5(2), pages 35-43.
    3. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    4. Mohanty, Roshni & P, Srinivasan, 2014. "The Time-Varying Risk and Return Trade Off in Indian Stock Markets," MPRA Paper 55660, University Library of Munich, Germany.
    5. Deuskar, Prachi & Gupta, Anurag & Subrahmanyam, Marti G., 2011. "Liquidity effect in OTC options markets: Premium or discount?," Journal of Financial Markets, Elsevier, vol. 14(1), pages 127-160, February.
    6. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "Analytical valuation for geometric Asian options in illiquid markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 175-191.
    7. Jin, Xiaoye, 2017. "Time-varying return-volatility relation in international stock markets," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 157-173.
    8. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    9. Kim, Donghyun & Shin, Yong Hyun & Yoon, Ji-Hun, 2024. "The valuation of real options for risky barrier to entry with hybrid stochastic and local volatility and stochastic investment costs," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    10. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2016. "The importance of stock liquidity on option pricing," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 457-467.
    11. Kim, Jeong-Hoon & Yoon, Ji-Hun & Lee, Jungwoo & Choi, Sun-Yong, 2015. "On the stochastic elasticity of variance diffusions," Economic Modelling, Elsevier, vol. 51(C), pages 263-268.
    12. Jeong‐Hoon Kim & Jungwoo Lee & Song‐Ping Zhu & Seok‐Hyon Yu, 2014. "A multiscale correction to the Black–Scholes formula," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(6), pages 753-765, November.
    13. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    14. León, Angel & Nave, Juan & Rubio Irigoyen, Gonzalo, 2005. "The Relationship between Risk and Expected Return in Europe," DFAEII Working Papers 1988-088X, University of the Basque Country - Department of Foundations of Economic Analysis II.
    15. Dufour, Jean-Marie & García, René, 2008. "Measuring causality between volatility and returns with high-frequency data," UC3M Working papers. Economics we084422, Universidad Carlos III de Madrid. Departamento de Economía.
    16. Bandi, Federico M. & Bretscher, Lorenzo & Tamoni, Andrea, 2023. "Return predictability with endogenous growth," Journal of Financial Economics, Elsevier, vol. 150(3).
    17. Kei Nakagawa & Yusuke Uchiyama, 2020. "GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    18. Takaishi, Tetsuya, 2017. "Rational GARCH model: An empirical test for stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 451-460.
    19. Olaf Korn & Paolo Krischak & Erik Theissen, 2019. "Illiquidity transmission from spot to futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1228-1249, October.
    20. Vincenzo Candila, 2013. "A Comparison of the Forecasting Performances of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.

    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:1409.6042. 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.