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An analytical approximation approach for pricing European options in a two-price economy

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Listed:
  • Li, Zhe
  • Zhang, Weiguo
  • Zhang, Yue
  • Yi, Zhigao

Abstract

Classical option pricing theories are usually built on the law of one price, while ignoring the impact of market liquidity on bid-ask spreads. The theory of conic finance replaces the law of one price by the law of two prices, allowing for market participants sell to the market at the bid price and buy from the market at the higher ask price. In this paper, we present a numerical method to calculate the bid and ask prices for the European options. The numerical method is based on the combination of Fourier cosine approximations and numerical integration, which provides an efficient and fast way to compute the bid and ask prices and calibrate the model parameters in real market. Numerical experiments demonstrate the accuracy of our presented numerical method by comparing with Monte Carlo simulation. To better illustrate the practicability of our presented numerical method, we consider the European options written on SSE 50 ETF traded at the Shanghai Stock Exchange.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:ecofin:v:50:y:2019:i:c:s1062940818306065
    DOI: 10.1016/j.najef.2019.100986
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    References listed on IDEAS

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    1. Guillaume, F., 2015. "The LIX: A model-independent liquidity index," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 214-231.
    2. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    3. 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.
    4. Umut Çetin & H. Soner & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," Finance and Stochastics, Springer, vol. 14(3), pages 317-341, September.
    5. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    6. 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..
    7. Energy Sonono, Masimba & Phillip Mashele, Hopolang, 2016. "Estimation of bid-ask prices for options on LIBOR based instruments," Finance Research Letters, Elsevier, vol. 19(C), pages 33-41.
    8. Soner, H. Mete & Cetin, Umut & Touzi, Nizar, 2010. "Option hedging for small investors under liquidity costs," LSE Research Online Documents on Economics 28992, London School of Economics and Political Science, LSE Library.
    9. Lars Nordén & Caihong Xu, 2012. "Option happiness and liquidity: Is the dynamics of the volatility smirk affected by relative option liquidity?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(1), pages 47-74, January.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Robin K. Chou & San‐Lin Chung & Yu‐Jen Hsiao & Yaw‐Huei Wang, 2011. "The impact of liquidity on option prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(12), pages 1116-1141, December.
    12. 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.
    13. 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.
    14. Albrecher, Hansjoerg & Guillaume, Florence & Schoutens, Wim, 2013. "Implied liquidity: Model sensitivity," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 48-67.
    15. Michael Ludkovski & Qunying Shen, 2013. "European Option Pricing With Liquidity Shocks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-30.
    16. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    17. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697, October.
    18. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    19. 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.
    20. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    21. 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.
    22. 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.
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    Cited by:

    1. Jing, Bo & Li, Shenghong & Ma, Yong, 2021. "Consistent pricing of VIX options with the Hawkes jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).

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    More about this item

    Keywords

    Conic finance; Option pricing; COS method; Bid-ask spreads; Implied liquidity;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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