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Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence

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  • U. �etin
  • R. Jarrow
  • P. Protter
  • M. Warachka

Abstract

This article studies the pricing of options in an extended Black Scholes economy in which the underlying asset is not perfectly liquid. The resulting liquidity risk is modeled as a stochastic supply curve, with the transaction price being a function of the trade size. Consistent with the market microstructure literature, the supply curve is upward sloping with purchases executed at higher prices and sales at lower prices. Optimal discrete time hedging strategies are then derived. Empirical evidence reveals a significant liquidity cost intrinsic to every option. Copyright 2006, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 19 (2006)
Issue (Month): 2 ()
Pages: 493-529

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Handle: RePEc:oup:rfinst:v:19:y:2006:i:2:p:493-529

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References

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  1. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
  2. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-93, March.
  3. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
  4. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
  5. Zhiwu Chen & Werner Stanzl & Masahiro Watanabe, 2002. "Price Impact Costs and the Limit of Arbitrage," Yale School of Management Working Papers ysm251, Yale School of Management, revised 08 Jun 2006.
  6. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
  7. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-46, June.
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Citations

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Cited by:
  1. 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.
  2. Rohini Grover & Susan Thomas, 2012. "Liquidity Considerations in Estimating Implied Volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(8), pages 714-741, 08.
  3. Elettra Agliardi & Rainer Andergassen, 2011. "(S,s)-adjustment Strategies and Hedging under Markovian Dynamics," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 36(2), pages 112-131, December.
  4. Wu, Wei-Shao & Liu, Yu-Jane & Lee, Yi-Tsung & Fok, Robert C.W., 2014. "Hedging costs, liquidity, and inventory management: The evidence from option market makers," Journal of Financial Markets, Elsevier, vol. 18(C), pages 25-48.
  5. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2013. "Illiquidity Premia in the Equity Options Market," CREATES Research Papers 2013-48, School of Economics and Management, University of Aarhus.
  6. Olivier Gu\'eant & Jiang Pu, 2013. "Option pricing and hedging with execution costs and market impact," Papers 1311.4342, arXiv.org, revised Aug 2014.
  7. Damiano Brigo & Mirela Predescu & Agostino Capponi, 2010. "Credit Default Swaps Liquidity modeling: A survey," Papers 1003.0889, arXiv.org, revised Mar 2010.
  8. H. Mete Soner & Umut Cetin & Nizar Touzi, 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. Gill, Ryan & Lee, Kiseop & Song, Seongjoo, 2007. "Computation of estimates in segmented regression and a liquidity effect model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6459-6475, August.
  10. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
  11. Adrien Nguyen Huu, 2012. "A note on super-hedging for investor-producers," Working Papers hal-00653982, HAL.
  12. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. I: single-period case," Papers 1110.3224, arXiv.org, revised Dec 2013.
  13. 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.
  14. Adrien Nguyen Huu, 2011. "A note on super-hedging for investor-producers," Papers 1112.4740, arXiv.org, revised Mar 2012.
  15. Marcel Blais & Philip Protter, 2012. "Signing trades and an evaluation of the Lee–Ready algorithm," Annals of Finance, Springer, vol. 8(1), pages 1-13, February.
  16. 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.
  17. Dylan Possamai & Nizar Touzi & H. Mete Soner, 2012. "Large liquidity expansion of super-hedging costs," Papers 1208.3785, arXiv.org.
  18. Ku, Hyejin & Lee, Kiseop & Zhu, Huaiping, 2012. "Discrete time hedging with liquidity risk," Finance Research Letters, Elsevier, vol. 9(3), pages 135-143.
  19. Frank Milne, 2008. "Credit Crises, Risk Management Systems and Liquidity Modelling," Working Papers 1, John Deutsch Institute for the Study of Economic Policy.
  20. Isaenko, Sergei, 2010. "Portfolio choice under transitory price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2375-2389, November.
  21. Cao, Melanie & Wei, Jason, 2010. "Option market liquidity: Commonality and other characteristics," Journal of Financial Markets, Elsevier, vol. 13(1), pages 20-48, February.

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