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On option pricing in illiquid markets with random jumps

Author

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  • El-khatib, Youssef
  • Hatemi-J, Abdulnasser

Abstract

One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This asumption can be fulfilled only in perfectly liquid markets. Since most markets are illqiud, this asumption might be too restrictive. Thus, taking into account the price impact in option pricing is an important issue. This issue has been dealt with, to some extent, for illiquid markets by assuming a continuous process, mainly based on the Brownian motion. However, the recent financial crisis and its effects on the global stock markets have propagated the urgent need for more realistic models where the stochastic process describing the price trajectories involves random jumps. Nontheless, works related to markets with jumps are scant compared to the continuous ones. In addition, these prevoius studies do not deal with illiquid markets. The contribution of this paper is to tackle the pricing problem for options in illiquid markets with jumps as well as the hedging strategy within this context, which is the first of its kind to the best knowledge.

Suggested Citation

  • El-khatib, Youssef & Hatemi-J, Abdulnasser, 2013. "On option pricing in illiquid markets with random jumps," MPRA Paper 45172, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:45172
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    File URL: https://mpra.ub.uni-muenchen.de/45172/1/MPRA_paper_45172.pdf
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. 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.
    3. Wu, Shu & Zeng, Yong, 2006. "The term structure of interest rates under regime shifts and jumps," Economics Letters, Elsevier, vol. 93(2), pages 215-221, November.
    4. 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.
    5. Keim, Donald B & Madhaven, Ananth, 1996. "The Upstairs Market for Large-Block Transactions: Analysis and Measurement of Price Effects," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 1-36.
    6. Chan, Louis K C & Lakonishok, Josef, 1995. " The Behavior of Stock Prices around Institutional Trades," Journal of Finance, American Finance Association, vol. 50(4), pages 1147-1174, September.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Options pricing; illiquid markets; jump diffusion; incomplete markets.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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