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Option pricing in constant elasticity of variance model with liquidity costs

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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