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Nonlinear option pricing models for illiquid markets: scaling properties and explicit solutions

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  • Ljudmila A. Bordag
  • Ruediger Frey

Abstract

Several models for the pricing of derivative securities in illiquid markets are discussed. A typical type of nonlinear partial differential equations arising from these investigation is studied. The scaling properties of these equations are discussed. Explicit solutions for one of the models are obtained and studied.

Suggested Citation

  • Ljudmila A. Bordag & Ruediger Frey, 2007. "Nonlinear option pricing models for illiquid markets: scaling properties and explicit solutions," Papers 0708.1568, arXiv.org.
    • Handle: RePEc:arx:papers:0708.1568
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    1. 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..
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    5. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    6. 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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