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Pricing spread option with liquidity adjustments

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  • Kevin Shuai Zhang
  • Traian Pirvu

Abstract

We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks prices. We consider a partial-impact and a full-impact model in which the price impact is caused by every trading strategy in the market. The generalized Black-Scholes pricing partial differential equations (PDEs) are obtained and analysed. We perform a numerical analysis to exhibit the illiquidity effect on the replication strategy of the European spread option. Compared to the Black-Scholes model or a partial impact model, the trader in the full impact model buys more stock to replicate the option, and this leads to a higher option price.

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  • Kevin Shuai Zhang & Traian Pirvu, 2021. "Pricing spread option with liquidity adjustments," Papers 2101.00223, arXiv.org.
    • Handle: RePEc:arx:papers:2101.00223
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    References listed on IDEAS

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    3. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    4. Ahmad Reza Yazdanian & T A Pirvu, 2014. "Numerical analysis for Spread option pricing model in illiquid underlying asset market: full feedback model," Papers 1406.1149, arXiv.org.
    5. Robert L. Johnson & Carl R. Zulauf & Scott H. Irwin & Mary E. Gerlow, 1991. "The soybean complex spread: An examination of market efficiency from the viewpoint of a production process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 11(1), pages 25-37, February.
    6. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    7. Kevin S. Zhang & Traian A. Pirvu, 2020. "Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model," Papers 2006.07771, arXiv.org.
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