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Spread Option Pricing Under Finite Liquidity Framework

Author

Listed:
  • Traian A. Pirvu

    (Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada)

  • Shuming Zhang

    (Independent Researcher, Toronto, ON M5V 0P5, Canada)

Abstract

This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging of a large investor. Our main contribution is a novel methodology to price spread options in this paradigm. Kirk approximation in conjunction with Monte Carlo simulations yields the spread option prices. Moreover, the antithetic and control variates variance reduction techniques improve the performance of our method. Numerical experiments reveal that the finite liquidity causes a liquidity value adjustment in option prices ranging from 0.53% to 2.81%. The effect of correlation on prices is also explored, and as expected the option price increases due to the diversification effect, but the liquidity impact decreases slightly.

Suggested Citation

  • Traian A. Pirvu & Shuming Zhang, 2024. "Spread Option Pricing Under Finite Liquidity Framework," Risks, MDPI, vol. 12(11), pages 1-14, October.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:11:p:173-:d:1511164
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    References listed on IDEAS

    as
    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    2. 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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