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Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model

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  • Kevin S. Zhang
  • Traian A. Pirvu

Abstract

In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading in our market model has a direct impact on the asset's price. The price impact is incorporated into the dynamics of the first asset through a specific trading strategy, as in large trader liquidity model. Two-dimensional Milstein scheme is implemented to simulate the pair of assets prices. The option value is numerically estimated by Monte Carlo with the Margrabe option as controlled variate. Time complexity of these numerical schemes are included. Finally, we provide a deep learning framework to implement this model effectively in a production environment.

Suggested Citation

  • Kevin S. Zhang & Traian A. Pirvu, 2020. "Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model," Papers 2006.07771, arXiv.org.
    • Handle: RePEc:arx:papers:2006.07771
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    References listed on IDEAS

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    1. Desmond J. Higham, 2015. "An Introduction to Multilevel Monte Carlo for Option Valuation," Papers 1505.00965, arXiv.org.
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    3. Elisa Al`os & Michael Coulon, 2018. "On the optimal choice of strike conventions in exchange option pricing," Papers 1807.05396, arXiv.org.
    4. Hainaut, Donatien, 2018. "Calendar spread exchange options pricing with Gaussian random fields," LIDAM Reprints ISBA 2018036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. 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.
    6. 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.
    7. Donatien Hainaut, 2018. "Calendar Spread Exchange Options Pricing with Gaussian Random Fields," Risks, MDPI, vol. 6(3), pages 1-33, August.
    8. Ahmadian, D. & Farkhondeh Rouz, O. & Ivaz, K. & Safdari-Vaighani, A., 2020. "Robust numerical algorithm to the European option with illiquid markets," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    9. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    10. Kristoffer Glover & Peter W Duck & David P Newton, 2010. "On nonlinear models of markets with finite liquidity: Some cautionary notes," Published Paper Series 2010-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Traian A. Pirvu & Shuming Zhang, 2024. "Spread Option Pricing Under Finite Liquidity Framework," Risks, MDPI, vol. 12(11), pages 1-14, October.
    2. Kevin Shuai Zhang & Traian Pirvu, 2021. "Pricing spread option with liquidity adjustments," Papers 2101.00223, arXiv.org.

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