IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2006.07771.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2006.07771
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Desmond J. Higham, 2015. "An Introduction to Multilevel Monte Carlo for Option Valuation," Papers 1505.00965, arXiv.org.
    2. Reuven Y. Rubinstein & Ruth Marcus, 1985. "Efficiency of Multivariate Control Variates in Monte Carlo Simulation," Operations Research, INFORMS, vol. 33(3), pages 661-677, June.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kevin Shuai Zhang & Traian Pirvu, 2021. "Pricing spread option with liquidity adjustments," Papers 2101.00223, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Behzad Alimoradian & Karim Barigou & Anne Eyraud-Loisel, 2022. "Derivatives under market impact: Disentangling cost and information," Working Papers hal-03668432, HAL.
    3. Manuel L. Esquível & Nadezhda P. Krasii & Pedro P. Mota & Victoria V. Shamraeva, 2023. "Coupled Price–Volume Equity Models with Auto-Induced Regime Switching," Risks, MDPI, vol. 11(11), pages 1-20, November.
    4. Xin‐Jiang He & Sha Lin, 2023. "Analytically pricing exchange options with stochastic liquidity and regime switching," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(5), pages 662-676, May.
    5. Unterschultz, James R., 2000. "New Instruments For Co-Ordination And Risk Sharing Within The Canadian Beef Industry," Project Report Series 24046, University of Alberta, Department of Resource Economics and Environmental Sociology.
    6. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
    7. Wu, Junqi & Niu, Zhibin & Li, Xiang & Huang, Lizhen & Nielsen, Per Sieverts & Liu, Xiufeng, 2023. "Understanding multi-scale spatiotemporal energy consumption data: A visual analysis approach," Energy, Elsevier, vol. 263(PD).
    8. Jérôme Detemple, 1999. "American Options: Symmetry Properties," CIRANO Working Papers 99s-45, CIRANO.
    9. Lee, Jinkyu & Bae, Sanghyeon & Kim, Woo Chang & Lee, Yongjae, 2023. "Value function gradient learning for large-scale multistage stochastic programming problems," European Journal of Operational Research, Elsevier, vol. 308(1), pages 321-335.
    10. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    11. Giovanni Villani, 2008. "R&D Cooperation in Real Option Game Analysis," Quaderni DSEMS 19-2008, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    12. Alnoor Bhimani & Kjell Hausken & Mthuli Ncube, 2010. "Agent takeover risk of principal in outsourcing relationships," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 12(4), pages 329-340.
    13. Daniel Oda, 2013. "Introducing Liquidity Risk in the Contingent-Claim Analysis for the Banks," Working Papers Central Bank of Chile 681, Central Bank of Chile.
    14. Jamshidian, Farshid, 2008. "Numeraire Invariance and application to Option Pricing and Hedging," MPRA Paper 7167, University Library of Munich, Germany.
    15. Olaf Korn & Paolo Krischak & Erik Theissen, 2019. "Illiquidity transmission from spot to futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1228-1249, October.
    16. Axarloglou, Kostas & Visvikis, Ilias & Zarkos, Stefanos, 2013. "The time dimension and value of flexibility in resource allocation: The case of the maritime industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 52(C), pages 35-48.
    17. Javier Pena & Juan Vera & Luis Zuluaga, 2010. "Static-arbitrage lower bounds on the prices of basket options via linear programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 819-827.
    18. Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
    19. João Adelino Ribeiro & Paulo Jorge Pereira & Elísio Brandão, 2013. "Volume Uncertainty in Construction Projects: a Real Options Approach," CEF.UP Working Papers 1309, Universidade do Porto, Faculdade de Economia do Porto.
    20. Tsai, Pei-Ling & Hsu, Yuan-Lin & Chih, Hsiang-Hsuan & Lin, Shih-Kuei, 2022. "Theoretical and empirical analysis of options in open market share repurchases of Taiwan companies," International Review of Economics & Finance, Elsevier, vol. 81(C), pages 205-226.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2006.07771. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.