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Calibration of the SABR Model in Illiquid Markets

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  • Graeme West

Abstract

Recently the SABR model has been developed to manage the option smile which is observed in derivatives markets. Typically, calibration of such models is straightforward as there is adequate data available for robust extraction of the parameters required asinputs to the model. The paper considers calibration of the model in situations where input data is very sparse. Although this will require some creative decision making, the algorithms developed here are remarkably robust and can be used confidently for mark to market and hedging of option portfolios.

Suggested Citation

  • Graeme West, 2005. "Calibration of the SABR Model in Illiquid Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 371-385.
    • Handle: RePEc:taf:apmtfi:v:12:y:2005:i:4:p:371-385
    DOI: 10.1080/13504860500148672
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    References listed on IDEAS

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    1. Emanuel Derman & Iraj Kani, 1998. "Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 61-110.
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    Citations

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    Cited by:

    1. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    2. Qasim Nasar-Ullah, 2013. "A parallel implementation of a derivative pricing model incorporating SABR calibration and probability lookup tables," Papers 1301.3118, arXiv.org.
    3. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    4. Kentaro Hoshisashi & Carolyn E. Phelan & Paolo Barucca, 2023. "No-Arbitrage Deep Calibration for Volatility Smile and Skewness," Papers 2310.16703, arXiv.org, revised Jan 2024.
    5. Kotzé, Antonie & Labuschagne, Coenraad C.A. & Nair, Merell L. & Padayachi, Nadine, 2013. "Arbitrage-free implied volatility surfaces for options on single stock futures," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 380-399.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2009. "Pricing Average Options on Commodities," CARF F-Series CARF-F-177, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2012.
    7. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
    8. Rene Carmona & Yi Ma & Sergey Nadtochiy, 2015. "Simulation of Implied Volatility Surfaces via Tangent Levy Models," Papers 1504.00334, arXiv.org.
    9. Harish S. Bhat & Nitesh Kumar, 2015. "Large-Scale Empirical Tests of the Markov Tree Model," IJFS, MDPI, vol. 3(3), pages 1-39, July.
    10. Petteri Piiroinen & Lassi Roininen & Tobias Schoden & Martin Simon, 2018. "Asset Price Bubbles: An Option-based Indicator," Papers 1805.07403, arXiv.org, revised Jul 2018.
    11. Jaegi Jeon & Kyunghyun Park & Jeonggyu Huh, 2021. "Extensive networks would eliminate the demand for pricing formulas," Papers 2101.09064, arXiv.org.
    12. Jonathan Chih Win Zaw Tun & Papitchaya Wisankosol, 2021. "The Impact of an ODI on the Development of Leadership, Employee Motivation and Employee Engagement towards Better Performance of Employees: A Case Study," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(2), pages 22-43.
    13. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    14. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    15. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    16. Kenichiro Shiraya & Akihiko Takahashi, 2010. "Pricing Average Options on Commodities," CIRJE F-Series CIRJE-F-747, CIRJE, Faculty of Economics, University of Tokyo.
    17. Gunter Meissner & Seth Rooder & Kristofor Fan, 2013. "The impact of different correlation approaches on valuing credit default swaps with counterparty risk," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1903-1913, December.

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