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A Spectral Approach to Pricing of Arbitrage-Free SABR Discrete Barrier Options

Author

Listed:
  • Nawdha Thakoor

    (University of Mauritius)

  • Désiré Yannick Tangman

    (University of Mauritius)

  • Muddun Bhuruth

    (University of Mauritius)

Abstract

Market volatility smile risk in derivative pricing can be modelled by the Stochastic Alpha Beta Rho (SABR) model. Once calibrated to market data, prices of European and continuously monitored barrier options can be obtained using equivalent Black’s implied volatility approximations. However these prices are only accurate for options with short maturities. On the other-hand, discretely monitored barrier options cannot be priced using this approach and a numerical technique is required. A novel computational method based on a spectral discretisation of the pricing equation is proposed for the solution of these problems. The high accuracy of the method is first established for special cases of the SABR model where analytical solutions are available and the method is then applied to the pricing of discrete barriers under the arbitrage-free SABR model.

Suggested Citation

  • Nawdha Thakoor & Désiré Yannick Tangman & Muddun Bhuruth, 2019. "A Spectral Approach to Pricing of Arbitrage-Free SABR Discrete Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1085-1111, October.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:3:d:10.1007_s10614-018-9868-8
    DOI: 10.1007/s10614-018-9868-8
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    References listed on IDEAS

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    1. Patrick Hagan & Diana Woodward, 1999. "Equivalent Black volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 147-157.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Tao L. Wu, 2012. "Pricing and Hedging the Smile with SABR : Evidence from the Interest Rate Caps Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(8), pages 773-791, August.
    4. Lindsay, A.E. & Brecher, D.R., 2012. "Simulation of the CEV process and the local martingale property," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 868-878.
    5. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-219, March.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Yang, Nian & Chen, Nan & Liu, Yanchu & Wan, Xiangwei, 2017. "Approximate arbitrage-free option pricing under the SABR model," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 198-214.
    8. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
    9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Cited by:

    1. Andrey Itkin & Dmitry Muravey, 2021. "Semi-analytical pricing of barrier options in the time-dependent $\lambda$-SABR model," Papers 2109.02134, arXiv.org.

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