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Sparse grid high-order ADI scheme for option pricing in stochastic volatility models

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  • Bertram During
  • Christian Hendricks
  • James Miles

Abstract

We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.

Suggested Citation

  • Bertram During & Christian Hendricks & James Miles, 2016. "Sparse grid high-order ADI scheme for option pricing in stochastic volatility models," Papers 1611.01379, arXiv.org.
    • Handle: RePEc:arx:papers:1611.01379
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    References listed on IDEAS

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    1. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    2. Bertram During & Michel Fourni'e & Christof Heuer, 2014. "High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids," Papers 1404.5138, arXiv.org.
    3. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    6. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
    7. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    8. Fournié, Michel & Düring, Bertram & Jüngel, Ansgar, 2004. "Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation," CoFE Discussion Papers 04/02, University of Konstanz, Center of Finance and Econometrics (CoFE).
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