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Semi-Analytical Pricing of Barrier Options in the Time-Dependent λ-SABR Model: Uncorrelated Case

A. Itkin and D. Muravey
The Journal of Derivatives Fall 2022, jod.2022.1.166; DOI: https://doi.org/10.3905/jod.2022.1.166
A. Itkin
is at the Tandon School of Engineering at New York University, Brooklyn, NY
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D. Muravey
is at the Moscow State University, Moscow, Russia
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Abstract

We consider semi-analytical pricing of barrier options for the time-dependent SABR stochastic volatility model (with drift in the instantaneous volatility) with zero correlation between spot and stochastic volatility. In doing so, we modify the general integral transform method (see Itkin et al. 2021) and deliver solution of this problem in the form of Fourier-Bessel series. The weights of this series solve a linear mixed Volterra-Fredholm equation (LMVF) of the second kind also derived in the article. Numerical examples illustrate speed and accuracy of our method, which are comparable with those of the finite-difference approach at small maturities and outperform them at high maturities even by using a simplistic implementation of the RBF method for solving the LMVF.

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The Journal of Derivatives: 29 (5)
The Journal of Derivatives
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Summer 2022
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Semi-Analytical Pricing of Barrier Options in the Time-Dependent λ-SABR Model: Uncorrelated Case
A. Itkin, D. Muravey
The Journal of Derivatives Jul 2022, jod.2022.1.166; DOI: 10.3905/jod.2022.1.166

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Semi-Analytical Pricing of Barrier Options in the Time-Dependent λ-SABR Model: Uncorrelated Case
A. Itkin, D. Muravey
The Journal of Derivatives Jul 2022, jod.2022.1.166; DOI: 10.3905/jod.2022.1.166
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  • Article
    • Abstract
    • THE PRICING PDE AND ITS SOLUTION
    • SOLUTION OF THE LMVF EQUATION EQ. (32)
    • NUMERICAL EXPERIMENTS
    • DISCUSSION
    • ACKNOWLEDGMENTS
    • ENDNOTES
    • REFERENCES
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