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An Expanded Local Variance Gamma Model

In: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models

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  • Andrey Itkin

Abstract

In this part of the book we consider another local volatility model. In this model the underlying is driven by a Variance Gamma process of [Madan and Seneta (1990)], rather than the Geometric Brownian Motion, but also equipped with a local volatility function. Such a model was first proposed in [Carr and Nadtochiy (2014)] to (i) improve computational efficiency of calibration of the local volatility surface, and (ii) to built a richer flavor of the local volatility model. The latter is achieved by adding a stochastic volatility component via a stochastic change of time. We will discuss this in more detail in what follows…

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  • Andrey Itkin, 2020. "An Expanded Local Variance Gamma Model," World Scientific Book Chapters, in: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, chapter 5, pages 101-136, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811212772_0005
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    3. Peter Carr & Sergey Nadtochiy, 2017. "Local Variance Gamma And Explicit Calibration To Option Prices," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 151-193, January.
    4. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    5. Andrey Itkin & Alexander Lipton, 2016. "Filling the gaps smoothly," Papers 1608.05145, arXiv.org.
    6. Levy, Haim, 1985. "Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
    7. Erik Ekström & Johan Tysk, 2012. "Dupire'S Equation For Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-12.
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    Cited by:

    1. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.
    2. Fabien Le Floc'h, 2020. "An arbitrage-free interpolation of class $C^2$ for option prices," Papers 2004.08650, arXiv.org, revised May 2020.
    3. Andrey Itkin, 2020. "Geometric Local Variance Gamma Model," World Scientific Book Chapters, in: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, chapter 6, pages 137-173, World Scientific Publishing Co. Pte. Ltd..

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    More about this item

    Keywords

    Local Volatility; Stochastic Clock; Geometric Process; Gamma Distribution; Piecewise Linear Volatility; Variance Gamma Process; Closed Form Solution; Fast Calibration; No-Arbitrage;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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