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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

Author

Listed:
  • 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…

Suggested Citation

  • 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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    Cited by:

    1. Fabien Le Floc'h, 2020. "An arbitrage-free interpolation of class $C^2$ for option prices," Papers 2004.08650, arXiv.org, revised May 2020.
    2. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.
    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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    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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