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Geometric 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

As mentioned in Chapter 5, the Local Variance Gamma (LVG) volatility model was first introduced by P. Carr in 2008 and then presented in [Carr and Nadtochiy (2014, 2017)] as an extension of the local volatility model by [Dupire (1994)] and [Derman and Kani (1994a)]. The latter was developed on top of the celebrating Black-Scholes model to take into account the existence of option smile. The main advantage of all local volatility models is that given European options prices or their implied volatilities at points (T, K) where K, T are the option strike and time to maturity, they are able to exactly replicate the local volatility function σ(T, K) at these points. This process is called calibration of the local volatility (or, alternatively, implied volatility) surface, and is one of the main topics of this book…

Suggested Citation

  • 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..
    • Handle: RePEc:wsi:wschap:9789811212772_0006
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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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