Geometric Local Variance Gamma Model

Andrey Itkin ()

Chapter 6 in Fitting Local Volatility:Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, 2020, pp 137-173 from World Scientific Publishing Co. Pte. Ltd.

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…

Keywords: Local Volatility; Stochastic Clock; Geometric Process; Gamma Distribution; Piecewise Linear Volatility; Variance Gamma Process; Closed Form Solution; Fast Calibration; No-Arbitrage (search for similar items in EconPapers)
JEL-codes: C02 C6 C63 (search for similar items in EconPapers)
Date: 2020
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Working Paper: Geometric Local Variance Gamma model (2018)
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