An Expanded Local Variance Gamma Model

Andrey Itkin ()

Chapter 5 in Fitting Local Volatility:Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, 2020, pp 101-136 from World Scientific Publishing Co. Pte. Ltd.

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…

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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Related works:
Journal Article: An Expanded Local Variance Gamma Model (2021)
Working Paper: An Expanded Local Variance Gamma model (2018)
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