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

Andrey Itkin ()

in World Scientific Books from World Scientific Publishing Co. Pte. Ltd.

Abstract: The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black–Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.

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
ISBN: 9789811212765
References: Add references at CitEc
Citations: View citations in EconPapers (4)

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Chapters in this book:

Ch 1 Local Volatility and Dupire’s Equation , pp 3-12

Andrey Itkin

Ch 2 Local Volatility Surface and No-arbitrage , pp 13-23

Andrey Itkin

Ch 3 Analytical Methods of Building the Local Volatility Surface , pp 27-60

Andrey Itkin

Ch 4 Regression-based Methods , pp 61-97

Andrey Itkin

Ch 5 An Expanded Local Variance Gamma Model , pp 101-136

Andrey Itkin

Ch 6 Geometric Local Variance Gamma Model , pp 137-173

Andrey Itkin

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