Analytical Methods of Building the Local Volatility Surface

Andrey Itkin ()

Chapter 3 in Fitting Local Volatility:Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, 2020, pp 27-60 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In Chapter 1 a general concept of the local volatility model invented by [Dupire (1994)] and [Derman and Kani (1994a)], and some basic definitions and notions have been introduced. This chapter continues studying this model in more detail. Throughout the chapter we deal with a classical flavor if the local volatility model where the underlying stochastic process is represented by the Geometric Brownian Motion with the constant volatility replaced by a local volatility function. The other model will be discussed in Part 3 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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