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Analytical Methods of Building the Local Volatility Surface

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

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  • Andrey Itkin

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…

Suggested Citation

  • Andrey Itkin, 2020. "Analytical Methods of Building the Local Volatility Surface," World Scientific Book Chapters, in: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, chapter 3, pages 27-60, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811212772_0003
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    Keywords

    Local Volatility; Stochastic Clock; Geometric Process; Gamma Distribution; Piecewise Linear Volatility; Variance Gamma Process; Closed Form Solution; Fast Calibration; No-Arbitrage;
    All these keywords.

    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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