Implied Volatility Smile with Non-Gaussian Processes

Michele Leonardo Bianchi, Stoyan V Stoyanov, Gian Luca Tassinari, Frank Fabozzi () and Sergio M Focardi

Chapter 11 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 463-516 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The main topics covered in this chapter are:basic definitions of option contracts, from plain-vanilla to more complex structures;a review of the Black–Scholes option pricing framework with the standard formulas to price call and put options;a review of the Lévy option pricing framework together with the implementation of the quasi-closed-form solution for the pricing of European contracts;a discussion on the implied volatility smile;an implementation of the algorithm to extract risk-neutral parameters from observed market quotes;an implementation of the joint calibration to simultaneously extract risk-neutral parameters from observed market quotes and historical parameters from the time series of stock returns;a detailed description of the change of measure for Lévy processes with a focus on the CTS model;a deep dive into the Esscher transform under a univariate framework for the CTS, the NTS, and the GH models;an implementation of a Monte Carlo pricing algorithm with non-Gaussian processes.

Keywords: Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2019
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