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Implied Volatility Smile with Non-Gaussian Processes

In: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT

Author

Listed:
  • Michele Leonardo Bianchi
  • Stoyan V Stoyanov
  • Gian Luca Tassinari
  • Frank J Fabozzi
  • Sergio M Focardi

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.

Suggested Citation

  • Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Implied Volatility Smile with Non-Gaussian Processes," World Scientific Book Chapters, in: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT, chapter 11, pages 463-516, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813276208_0011
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    More about this item

    Keywords

    Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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