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Multivariate Time-Changed Brownian Motion

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:the history of time-changed Brownian motion and why this process has been applied to finance;the main properties and formulas for different parametric examples of multivariate time-changed Brownian motion;the relation between multivariate time-changed Brownian motion and multivariate normal mean–variance mixture distributions;the derivation of the closed formula for the density function of some multivariate normal mean–variance mixture laws;the evaluation of the probability density function of a multivariate normal mean–variance mixture law when only the characteristic function of the mixing distribution is available in closed form while the density function is not;how to generate sample draws from a multivariate normal mean–variance mixture law.

Suggested Citation

  • Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Multivariate Time-Changed Brownian Motion," World Scientific Book Chapters, in: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT, chapter 7, pages 277-321, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813276208_0007
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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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