12. Financial Applications

  1. Christian Francq1 and
  2. Jean-Michel Zakoïan1,2

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch12

GARCH Models: Structure, Statistical Inference and Financial Applications

GARCH Models: Structure, Statistical Inference and Financial Applications

How to Cite

Francq, C. and Zakoïan, J.-M. (2010) Financial Applications, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch12

Author Information

  1. 1

    University Lille 3, Lille, France

  2. 2

    CREST, Paris, France

Publication History

  1. Published Online: 14 JUL 2010
  2. Published Print: 23 JUL 2010

ISBN Information

Print ISBN: 9780470683910

Online ISBN: 9780470670057

SEARCH

Keywords:

  • Black–Scholes model;
  • continuous-time processes;
  • financial applications;
  • GARCH models;
  • stochastic differential equations

Summary

This chapter discusses several financial applications of GARCH models. It explains the relation between GARCH and continuous-time processes. The chapter presents sufficient conditions for a sequence of stochastic difference equations to converge in distribution to a stochastic differential equation as the length of the discrete time intervals between observations goes to zero. It then applies these results to GARCH(1, 1)-type models. The chapter devotes to the pricing of derivatives and introduces the notion of the stochastic discount factor and shows how it can be used in the GARCH framework. It then focuses on risk measurement. The chapter also discusses and recalls the terminology and basic concepts related to the Black–Scholes model.

Controlled Vocabulary Terms

continuous-time stochastic processes; generalized autoregressive conditional heteroskedasticity