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A Time Series Approach to Option PricingThe Time Series Toolbox for Financial Returns

A Time Series Approach to Option Pricing: The Time Series Toolbox for Financial Returns [The evaluation of financial risks and the pricing of financial derivatives are based on statistical models trying to encompass the main features of underlying asset prices. From the seminal works of Bachelier (Ann Sci Ecole Norm Supér 17:21–86, 1900) based on Gaussian distributions, the random walk hypothesis for the returns or the log-returns has frequently been suggested. Its remarkable mathematical tractability, in particular in the multidimensional case, was the keystone of nice financial theories like Markowitz’s (Portfolio selection: efficient diversification of investments. Wiley, New York, 1959) portfolio management or Black and Scholes (J Polit Econ 81:637–659, 1973) option pricing model, among others. Nevertheless, during the last decades, the explosion of computational tools efficiency has allowed researchers to pay more attention to the analysis of financial datasets and the test of models assumptions. It is now well-documented that in spite of their huge heterogeneity concerning the nature of financial assets (stocks, commodities, interest rates, currencies…), the frequency of observations or the multiplication of financial centers, financial time series exhibit common statistical regularities (called stylized facts) that make satisfactory models difficult to obtain. A major attempt in this direction was done during the 1980s by Engle (Econometrica 50:987–1007, 1982) and Bollerslev (J Econ 31:307–327, 1986) through the ARCH/GARCH approach. After a brief reminder of the classical stylized facts observed for the daily log-returns of financial indices, the aim of the chapter is to present the main features of the GARCH modelling approach and its recent extensions.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Time Series Approach to Option PricingThe Time Series Toolbox for Financial Returns

Chorro, Christophe; Guégan, Dominique; Ielpo, Florian
Springer Journals — Nov 22, 2014
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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2015
ISBN
978-3-662-45036-9
Pages
11 –66
DOI
10.1007/978-3-662-45037-6_2
Publisher site
See Chapter on Publisher Site

Abstract

[The evaluation of financial risks and the pricing of financial derivatives are based on statistical models trying to encompass the main features of underlying asset prices. From the seminal works of Bachelier (Ann Sci Ecole Norm Supér 17:21–86, 1900) based on Gaussian distributions, the random walk hypothesis for the returns or the log-returns has frequently been suggested. Its remarkable mathematical tractability, in particular in the multidimensional case, was the keystone of nice financial theories like Markowitz’s (Portfolio selection: efficient diversification of investments. Wiley, New York, 1959) portfolio management or Black and Scholes (J Polit Econ 81:637–659, 1973) option pricing model, among others. Nevertheless, during the last decades, the explosion of computational tools efficiency has allowed researchers to pay more attention to the analysis of financial datasets and the test of models assumptions. It is now well-documented that in spite of their huge heterogeneity concerning the nature of financial assets (stocks, commodities, interest rates, currencies…), the frequency of observations or the multiplication of financial centers, financial time series exhibit common statistical regularities (called stylized facts) that make satisfactory models difficult to obtain. A major attempt in this direction was done during the 1980s by Engle (Econometrica 50:987–1007, 1982) and Bollerslev (J Econ 31:307–327, 1986) through the ARCH/GARCH approach. After a brief reminder of the classical stylized facts observed for the daily log-returns of financial indices, the aim of the chapter is to present the main features of the GARCH modelling approach and its recent extensions.]

Published: Nov 22, 2014

Keywords: Conditional Variance; Stylize Fact; Exponentially Weight Move Average; Financial Time Series; Leverage Effect

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