Download PDF by Christophe Chorro, Dominique Guégan, Florian Ielpo: A Time Series Approach to Option Pricing: Models, Methods

By Christophe Chorro, Dominique Guégan, Florian Ielpo

ISBN-10: 3662450364

ISBN-13: 9783662450369

ISBN-10: 3662450372

ISBN-13: 9783662450376

The present global monetary scene shows at an intertwined and interdependent courting among monetary marketplace job and financial overall healthiness. This publication explains how the commercial messages added via the dynamic evolution of economic asset returns are strongly with regards to alternative costs. The Black Scholes framework is brought and by means of underlining its shortcomings, an alternate technique is gifted that has emerged over the last ten years of educational examine, an procedure that's even more grounded on a pragmatic statistical research of knowledge instead of on advert hoc tractable non-stop time choice pricing types. The reader then learns what it takes to appreciate and enforce those choice pricing types in accordance with time sequence research in a self-contained manner. The dialogue covers modeling offerings on hand to the quantitative analyst, in addition to the instruments to determine upon a specific version according to the historic datasets of monetary returns. The reader is then guided into numerical deduction of alternative costs from those types and illustrations with actual examples are used to mirror the accuracy of the technique utilizing datasets of recommendations on fairness indices.

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Extra resources for A Time Series Approach to Option Pricing: Models, Methods and Empirical Performances

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Time-varying variance has been filtered out using a GARCH(1,1) process to obtain the residuals 2 other words the tails decrease slower than e x ). First pointed out by Mandelbrot (1963), the deviation from the classical Gaussian hypothesis is now well known and documented, see for example Bouchaud and Potters (2000) or Embrechts et al. (2005). In Fig. 5 we compare a Gaussian kernel estimator2 of the density of the log-returns with respect to a Gaussian density with the same mean and the same variance.

This relation explains why, in general, this model is not capable of producing realizations with both high kurtosis and low, slowly decaying autocorrelations. To illustrate this phenomena, we have represented in Fig. 1/) for various values of a1 C b1 . 1/) are below the lowest isoquant obtained when the persistence parameter a1 C b1 ! 1 (explaining why GARCH(1,1) models estimated on financial datasets are very closed to IGARCH(1,1) specifications). In the GARCH(1,1) setting, we may overcome this problem using for the zt a leptokurtic distribution (see Terasvirta and Zhao 2011).

Nevertheless, we can also remark, from this figure, one of the major drawback of this approach: small prices increases may produce a smaller volatility than log-returns equal to zero (the minimum of the news impact curve being achieved for Xt 1 D ). To avoid this counterintuitive property, we introduce, in the following, three particular GARCH extensions accommodating with asymmetric volatility responses, namely, the GJR GARCH model introduced by Glosten et al. (1993), the exponential GARCH (EGARCH) model of Nelson (1991) and the asymmetric power ARCH (APARCH) model developed by Ding et al.

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A Time Series Approach to Option Pricing: Models, Methods and Empirical Performances by Christophe Chorro, Dominique Guégan, Florian Ielpo

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