ADVANCED TEXTS IN ECONOMETRICS pptx

[...]... applications of SV into the important arena of risk assessment and asset allocation In this introduction I will briefly outline some of the literature on SV models, providing links to the papers reprinted in this book I have organised General Introduction 3 the discussion into models, inference, options and realised volatility The SV literature has grown rather organically, with a variety of papers playing important... provide links with the basic models used today in the literature In section 3 I will briefly discuss some of the innovations in the second generation of SV models These include the use of long-memory volatility processes, the introduction of jumps into the price and volatility processes and the use of SV in interest rate models The section will finish by discussing various multivariate SV models In section... from their viewpoint of fast reverting volatility processes The first analytic option pricing formula was developed by Stein and Stein (1991) who modelled s as a Gaussian OU process A European option could then be computed using a single Fourier inverse In this literature, such a level of computational complexity is called ‘‘closed form.’’ A modelling difficulty with the Stein and Stein approach is that... recapture completeness in stochastic volatility modelling Econometrics of SV option pricing In theory, option prices themselves should provide rich information for estimating and testing volatility models In the Black–Scholes–Merton world, a single option price would allow us to determine uniquely the volatility with no measurement error Such ‘‘estimates’’ are called implied volatilities in the literature... trading using different time horizons (e.g Granger (1980) ) A recent volume of readings on the econometrics of long memory is given in Robinson (2003) Leading advocates of this line of argument in financial ¨ econometrics are Dacorogna, Gencay, Muller, Olsen, and Pictet (2001), Andersen and Bollerslev (1997a) and Andersen and Bollerslev (1998b) who have been motivated by their careful empirical findings... that p will have to change through time in response to the moving s2 We continue to maintain that r is constant In this case B is again redundant in the SDF (but not in the volatility) so the usual SDF conditions again imply h ¼ Àr À 1 a2 and p þ bs ¼ 0 This implies that the move to the SV case has little 2 impact, except that the sample path of s2 is random, but independent of W So the generalised BS... financial instruments The first exposure many econometricians had to this were the famous Olsen ¨ datasets, discussed in detail in the seminal work of Dacorogna, Gencay, Muller, Olsen, and Pictet (2001) Later econometricians started to use data from the main equity exchanges in the U.S and Europe This moved us away from thinking about a fixed time interval, such as a day, into the realm where, at least in theory,... multidisciplinary nature of the research on this topic and has made my task of selecting the papers particularly difficult Inevitably my selection of articles to appear in this book has been highly subjective I hope that the authors of the many interesting papers on this topic which I have not included will forgive my choice The outline of this Chapter is as follows In section 2 I will trace the origins of... computationally simple In continuous time there is work on modelling the log of volatility as fractionally integrated Brownian motion by Comte and Renault (1998) and Gloter and Hoffmann (2004) More recent work, which is econometrically easier to deal with, is the square root model driven by fractionally integrated BM introduced in an in uential paper by Comte, Coutin, and Renault (2003) and the in nite superposition... models, while an alternative strategy for performing a kind of filtering is the reprojection algorithm of Gallant and Tauchen (1998) As well as being of substantial scientific interest for decision making, the advantage of having a filtering method is that it allows us to compute marginal likelihoods for model comparison and one-step-ahead predictions for model testing This allowed us to see if these SV models . alt="" ADVANCED TEXTS IN ECONOMETRICS General Editors Manuel Arellano Guido Imbens Grayham E. Mizon Adrian Pagan Mark Watson Advisory Editor C. W. J. Granger Other Advanced Texts in Econometrics ARCH:. Pondicherry, India. Printed in Great Britain on acid-free paper by Biddles Ltd, King’s Lynn, Norfolk Contents List of Contributors vii General Introduction 1 Part I. Model building 35 1. A Subordinated. SV into the important arena of risk assessment and asset allocation. In this introduction I will briefly outline some of the literature on SV models, providing links to the papers reprinted in