[...]... 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... 243–88 Andersen, T G (1994) Stochastic autoregressive volatility: a framework for volatility modelling Mathematical Finance 4, 75–102 —— (1996) Return volatility and trading volume: an information flow interpretation of stochastic volatility Journal of Finance 51, 169–204 —— Benzoni, L., and Lund J (2002) An empirical investigation of continuous-time equity return models Journal of Finance 57, 1239–84 ——... 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 the volatility. .. 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 SV and 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... first use of continuous time SV models in financial economics was, to my knowledge, in the unpublished Johnson (1979) who studied the pricing of options using time-changing volatility models in continuous time This paper evolved into Johnson and Shanno (1987) Wiggins (1987) studied similar types of problems, recording his work first in his 1986 MIT Ph.D thesis The most well known paper in this area is... evaluation of volatility forecasts International Economic Review 45, Forthcoming —— Lund, J (1997) Estimating continuous-time stochastic volatility models of the short term interest rate Journal of Econometrics 2, 343–77 —— Sørensen, B E (1996) GMM estimation of a stochastic volatility model: a Monte Carlo study Journal of Business and Economic Statistics 14, 328–52 Andreou, E and Ghysels, E (2002) Rolling-sampling... 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... resorting to empirically unattractive stable processes Clark’s arguments were in continuous time, which nicely matches much of the modern literature However, a careful reading of the paper leads to the conclusion that it does not really deal with time-varying volatility in the modern sense In the Clark paper no mechanism is proposed that would explicitly generate volatility clustering in M by modelling... (1997a) Heterogeneous information arrivals and return volatility dynamics: Uncovering the long-run in high frequency returns Journal of Finance 52, 975–1005 —— Bollerslev, T (1997b) Intraday periodicity and volatility persistence in financial markets Journal of Empirical Finance 4, 115–58 —— —— (1998a) Answering the skeptics: yes, standard volatility models to provide accurate forecasts International Economic... 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 . 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 2 Stochastic Volatility the discussion into. time-varying volatility in the modern sense. In the Clark paper no mechanism is proposed that would explicitly generate volatility clustering in M by modelling t as having serially dependent increments. To. Relationships: Readings in Cointegration EditedbyR.F.EngleandC.W.J.Granger Micro -Econometrics for Policy, Program, and Treatment Effect By Myoung-jae Lee Modelling Econometric Series: Readings in Econometric