Abstract not found

There are two variance components embedded in the returns constructed using high frequency asset prices: the time-varying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components. In the context of a volatility-timing trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent non-parametric asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a) along with new results explicitly allowing for leverage effects, are both easy-to-implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return volatility predictability.

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

informs doi 10.1287/mnsc.1060.0520

The growth of the option pricing literature parallels the spectacular developments of deriva-tive securities and the rapid expansion of markets for derivatives in the last three decades. Writing a survey of option pricing models appears therefore like a formidable task. To delimit our focus we will put emphasis on the more recent contributions since there are

Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) wrote “... there is evidence of non-stationarity in the variance. More work must be done to predict variances using the information available. ” Heterogeneity has deep implications for the theory and practice of financial economics and econometrics. In particular, asset pricing theory is dominated by the idea that higher rewards may be expected when we face higher risks, but these risks change through time in complicated ways. Some of the changes in the level of risk can be modelled stochastically, where the level of volatility and degree of codependence between assets is allowed to change over time. Such models allow us to explain, for example, empirically observed departures from Black-Scholes-Merton prices for options and understand why we should expect to see occasional dramatic moves in financial markets. The outline of this article 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. In section 4 I will briefly discuss the literature on conducting inference for SV models. In section 5 I will talk about the use of SV to price options. In section 6 I will consider the connection of SV with realised volatility. A extensive reviews of this literature is given in Shephard (2005). 2 The origin of SV models The origins of SV are messy, I will give five accounts, which attribute the subject to different sets of people.

In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of time-changed Levy processes. We show that in general realised variance is an inconsistent estimator of the time-change, however we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the time-change in the non-Brownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.

This note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy-to-implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.

Abstract not found