The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We motivate our study with analytical results on the distortions caused by some widely used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. We then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of “robust” loss functions. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.
We measured a large suite of gas- and particle-phase multi-functional organic compounds with a Filter Inlet for Gases and AEROsols (FIGAERO) coupled to a high-resolution time-of-flight chemical ionization mass spectrometer (HR-ToF-CIMS) developed at the University of Washington. The instrument was deployed on environmental simulation chambers to study monoterpene oxidation as a secondary organic aerosol (SOA) source. We focus here on results from experiments utilizing an ionization method most selective towards acids (acetate negative ion proton transfer), but our conclusions are based on more general physical and chemical properties of the SOA. Hundreds of compounds were observed in both gas and particle phases, the latter being detected by temperature-programmed thermal desorption of collected particles. Particulate organic compounds detected by the FIGAERO-HR-ToF-CIMS are highly correlated with, and explain at least 25-50% of, the organic aerosol mass measured by an Aerodyne aerosol mass spectrometer (AMS). Reproducible multi-modal structures in the thermograms for individual compounds of a given elemental composition reveal a significant SOA mass contribution from high molecular weight organics and/or oligomers (i.e., multi-phase accretion reaction products). Approximately 50% of the HR-ToF-CIMS particle-phase mass is associated with compounds having effective vapor pressures 4 or more orders of magnitude lower than commonly measured monoterpene oxidation products. The relative importance of these accretion-type and other extremely low volatility products appears to vary with photochemical conditions. We present a desorption-temperature-based framework for apportionment of thermogram signals into volatility bins. The volatility-based apportionment greatly improves agreement between measured and modeled gas-particle partitioning for select major and minor components of the SOA, consistent with thermal decomposition during desorption causing the conversion of lower volatility components into the detected higher volatility compounds.
We show that market volatility of volatility is a significant risk factor that affects index and volatility index option returns, beyond volatility itself. The volatility and volatility of volatility indices, identified model-free as the VIX and VVIX, respectively, are only weakly related to each other. Delta-hedged index and VIX option returns are negative on average and are more negative for strategies that are more exposed to volatility and volatility-of-volatility risks. Further, volatility and volatility of volatility significantly negatively predict future delta-hedged option payoffs. The evidence suggests that volatility and volatility-of-volatility risks are jointly priced and have negative market prices of risk.
The article undertakes a nonparametric analysis of the high-frequency movements in stock market volatility using very finely sampled data on the VIX volatility index compiled from options data by the CBOE. We derive theoretically the link between pathwise properties of the latent spot volatility and the VIX index, such as presence of continuous martingale and/or jumps, and further show how to make statistical inference about them from the observed data. Our empirical results suggest that volatility is a pure jump process with jumps of infinite variation and activity close to that of a continuous martingale. Additional empirical work shows that jumps in volatility and price level in most cases occur together, are strongly dependent, and have opposite sign. The latter suggests that jumps are an important channel for generating leverage effect.
Using an expansion of the transition density function of a one‐dimensional time inhomogeneous diffusion, we obtain the first‐ and second‐order terms in the short time asymptotics of European call option prices. The method described can be generalized to any order. We then use these option prices approximations to calculate the first‐ and second‐order deviation of the implied volatility from its leading value and obtain approximations which we numerically demonstrate to be highly accurate.
The high food prices experienced over recent years have led to the widespread view that food price volatility has increased. However, volatility has generally been lower over the two most recent decades than previously. Variability over the most recent period has been high but, with the important exception of rice, not out of line with historical experience. There is weak evidence that grains price volatility more generally may be increasing but it is too early to say.
Persistence and unpredictable large increments characterize the volatility of financial returns. We propose the Multiplicative Error Model with volatility jumps (MEM-J) to describe and predict the probability and the size of these extreme events. Under the MEM-J, the conditional density of the realized measure is a countably infinite mixture of Gamma and distributions, with closed form conditional moments. We derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation. Estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises. The MEM-J improves over other models with fat tails.
The average monthly premium of the Market return over the one-month T-bill return is substantial, as are average premiums of value and small stocks over Market. As the return horizon increases, premium distributions become more disperse, but they move to the right (toward higher values) faster than they become more disperse. There is, however, some bad news. Even if future expected premiums match high past averages, high volatility means that for the 3- and 5-year periods commonly used to evaluate asset allocations, the probabilities of negative realized premiums are substantial, and the probabilities are nontrivial for 10- and 20-year periods. A practitioner's perspective on this article is provided in the In Practice piece " Volatility: It's Worse Than You Thought " by Phil Davis, online 6 August 2018. Disclosure: The authors are consultants to, board members of, and shareholders in Dimensional Fund Advisors. Editor's Note This article was externally reviewed using our double-blind peer-review process. When the article was accepted for publication, the authors thanked the reviewers in their acknowledgments. Lisa Goldberg was one of the reviewers for this article. Submitted 30 November 2017 Accepted 25 April 2018 by Stephen J. Brown