A Fourier transform method for nonparametric estimation of multivariate volatility

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOS633 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modelling Volatility Spillovers for Bio-ethanol, Sugarcane and Corn Spot and Futures Prices

The recent and rapidly growing interest in biofuel as a green energy source has raised concerns about its impact on the prices, returns and volatility of related agricultural commodities. Analyzing the spillover effects on agricultural commodities and biofuel helps commodity suppliers hedge their portfolios, and manage the risk and co-risk of their biofuel and agricultural commodities. There have been many papers concerned with analyzing crude oil and agricultural commodities separately. The purpose of this paper is to examine the volatility spillovers for spot and futures returns on bio-ethanol and related agricultural commodities, specifically corn and sugarcane. The diagonal BEKK model is used as it is the only multivariate conditional volatility model with well-established regularity conditions and known asymptotic properties. The daily data used are from 31 October 2005 to 14 January 2015. The empirical results show that, in 2 of 6 cases for the spot market, there were significant negative co-volatility spillover effects: specifically, corn on subsequent sugarcane co-volatility with corn, and sugarcane on subsequent corn co-volatility with sugarcane. In the other 4 cases, there are no significant co-volatility spillover effects. There are significant positive co-volatility spillover effects in all 6 cases, namely between corn and sugarcane, corn and ethanol, and sugarcane and ethanol, and vice-versa, for each of the three pairs of commodities. It is clear that the futures prices of bio-ethanol and the two agricultural commodities, corn and sugarcane, have stronger co-volatility spillovers than their spot price counterparts. These empirical results suggest that the bio-ethanol and agricultural commodities should be considered as viable futures products in financial portfolios for risk management

Modelling Volatility Spillovers for Bio-ethanol, Sugarcane and Corn Spot and Futures Prices

The recent and rapidly growing interest in biofuel as a green energy source has raised concerns about its impact on the prices, returns and volatility of related agricultural commodities. Analyzing the spillover effects on agricultural commodities and biofuel helps commodity suppliers hedge their portfolios, and manage the risk and co-risk of their biofuel and agricultural commodities. There have been many papers concerned with analyzing crude oil and agricultural commodities separately. The purpose of this paper is to examine the volatility spillovers for spot and futures returns on bio-ethanol and related agricultural commodities, specifically corn and sugarcane. The diagonal BEKK model is used as it is the only multivariate conditional volatility model with well-established regularity conditions and known asymptotic properties. The daily data used are from 31 October 2005 to 14 January 2015. The empirical results show that, in 2 of 6 cases for the spot market, there were significant negative co-volatility spillover effects: specifically, corn on subsequent sugarcane co-volatility with corn, and sugarcane on subsequent corn co-volatility with sugarcane. In the other 4 cases, there are no significant co-volatility spillover effects. There are significant positive co-volatility spillover effects in all 6 cases, namely between corn and sugarcane, corn and ethanol, and sugarcane and ethanol, and vice-versa, for each of the three pairs of commodities. It is clear that the futures prices of bio-ethanol and the two agricultural commodities, corn and sugarcane, have stronger co-volatility spillovers than their spot price counterparts. These empirical results suggest that the bio-ethanol and agricultural commodities should be considered as viable futures products in financial portfolios for risk managemen

Latent Volatility Granger Causality and Spillovers in Renewable Energy and Crude Oil ETFs

The purpose of the paper is to examine latent volatility Granger causality for four renewable energy Exchange Traded Funds (ETFs) and crude oil ETF (USO), namely solar (TAN), wind (FAN), water (PIO), and nuclear (NLR). Data on the renewable energy and crude oil ETFs are from 18 June 2008 to 20 March 2017. From the underlying stochastic process of a vector random coefficient autoregressive (VRCAR) process for the shocks of returns, we derive Latent Volatility Granger causality from the Diagonal BEKK multivariate conditional volatility model. We follow Chang et al. (2015)’s definition of the co-volatility spillovers of shocks, which calculate the delayed effect of a returns shock in one asset on the subsequent volatility or co-volatility in another asset, and extend the effects of the covolatility spillovers of shocks to the effects of the co-volatility spillovers of squared shocks. The empirical results show there are significant positive latent volatility Granger causality relationships between solar (TAN), wind (FAN), nuclear (NLR), and crude oil (USO) ETFs, specifically significant volatility spillovers of shocks from solar ETF on the subsequent wind ETF co-volatility with solar ETF, and wind ETF on the subsequent solar ETF covolatility with wind ETF. Interestingly, there are significant volatility spillovers of squared shocks for the renewable energy ETFs, but not with crude oil ETFs

Modelling volatility spillovers for bio-ethanol, sugarcane and corn

The recent and rapidly growing interest in biofuel as a green energy source has raised concerns about its impact on the prices, returns and volatility of related agricultural commodities. Analyzing the spillover effects on agricultural commodities and biofuel helps commodity suppliers hedge their portfolios, and manage the risk and co-risk of their biofuel and agricultural commodities. There have been many papers concerned with analyzing crude oil and agricultural commodities separately. The purpose of this paper is to examine the volatility spillovers for spot and futures returns on bio-ethanol and related agricultural commodities, specifically corn and sugarcane, using the multivariate diagonal BEKK conditional volatility model. The daily data used are from 31 October 2005 to 14 January 2015. The empirical results show that in 2 of 6 cases for the spot market, there were significant negative co-volatility spillover effects, specifically corn on subsequent sugarcane co-volatility with corn, and sugarcane on subsequent corn co-volatility with sugarcane. In the other 4 cases, there are no significant co-volatility spillover effects. There are significant positive co-volatility spillover effects in all 6 cases, namely between corn and sugarcane, corn and ethanol, and sugarcane and ethanol, and vice-versa, for each of the three pairs of commodities. It is clear that the futures prices of bio-ethanol and the two agricultural commodities, corn and sugarcane, have stronger co-volatility spillovers than their spot price counterparts. These empirical results suggest that the bio-ethanol and agricultural commodities should be considered as viable futures products in financial portfolios for risk management

The Impact of Jumps and Leverage in Forecasting Co-Volatility

__Abstract__ The paper investigates the impact of jumps in forecasting co-volatility, accommodating leverage effects. We modify the jump-robust two time scale covariance estimator of Boudt and Zhang (2013) such that the estimated matrix is positive definite. Using this approach we can disentangle the estimates of the integrated co-volatility matrix and jump variations from the quadratic covariation matrix. Empirical results for three stocks traded on the New York Stock Exchange indicate that the co-jumps of two assets have a significant impact on future co-volatility, but that the impact is negligible for forecasting weekly and monthly horizons

Dynamic conditional correlation in Latin-American asset markets

ABSTRACT: In this paper we reviewed the models of volatility for a group of five Latin American countries, mainly motivated by the recent periods of financial turbulence. Our results based on high frequency data suggest that Dynamic multivariate models are more powerful to study the volatilities of asset returns than Constant Conditional Correlation models. For the group ofcountries included, we identified that domestic volatilities of asset marketshave been increasing; but the co-volatility of the region is still moderate.

Vast volatility matrix estimation for high-frequency financial data

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems involving a large number of assets, the estimation objects we face are volatility matrices of large size. The existing volatility estimators work well for a small number of assets but perform poorly when the number of assets is very large. In fact, they are inconsistent when both the number, $p$, of the assets and the average sample size, $n$, of the price data on the $p$ assets go to infinity. This paper proposes a new type of estimators for the integrated volatility matrix and establishes asymptotic theory for the proposed estimators in the framework that allows both $n$ and $p$ to approach to infinity. The theory shows that the proposed estimators achieve high convergence rates under a sparsity assumption on the integrated volatility matrix. The numerical studies demonstrate that the proposed estimators perform well for large $p$ and complex price and volatility models. The proposed method is applied to real high-frequency financial data.Comment: Published in at http://dx.doi.org/10.1214/09-AOS730 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org