Covariance estimation using high-frequency data: Analysis of Nord Pool electricity forward data

Abstract

Abstract:The modeling of volatility and correlation is important in order to calculate hedge ratios, value at risk estimates, CAPM (Capital Asset Pricing Model betas), derivate pricing and risk management in general. Recent access to intra-daily high-frequency data for two of the most liquid contracts at the Nord Pool exchange has made it possible to apply new and promising methods for analyzing volatility and correlation. The concepts of realized volatility and realized correlation are applied, and this study statistically describes the distribution (both distributional properties and temporal dependencies) of electricity forward data from 2005 to 2009. The main findings show that the logarithmic realized volatility is approximately normally distributed, while realized correlation seems not to be. Further, realized volatility and realized correlation have a long-memory feature. There also seems to be a high correlation between realized correlation and volatilities and positive relations between trading volume and realized volatility and between trading volume and realized correlation. These results are to a large extent consistent with earlier studies of stylized facts of other financial and commodity markets.

Option‐based portfolio risk hedging strategy for gas generator based on mean‐variance utility model

“…$$E( {{r_{sp,lp\;\& \;sc}}(T)} )$$ is the average rate of return of short call, long put, and short put for total time slots N; $$\sigma {( {{r_{sp,lp\;\& \;sc}}(T)} )^2}$$ is the variance of the short call, long put, and short put for total time slots N ; i and j belong to the set of options, i.e. short put, long put, and short call option, i ≠ j ; $${\rho _{i,j}}$$ is the correlation coefficient of any two options within the pool of options; $$CO{V_{i,j}}$$ is the covariance for any two options within the pool of options [28]); $${W_{_{sp}}}$$, $${W_{_{lp}}}$$, and $${W_{_{sc}}}$$ are the weights of investment on short put, long put and short call; $${E_{MP}}$$ is the target return.…”

A comparison of implied and realized volatility in the Nordic power forward market

“…The expected parabolic decrease in volatility for longer tick intervals is not observed and the plot fails to give a clear indication of the best sampling frequency. Lien et al (2012) chose a 30 minute sampling interval when studying the electricity forward market. We see from the volatility signature plot that the volatility in our data The choice of this interval in realized volatility calculations has ramifications for what days that should be removed from our sample.…”