Article
Multiple Hedging on Energy Market
The article is devoted to the calculation of the dynamic hedge ratio based on three different types of volatility models, among which S-BEKK GARCH model takes into account cross-sectional dependence. The hedging strategy is built for eight stock-futures pairs on energy market in Russia.
This paper studies the problem of calculation the dynamic hedge ratio for the portfolio consisted of two assets. Commonly it’s solved assuming that the investor’s risk aversion is infinite. Then the optimal hedge coefficient is equal to ratio of covariance of the hedged and hedging assets to the variance of the latter. It’s natural to assume that the optimal hedge ratio also dependы on the investor’s attitude to risk. In this paper this fact is implemented via maximization of the investor’s expected utility, which depend on the portfolio return and variance. Consequently if, for example, prices move upwards, the optimal hedge ratio is less than under the assumption of absolute risk aversion and vice versa. In the paper eight portfolios, consisted of Russian blue-chip stocks and futures, are estimated. Multivariate volatility models GO-GARCH and cop-GARCH are applied to estimate the conditional covariances and variances of hedged portfolio returns. There are additional parameters in the error term distribution, including skewness parameter, due to the existence of asymmetry effects in the financial assets returns’ distribution [Kroner, Ng, 1998]. The hedge effectiveness is estimated on the out-of-sample period using the maximum attainable risk reduction, unconditional variance of hedged portfolio returns and financial result. It’s shown that in six cases cop-GARCH surpasses GO-GARCH in hedge. Including the degree of risk aversion in the investor’s utility function together with above-mentioned volatility models allows to increase hedge effectiveness up to 65% for some assets
The article is devoted to the estimation of multivariate volatility of a portfolio consisted from twenty American stocks. The six specifications of multivariate volatility models are formulated and estimated. It’s demonstrated that spatial specifications of multivariate volatility models allow not only reduce the dimension of the problem, but in some cases outdo original specifications at in-sample and out-of-sample comparison.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.