Multi-asset generalized variance swaps in Barndorff-Nielsen and Shephard model

2020 ◽  
Vol 07 (04) ◽  
pp. 2050051
Author(s):  
Subhojit Biswas ◽  
Diganta Mukherjee ◽  
Indranil SenGupta
Keyword(s):  
Financial Markets ◽  
Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Variance Swaps ◽  
Numerical Examples ◽  
Generalized Variance ◽  
Multiple Assets

This paper proposes swaps on two important new measures of generalized variance, namely, the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for Barndorff-Nielsen and Shephard model used in financial markets. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.

A PROPOSAL FOR MULTI-ASSET GENERALIZED VARIANCE SWAPS

2019 ◽  
Vol 14 (04) ◽  
pp. 1950019
Author(s):  
SUBHOJIT BISWAS ◽  
DIGANTA MUKHERJEE
Keyword(s):  
Financial Markets ◽  
Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Variance Swaps ◽  
Numerical Examples ◽  
Generalized Variance ◽  
Multiple Assets ◽  
Markov Modulated

This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with Markov-modulated volatilities. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.

Analysis of grid operation state based on improved maximum eigenvalue sample covariance matrix algorithm

2021 ◽  
pp. 095965182110012
Author(s):  
Dinghui Wu ◽  
Juan Zhang ◽  
Bo Wang ◽  
Tinglong Pan
Keyword(s):  
Covariance Matrix ◽  
Signal To Noise Ratio ◽  
Poor Performance ◽  
Sample Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Signal To Noise ◽  
Matrix Algorithm ◽  
Sample Covariance ◽  
Noise Ratio ◽  
Application Fields

Traditional static threshold–based state analysis methods can be applied to specific signal-to-noise ratio situations but may present poor performance in the presence of large sizes and complexity of power system. In this article, an improved maximum eigenvalue sample covariance matrix algorithm is proposed, where a Marchenko–Pastur law–based dynamic threshold is introduced by taking all the eigenvalues exceeding the supremum into account for different signal-to-noise ratio situations, to improve the calculation efficiency and widen the application fields of existing methods. The comparison analysis based on IEEE 39-Bus system shows that the proposed algorithm outperforms the existing solutions in terms of calculation speed, anti-interference ability, and universality to different signal-to-noise ratio situations.

scholarly journals On Asymptotic Efficiency of the M2M4 Signal-to-Noise Estimator for Deterministic Complex Sinusoids

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 4950
Author(s):  
Gianmarco Romano
Keyword(s):  
Covariance Matrix ◽  
Gaussian Noise ◽  
Asymptotic Efficiency ◽  
Noise Power ◽  
Finite Sample ◽  
Signal To Noise ◽  
Numerical Examples ◽  
Unknown Phase ◽  
The Moment ◽  
Asymptotically Efficient

The moment-based M2M4 signal-to-noise (SNR) estimator was proposed for a complex sinusoidal signal with a deterministic but unknown phase corrupted by additive Gaussian noise by Sekhar and Sreenivas. The authors studied its performances only through numerical examples and concluded that the proposed estimator is asymptotically efficient and exhibits finite sample super-efficiency for some combinations of signal and noise power. In this paper, we derive the analytical asymptotic performances of the proposed M2M4 SNR estimator, and we show that, contrary to what it has been concluded by Sekhar and Sreenivas, the proposed estimator is neither (asymptotically) efficient nor super-efficient. We also show that when dealing with deterministic signals, the covariance matrix needed to derive asymptotic performances must be explicitly derived as its known general form for random signals cannot be extended to deterministic signals. Numerical examples are provided whose results confirm the analytical findings.

scholarly journals The use of principal components and univariate charts to control multivariate processes

2008 ◽  
Vol 28 (1) ◽  
pp. 173-196 ◽  
Author(s):  
Marcela A. G. Machado ◽  
Antonio F. B. Costa
Keyword(s):  
Dimensionality Reduction ◽  
Covariance Matrix ◽  
Principal Components ◽  
Control Charts ◽  
Principal Component ◽  
Multivariate Processes ◽  
Generalized Variance ◽  
Overall Performance ◽  
The Way

In this article, we evaluate the performance of the T² chart based on the principal components (PC X chart) and the simultaneous univariate control charts based on the original variables (SU charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU , the SUPC and the T² charts we conclude that the SU X charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S² charts designed for monitoring the covariance matrix. These joint S² charts are, in the majority of the cases, more efficient than the generalized variance chart.

COVARIANCE AND CORRELATION SWAPS FOR FINANCIAL MARKETS WITH MARKOV-MODULATED VOLATILITIES

2014 ◽  
Vol 17 (01) ◽  
pp. 1450006 ◽  
Author(s):  
GIOVANNI SALVI ◽  
ANATOLIY V. SWISHCHUK
Keyword(s):  
Markov Chain ◽  
Financial Markets ◽  
Stochastic Volatility ◽  
Numerical Examples ◽  
Numerical Result ◽  
Markov Modulated

In this paper, we price covariance and correlation swaps for financial markets with Markov-modulated volatilities. As an example, we consider stochastic volatility driven by a two-state continuous Markov chain. In this case, numerical examples are presented for VIX and VXN volatility indices (S&P 500 and NASDAQ-100, from January 2004 to June 2012). We also use VIX (January 2004 to June 2012) to price variance and volatility swaps for the two-state Markov-modulated volatility, and we present a numerical result in this case.

scholarly journals Monitoring bivariate process

2009 ◽  
Vol 29 (3) ◽  
pp. 547-562 ◽  
Author(s):  
Marcela A. G. Machado ◽  
Antonio F. B. Costa ◽  
Fernando A. E. Claro
Keyword(s):  
Covariance Matrix ◽  
Control Charts ◽  
Joint Control ◽  
Multivariate Processes ◽  
Generalized Variance ◽  
Main Drawback ◽  
The Mean ◽  
Sample Variances ◽  
Mean Vector

The T² chart and the generalized variance |S| chart are the usual tools for monitoring the mean vector and the covariance matrix of multivariate processes. The main drawback of these charts is the difficulty to obtain and to interpret the values of their monitoring statistics. In this paper, we study control charts for monitoring bivariate processes that only requires the computation of sample means (the ZMAX chart) for monitoring the mean vector, sample variances (the VMAX chart) for monitoring the covariance matrix, or both sample means and sample variances (the MCMAX chart) in the case of the joint control of the mean vector and the covariance matrix.

scholarly journals Asymptotic Comparison of Parameters Estimates of Two-parameter Weibull Distribution

2019 ◽  
Vol 67 (1) ◽  
pp. 253-263
Author(s):  
Tereza Konečná ◽  
Zuzana Hübnerová
Keyword(s):  
Weibull Distribution ◽  
Covariance Matrix ◽  
Asymptotic Efficiency ◽  
Parameter Estimates ◽  
Asymptotic Covariance Matrix ◽  
Generalized Variance ◽  
Asymptotic Covariance ◽  
Probability Plot ◽  
Efficiency Comparison ◽  
Two Parameter

The Weibull distribution is frequently applied in various fields, ranging from economy, business, biology, to engineering. This paper aims at estimating the parameters of two-parameter Weibull distribution are determined. For this purpose, the method of quantiles (three different choices of quantiles) and Weibull probability plot method is utilized. The asymptotic covariance matrix of the parameter estimates is derived for both methods. For optimal random choices of quantiles, the variance, covariance and generalized variance is computed. The main contribution of this study is the introduction of the best choice of percentiles for the method of quantiles and the joint asymptotic efficiency comparison of applied methods.

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