149 research outputs found
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Entropy and Efficiency of the ETF Market
We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-min and 5-min price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate residual inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure
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Identifying jumps in financial assets: A comparison between nonparametric jump tests
We perform a comprehensive Monte Carlo comparison between nine alternative procedures available in the literature to detect jumps in financial assets using high-frequency data. We evaluate size and power properties of the procedures under alternative sampling frequencies, persistence in volatility, jump size and intensity, and degree of contamination with microstructure noise. The overall best performance is shown by the Andersen, Bollerslev, and Dobrev (2007) and Lee and Mykland (2008) intraday procedures (ABD-LM), provided the price process is not very volatile. We propose two extensions to the existing battery of tests. The first regards the finite sample improvements based on simulated critical values for the ABD-LM procedure. The second regards a procedure that combines frequencies and tests able to reduce the number of spurious jumps. Finally, we report an empirical analysis using real high frequency data on five stocks listed in the New York Stock Exchange
Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance
Published in Handbook of financial time series, 2008, https://doi.org/10.1007/978-3-540-71297-8_22</p
Maximum likelihood and Gaussian estimation of continuous time models in finance
Ministry of Education, Singapore under its Academic Research Funding Tier
Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model
Path integral techniques for the pricing of financial options are mostly
based on models that can be recast in terms of a Fokker-Planck differential
equation and that, consequently, neglect jumps and only describe drift and
diffusion. We present a method to adapt formulas for both the path-integral
propagators and the option prices themselves, so that jump processes are taken
into account in conjunction with the usual drift and diffusion terms. In
particular, we focus on stochastic volatility models, such as the exponential
Vasicek model, and extend the pricing formulas and propagator of this model to
incorporate jump diffusion with a given jump size distribution. This model is
of importance to include non-Gaussian fluctuations beyond the Black-Scholes
model, and moreover yields a lognormal distribution of the volatilities, in
agreement with results from superstatistical analysis. The results obtained in
the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl
A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function
In the present paper, we derive a closed-form solution of the multi-period
portfolio choice problem for a quadratic utility function with and without a
riskless asset. All results are derived under weak conditions on the asset
returns. No assumption on the correlation structure between different time
points is needed and no assumption on the distribution is imposed. All
expressions are presented in terms of the conditional mean vectors and the
conditional covariance matrices. If the multivariate process of the asset
returns is independent it is shown that in the case without a riskless asset
the solution is presented as a sequence of optimal portfolio weights obtained
by solving the single-period Markowitz optimization problem. The process
dynamics are included only in the shape parameter of the utility function. If a
riskless asset is present then the multi-period optimal portfolio weights are
proportional to the single-period solutions multiplied by time-varying
constants which are depending on the process dynamics. Remarkably, in the case
of a portfolio selection with the tangency portfolio the multi-period solution
coincides with the sequence of the simple-period solutions. Finally, we compare
the suggested strategies with existing multi-period portfolio allocation
methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process
dynamics and the analysis of increasing horizon are included in the
simulation study, under revision in Annals of Operations Researc
Simulation-based Estimation Methods for Financial Time Series Models
Published in Handbook of computational finance, 2010, https://doi.org/10.1007/978-3-642-17254-0_15</p
Estimation of high-frequency volatility: An autoregressive conditional duration approach
Ministry of Education, Singapore under its Academic Research Funding Tier
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