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Register a new userA micro-to-macro approach to returns, volumes and waiting times
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Fundamental variables in financial market are not only price and return but a very important role is also played by trading volumes. Here we propose a new multivariate model that takes into account price returns, logarithmic variation of trading volumes and also waiting times, the latter to be intended as the time interval between changes in trades, price, and volume of stocks. Our approach is based on a generalization of semi-Markov chains where an endogenous index process is introduced. We also take into account the dependence structure between the above mentioned variables by means of copulae. The proposed model is motivated by empirical evidences which are known in financial literature and that are also confirmed in this work by analysing real data from Italian stock market in the period August 2015 - August 2017. By using Monte Carlo simulations, we show that the model reproduces all these empirical evidences.
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This paper presents probability distributions for price and returns random processes for averaging time interval {Delta}. These probabilities determine properties of price and returns volatility. We define statistical moments for price and returns random processes as functions of the costs and the volumes of market trades aggregated during interval {Delta}. These sets of statistical moments determine characteristic functionals for price and returns probability distributions. Volatilities are described by first two statistical moments. Second statistical moments are described by functions of second degree of the cost and the volumes of market trades aggregated during interval {Delta}. We present price and returns volatilities as functions of number of trades and second degree costs and volumes of market trades aggregated during interval {Delta}. These expressions support numerous results on correlations between returns volatility, number of trades and the volume of market transactions. Forecasting the price and returns volatilities depend on modeling the second degree of the costs and the volumes of market trades aggregated during interval {Delta}. Second degree market trades impact second degree of macro variables and expectations. Description of the second degree market trades, macro variables and expectations doubles the complexity of the current macroeconomic and financial theory.
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