A New Approach to the Modeling of Financial Volumes

D’Amico, Guglielmo; Gismondi, Fulvio; Petroni, Filippo

doi:10.1007/978-3-030-02825-1_15

Cited by 5 publications

(5 citation statements)

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“…In this research we consider also financial volume as one important variable worthwhile to be investigated. The WISMC model was also applied to the modelling of financial volumes in a recent article by D'Amico et al 39 and revealed to be able to reproduce several statistical properties of volumes at high‐frequency scales. In order to be able to distinguish between the WISMC model for returns and that for volumes we introduce an additional notation for the volume model.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…To verify the validity of the model described above, we applied it to the database introduced in Section 2. Following References 39,53 we use, as definition of the function

f^{λ}

in (1), an exponentially weighted moving average (EWMA) of the squares of J n which has the following expression:

f^{λ} (J_{n - 1 - k}, T_{n}^{J}, a) = \frac{λ^{T_{n}^{J} - a} J_{n - 1 - k}^{2}}{\sum_{k = 0}^{m + n - 1} \sum_{a = T_{n - 1 - k}^{J}}^{T_{n - k}^{J} - 1} λ^{T_{n}^{J} - a} + 1} = \frac{λ^{T_{n}^{J} - a} J_{n - 1 - k}^{2}}{\sum_{a = T_{- m}^{J}}^{T_{n}^{J}} λ^{a}} .

…”

Section: Application To Real High Frequency Datamentioning

confidence: 99%

“…WISMC models were extended using different strategies to multivariate settings and applied to measure the risk of financial portfolios, see References 37 and 38. In the meantime, they were also successfully applied to the modelling of financial volumes by D'Amico et al 39 …”

Section: Introductionmentioning

confidence: 99%

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A micro‐to‐macro approach to returns, volumes and waiting times

D’Amico

Petroni

2021

Appl Stoch Models Bus & Ind

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Modelling stock prices has been a research topic for many decades and it is still an open question. Different approaches have been used in the literature, the majority of which can be classified within the so‐called econometric framework and sometimes also referred to as the macro‐to‐micro approach. Another strand of literature relies on the modelling of directly observable quantities, the so‐called micro‐to‐macro approach. Based on this second line of research, we propose a new multivariate stochastic process to model simultaneously price returns, trading volumes and the time interval between changes in trades, price and volume. The proposed model is based on a generalization of semi‐Markov chain models and copulas and is motivated by empirical evidence that the three mentioned variables are correlated and long‐range autocorrelated. Utilizing Monte Carlo simulations, we compared our model with real data from the Italian stock market and show that it can reproduce many empirical pieces of evidence. The proposed model can be used in the field of portfolio optimization, development of risk measure and volatility forecasting.

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Section: Mathematical Modelmentioning

confidence: 99%

“…To verify the validity of the model described above, we applied it to the database introduced in Section 2. Following References 39,53 we use, as definition of the function

f^{λ}

in (1), an exponentially weighted moving average (EWMA) of the squares of J n which has the following expression:

f^{λ} (J_{n - 1 - k}, T_{n}^{J}, a) = \frac{λ^{T_{n}^{J} - a} J_{n - 1 - k}^{2}}{\sum_{k = 0}^{m + n - 1} \sum_{a = T_{n - 1 - k}^{J}}^{T_{n - k}^{J} - 1} λ^{T_{n}^{J} - a} + 1} = \frac{λ^{T_{n}^{J} - a} J_{n - 1 - k}^{2}}{\sum_{a = T_{- m}^{J}}^{T_{n}^{J}} λ^{a}} .

…”

Section: Application To Real High Frequency Datamentioning

confidence: 99%

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A micro‐to‐macro approach to returns, volumes and waiting times

D’Amico

Petroni

2021

Appl Stoch Models Bus & Ind

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“…In this research we consider also financial volume as one important variable worthwhile to be investigated. The WISMC model was also applied to the modeling of financial volumes in a recent article by [12] and revealed to be able to reproduce several statistical properties of volumes at high-frequency scales. In order to be able to distinguish between the WISMC model for returns and that for volumes we introduce an additional notation for the volume model.…”

Section: Definitionmentioning

confidence: 99%

“…WISMC models were extended using different strategies to multivariate settings and applied to measure risk of financial portfolios, see [18] and [19]. In the meantime they were also successfully applied to the modelling of financial volumes by [12].…”

Section: Introductionmentioning

confidence: 99%

A micro-to-macro approach to returns, volumes and waiting times

D’Amico¹,

Petroni²

2020

Preprint

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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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