scholarly journals Lévy copulae for financial returns

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Ostap Okhrin
Keyword(s):  
Time Series ◽  
Stock Returns ◽  
Lévy Processes ◽  
Levy Processes ◽  
Time Series Models ◽  
Financial Returns ◽  
Levy Copula

AbstractThe paper uses Lévy processes and bivariate Lévy copulae in order to model the behavior of intraday log-returns. Based on assumptions about the form of marginal tail integrals and a Clayton Lévy copula, the model allows for capturing intraday cross-dependency. The model is applied to VaR of the portfolios constructed on stock returns as well as on cryptocurrencies. The proposed method shows fair performance compared to classical time series models.

Extracting Forward-Looking Information from Security Prices: A New Approach

2008 ◽  
Vol 83 (4) ◽  
pp. 1101-1124 ◽  
Author(s):  
Dan Weiss ◽  
Prasad A. Naik ◽  
Chih-Ling Tsai
Keyword(s):  
Time Series ◽  
Stock Returns ◽  
Time Series Models ◽  
Security Prices ◽  
Firm Level ◽  
Analyst Following ◽  
New Approach ◽  
Future Earnings ◽  
Market Participants ◽  
Forward Looking

ABSTRACT: This paper proposes a new index to extract forward-looking information from security prices and infer market participants’ expectations of future earnings. The index, called market-adapted earnings (MAE), utilizes stock returns and fundamental accounting signals to estimate market expectations of future earnings at the firm level. MAE outperforms time-series models (e.g., random-walk) in predicting future earnings. Results demonstrate the usefulness of MAE for firms that have no analyst following.

scholarly journals Application of Lévy processes in modelling (geodetic) time series with mixed spectra

2021 ◽  
Vol 28 (1) ◽  
pp. 121-134
Author(s):  
Jean-Philippe Montillet ◽  
Xiaoxing He ◽  
Kegen Yu ◽  
Changliang Xiong
Keyword(s):  
Time Series ◽  
Lévy Processes ◽  
Stable Process ◽  
Functional Model ◽  
Noise Spectrum ◽  
Levy Processes ◽  
Infinite Variance ◽  
Residual Time ◽  
First Case ◽  
Heavy Tailed

Abstract. Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series after deterministically subtracting geophysical signals from the observations. This residual time series is then assumed to be a sum of three stochastic processes, including the family of Lévy processes. The introduction of a third stochastic term models the remaining residual signals and other correlated processes. Via simulations and real time series, we identify three classes of Lévy processes, namely Gaussian, fractional and stable. In the first case, residuals are predominantly constituted of short-memory processes. The fractional Lévy process can be an alternative model to the fBm in the presence of long-term correlations and self-similarity properties. The stable process is here restrained to the special case of infinite variance, which can be only satisfied in the case of heavy-tailed distributions in the application to geodetic time series. Therefore, the model implies potential anxiety in the functional model selection, where missing geophysical information can generate such residual time series.

scholarly journals Application of Levy Processes in Modelling (Geodetic) Time Series With Mixed Spectra

2019 ◽  
Author(s):  
Jean-Philippe Montillet ◽  
Xiaoxing He ◽  
Kegen Yu
Keyword(s):  
Time Series ◽  
Lévy Processes ◽  
Stable Process ◽  
Functional Model ◽  
Noise Spectrum ◽  
Levy Processes ◽  
Residual Time ◽  
Heavy Tailed Distributions ◽  
First Case ◽  
Heavy Tailed

Abstract. Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the extraction of geophysical signals. The noise spectrum of these time series is generally modeled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series, after deterministically subtracting geophysical signals from the observations. This residual time series is then assumed to be a sum of three random variables (r.v.), with the last r.v. belonging to the family of Levy processes. This stochastic term models the remaining residual signals and other correlated processes. Via simulations and real time series, we identify three classes of Levy processes: Gaussian, fractional and stable. In the first case, residuals are predominantly constituted of short-memory processes. Fractional Levy process can be an alternative model to the fBm in the presence of long-term correlations and self-similarity property. Stable process is characterized by a large variance, which can be satisfied in the case of heavy-tailed distributions. The application to geodetic time series implies potential anxiety in the functional model selection where missing geophysical information can generate such residual time series.

scholarly journals Quantile Double AR Time Series Models for Financial Returns

2013 ◽  
Vol 32 (6) ◽  
pp. 551-560 ◽  
Author(s):  
Yuzhi Cai ◽  
Gabriel Montes-Rojas ◽  
Jose Olmo
Keyword(s):  
Time Series ◽  
Time Series Models ◽  
Financial Returns

scholarly journals Capturing non-exchangeable dependence in multivariate loss processes with nested Archimedean Lévy copulas

2015 ◽  
Vol 10 (1) ◽  
pp. 87-117 ◽  
Author(s):  
Benjamin Avanzi ◽  
Jamie Tao ◽  
Bernard Wong ◽  
Xinda Yang
Keyword(s):  
Detailed Analysis ◽  
Lévy Processes ◽  
Model Fitting ◽  
Random Variables ◽  
Operational Risk ◽  
Levy Processes ◽  
Dependence Structure ◽  
Levy Copula

AbstractThe class of spectrally positive Lévy processes is a frequent choice for modelling loss processes in areas such as insurance or operational risk. Dependence between such processes (e.g. between different lines of business) can be modelled with Lévy copulas. This approach is a parsimonious, efficient and flexible method which provides many of the advantages akin to distributional copulas for random variables. Literature on Lévy copulas seems to have primarily focussed on bivariate processes. When multivariate settings are considered, these usually exhibit an exchangeable dependence structure (whereby all subset of the processes have an identical marginal Lévy copula). In reality, losses are not always associated in an identical way, and models allowing for non-exchangeable dependence patterns are needed. In this paper, we present an approach which enables the development of such models. Inspired by ideas and techniques from the distributional copula literature we investigate the procedure of nesting Archimedean Lévy copulas. We provide a detailed analysis of this construction, and derive conditions under which valid multivariate (nested) Lévy copulas are obtained. Our results are discussed and illustrated, notably with an example of model fitting to data.

scholarly journals PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES

2004 ◽  
Vol 07 (03) ◽  
pp. 303-335 ◽  
Author(s):  
S. Z. Levendorskiǐ
Keyword(s):  
Stock Returns ◽  
Lévy Processes ◽  
Diffusion Processes ◽  
Method Of Lines ◽  
Levy Processes ◽  
Strike Price ◽  
Early Exercise ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Put

We consider the American put with finite time horizon T, assuming that, under an EMM chosen by the market, the stock returns follow a regular Lévy process of exponential type. We formulate the free boundary value problem for the price of the American put, and develop the non-Gaussian analog of the method of lines and Carr's randomization method used in the Gaussian option pricing theory. The result is the (discretized) early exercise boundary and prices of the American put for all strikes and maturities from 0 to T. In the case of exponential jump-diffusion processes, a simple efficient pricing scheme is constructed. We show that for many classes of Lévy processes, the early exercise boundary is separated from the strike price by a non-vanishing margin on the interval [0, T), and that as the riskless rate vanishes, the optimal exercise price goes to zero uniformly over the interval [0, T), which is in the stark contrast with the Gaussian case.

scholarly journals Application of Lévy Processes in Modelling (Geodetic) Time Series With Mixed Spectra

2020 ◽  
Author(s):  
Jean-Philippe Montillet ◽  
Xiaoxing He ◽  
Kegen Yu ◽  
Changliang Xiong
Keyword(s):  
Time Series ◽  
Lévy Processes ◽  
Stable Process ◽  
Functional Model ◽  
Noise Spectrum ◽  
Levy Processes ◽  
Infinite Variance ◽  
Residual Time ◽  
First Case ◽  
Heavy Tailed

Abstract. Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series, after deterministically subtracting geophysical signals from the observations. This residual time series is then assumed to be a sum of three stochastic processes, including the family of Lévy processes. The introduction of a third stochastic term models the remaining residual signals and other correlated processes. Via simulations and real time series,we identify three classes of Lévy processes: Gaussian, fractional and stable. In the first case, residuals are predominantly constituted of short-memory processes. Fractional Lévy process can be an alternative model to the fBm in the presence of long-term correlations and self-similarity property. Stable process is here restrained to the special case of infinite variance, which can be only satisfied in the case of heavy-tailed distributions in the application to geodetic time series. Therefore, it implies potential anxiety in the functional model selection where missing geophysical information can generate such residual time series.

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