ARMA process for speckled data

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

Экономика и математические методы ◽

10.31857/s042473880016417-7 ◽

2021 ◽

Vol 57 (3) ◽

pp. 126

Author(s):

Nikolai Berzon

Keyword(s):

Time Series ◽

Option Pricing ◽

Discrete Time ◽

Value At Risk ◽

Probability Of Default ◽

Pricing Models ◽

Arma Process ◽

Underlying Asset ◽

Black Scholes

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

Download Full-text

Were the chaotic ELMs in TCV the result of an ARMA process?

Plasma Physics and Controlled Fusion ◽

10.1088/0741-3335/46/10/l01 ◽

2004 ◽

Vol 46 (10) ◽

pp. L15-L21 ◽

Cited By ~ 5

Author(s):

A W Degeling ◽

J B Lister ◽

Y R Martin ◽

G Zvejnieks

Keyword(s):

Arma Process

Download Full-text

Single step estimation of ARMA roots for non-fundamental nonstationary fractional models

Econometrics Journal ◽

10.1093/ectj/utac001 ◽

2022 ◽

Author(s):

Ignacio N Lobato ◽

Carlos Velasco

Keyword(s):

Stock Market ◽

Strong Evidence ◽

Long Memory ◽

Trading Volume ◽

Moving Average ◽

Single Step ◽

Arma Process ◽

Dow Jones Industrial Average ◽

Fractional Models ◽

Stock Market Trading

Abstract We propose a single step estimator for the autoregressive and moving-average roots (without imposing causality or invertibility restrictions) of a nonstationary Fractional ARMA process. These estimators employ an efficient tapering procedure, which allows for a long memory component in the process, but avoid estimating the nonstationarity component, which can be stochastic and/or deterministic. After selecting automatically the order of the model, we robustly estimate the AR and MA roots for trading volume for the thirty stocks in the Dow Jones Industrial Average Index in the last decade. Two empirical results are found. First, there is strong evidence that stock market trading volume exhibits non-fundamentalness. Second, non-causality is more common than non-invertibility.

Download Full-text

ON ESTIMATING THE ORDER OF AN ARMA PROCESS

Adaptive Systems in Control and Signal Processing 1986 ◽

10.1016/b978-0-08-034085-2.50067-5 ◽

1987 ◽

pp. 375-380

Author(s):

J.-J. Fuchs

Keyword(s):

Arma Process

Download Full-text

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

Advances in Applied Probability ◽

10.1017/s0001867800015421 ◽

1985 ◽

Vol 17 (04) ◽

pp. 810-840 ◽

Cited By ~ 1

Author(s):

Jürgen Franke

Keyword(s):

Time Series ◽

Impulse Response ◽

Moving Average ◽

Autoregressive Process ◽

Natural Generalization ◽

Maximal Entropy ◽

Autoregressive Moving Average ◽

Moving Average Process ◽

Arma Process ◽

Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

Download Full-text

Significance and Causality in Continuous Wavelet and Wavelet Coherence Spectra Applied to Hydrological Time Series

Hydrology ◽

10.3390/hydrology7040082 ◽

2020 ◽

Vol 7 (4) ◽

pp. 82

Author(s):

Juan Carlos Rodríguez-Murillo ◽

Montserrat Filella

Keyword(s):

Time Series ◽

Multiple Testing ◽

Power Spectra ◽

Wavelet Coherence ◽

Data Series ◽

Arma Process ◽

Significance Level ◽

Common Effect ◽

Measured Time ◽

Wavelet Spectra

Wavelet transform, wavelet spectra, and coherence are popular tools for studying fluctuations in time series in the form of a bidimensional time and scale representation. We discuss two aspects of wavelet analysis—namely the significance and stochastic/deterministic character of the wavelet spectra. Real-time series of discharge, sodium, and sulfate concentrations in the alpine Rhône River, Switzerland, are used to illustrate these issues. First, the consequences of using an arbitrary stochastic process (usually, AR (1)) instead of the best-fitted general ARMA process in the evaluation of the significance of wavelet spectra are analyzed. Using a general ARMA instead of AR (1) decreases the significance level of the differences in wavelet power spectra (WPS) of ARMA and AR (1) compared to the WPS of the time series in all cases studied and points to a possible systematic overestimation of significance in many published studies. Besides, the significance of particular patches in the spectra is affected by multiple testing. A (conservative) way to circumvent this problem, using global wavelet spectra and global coherence spectra, is evaluated. Finally, we discuss the issue of causality and investigated it in the three measured time series mentioned above. Even if the use of the best fitted ARMA pointed to no deterministic features being present in the corrected series studied (i.e., stochastic processes are dominant in the three data series), coherence spectra between variables allowed to reveal cause-effect relationships between two “coherent” variables and/or the existence of a common effect on both variables. Therefore, such type of analysis provides a useful tool to better understand data causal relationships.

Download Full-text