Related papers: ARCH and GARCH Models vs. Martingale Volatility of…
In order to calculate the unobserved volatility in conditional heteroscedastic time series models, the natural recursive approximation is very often used. Following \cite{StraumannMikosch2006}, we will call the model \emph{invertible} if…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
Here, we have analysed a GARCH(1,1) model with the aim to fit higher order moments for different companies' stock prices. When we assume a gaussian conditional distribution, we fail to capture any empirical data when fitting the first three…
This paper proposes a novel hybrid model, termed GARCH-FIS, for recursive rolling multi-step forecasting of financial time series. It integrates a Fuzzy Inference System (FIS) with a Generalized Autoregressive Conditional Heteroskedasticity…
Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments…
The Bayesian estimation of GARCH-family models has been typically addressed through Monte Carlo sampling. Variational Inference is gaining popularity and attention as a robust approach for Bayesian inference in complex machine learning…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional…
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…
We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the…
A general class of time-varying regression models is considered in this paper. We estimate the regression coefficients by using local linear M-estimation. For these estimators, weak Bahadur representations are obtained and are used to…
Price range contains important information about the asset volatility, and has long been considered an important indicator for it. In this paper, we propose to jointly model the [low, high] price range as a random interval and introduce an…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict…
It is common for long financial time series to exhibit gradual change in the unconditional volatility. We propose a new model that captures this type of nonstationarity in a parsimonious way. The model augments the volatility equation of a…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…
Asymmetric power GARCH models have been widely used to study the higher order moments of financial returns, while their quantile estimation has been rarely investigated. This paper introduces a simple monotonic transformation on its…
We solved a stylized fact on a long memory process of volatility cluster phenomena by using Minkowski metric for GARCH(1,1) under assumption that price and time can not be separated. We provide a Yang-Mills equation in financial market and…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…