Related papers: Inference on Self-Exciting Jumps in Prices and Vol…
This paper estimates models of high frequency index futures returns using `around the clock' 5-minute returns that incorporate the following key features: multiple persistent stochastic volatility factors, jumps in prices and volatilities,…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…
Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we integrate price--volatility co-jumps and volatility short-term dependency into a coherent…
The paper investigates the effect of the label green in bond markets from the lens of the trading activity. The idea is that jumps in the dynamics of returns have a specific memory nature that can be well represented through a self-exciting…
We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [Bacry, Delattre, Hoffmann, Muzy, Modelling microstructure noise with…
In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in…
A new branch based on Markov processes is developing in the recent literature of financial time series modeling. In this paper, an Indexed Markov Chain has been used to model high frequency price returns of quoted firms. The peculiarity of…
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
In this paper we describe three stochastic models based on a semi-Markov chains approach and its generalizations to study the high frequency price dynamics of traded stocks. The three models are: a simple semi-Markov chain model, an indexed…
The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we…
Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a…
We present an agent behavior based microscopic model that induces jumps, spikes and high volatility phases in the price process of a traded asset. We transfer dynamics of thermally activated jumps of an unexcited/ excited two state system…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…