Related papers: Modeling high-frequency financial data by pure jum…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…
Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
Estimating spot covariance is an important issue to study, especially with the increasing availability of high-frequency financial data. We study the estimation of spot covariance using a kernel method for high-frequency data. In…
Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the…
We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the…
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…
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…
We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…
During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…
A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion…
We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the…
We consider a bivariate process $X_t=(X^1_t,X^2_t)$, which is observed on a finite time interval $[0,T]$ at discrete times $0,\Delta_n,2\Delta_n,....$ Assuming that its two components $X^1$ and $X^2$ have jumps on $[0,T]$, we derive tests…
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…