Related papers: Modeling high-frequency financial data by pure jum…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
The paper demonstrates that a pure-diffusion 3/2 model is able to capture the observed upward-sloping implied volatility skew in VIX options. This observation contradicts a common perception in the literature that jumps are required for the…
In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection…
In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the…
We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and…
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an…
In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market…
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The…
We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is…
We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the…
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
Identifying the instances of jumps in a discrete-time-series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data…
A new Bayesian significance test is adjusted for jump detection in a diffusion process. This is an advantageous procedure for temporal data having extreme valued outliers, like financial data, pluvial or tectonic forces records and others.
Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…
The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at…
We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity…
A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond…
Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…