Related papers: Efficient posterior inference on the volatility of…
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet…
In this paper, we consider a one-dimensional diffusion process with jumps driven by a Hawkes process. We are interested in the estimations of the volatility function and of the jump function from discrete high-frequency observations in a…
In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of…
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…
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…
We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension.…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…
In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the…
We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma…
We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian…
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…
We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo…
In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump…
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…