Related papers: Global jump filters and realized volatility
Consider the sum $Y=B+B(H)$ of a Brownian motion $B$ and an independent fractional Brownian motion $B(H)$ with Hurst parameter $H\in(0,1)$. Even though $B(H)$ is not a semimartingale, it was shown in [\textit{Bernoulli} \textbf{7} (2001)…
A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting…
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: $dX_t=a_tdt+\sigma_tdW_t$, where $X$ denotes the log-price and $\sigma$ is a c\`adl\`ag semi-martingale. In the…
We study a new measure of codependency in the second moment of a continuous-time multivariate asset price process, which we name the realized copula of volatility. The statistic is based on local volatility estimates constructed from…
We give a proof of Varadhan estimates for a degenerated jump process with independent increments with more and more jumps which become smaller and smaller. The proof uses the Malliavin Calculus of Bismut type for jump process in semi-group…
We study the asymptotic normality of two feasible estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected…
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…
This work develops techniques for the sequential detection and location estimation of transient changes in the volatility (standard deviation) of time series data. In particular, we introduce a class of change detection algorithms based on…
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental…
The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…
The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular,…
The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multiple-try version of this algorithm is proposed. The algorithm is based on…
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is…
We present a theoretical framework for M-FISHER, a method for sequential distribution shift detection and stable adaptation in streaming data. For detection, we construct an exponential martingale from non-conformity scores and apply…
We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete-time observations. Specifically, we consider $N$ independent…
Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see [1983, Z. Wahrsch.…
In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodness-of-fit tests. In this paper, we give a new goodness-of-fit test for volatility-like…