It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin…
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48 results for “local stochastic intensity”
This paper solves the inversion problem for jump processes using Markovian projections.
problem Calibrating jump-diffusion models with both local and stochastic features.
method Inverting Markovian projections for pure jump processes.
result Constructs calibrated local stochastic intensity (LSI) models for credit risk applications.
Method uses deep learning to estimate traffic intensity.
problem Estimating stochastic intensity of traffic processes.
method Deep neural networks for nonlinear filtering.
result Deep learning method accurately estimates traffic intensity.
MSGD outperforms SGD in overparametrized settings with faster convergence rates.
problem Optimization of non-convex functions with momentum.
method Momentum Stochastic Gradient Descent (MSGD) with rigorous analysis.
result MSGD converges exponentially faster than SGD in overparametrized settings.
This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP) where the intensity process belongs to a class of affine diffusions. For any intensity process from this class we derive an analytical expression for probability distribution functions of the corresponding DSPP. A specification of our results…
We provide analytical pricing formula of corporate defaultable bond with both expected and unexpected default in the case with stochastic default intensity. In the case with constant short rate and exogenous default recovery using PDE method, we gave some pricing formula of the defaultable bond under the conditions tha…
Neural Diffusion Intensity Models simplify Cox processes inference.
problem Intractable nonparametric estimation and posterior inference of latent stochastic intensity in Cox processes.
method Variational framework using neural SDEs, with theoretical guarantee of ELBO maximization coinciding with maximum likelihood estimation.
result Accurate recovery of latent intensity dynamics and posterior paths with significant speedup.
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
problem Pricing and delta computation of financial derivatives in jump-diffusion models with stochastic intensity.
method Utilizes Malliavin calculus to price and compute delta, applying the Euler scheme for convergence analysis.
result Established the convergence of approximated solution, financial derivative, and its delta Greeks.
Additive Poisson Process: Learning Intensity of Higher-Order Interaction in Stochastic Processesstat.ML
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
problem Estimating higher-order interaction effects in stochastic processes with limited data.
method Additive Poisson Process (APP) combines information geometry and generalized additive models to model intensity functions in lower dimensions.
result The model can estimate higher-order intensity functions with sparse data.
New model predicts credit spreads using stochastic CIR++ intensities.
problem Lack of continuous stochastic credit spread models and limited term structure models.
method Stochastic CIR++ model for default intensities in risk-neutral space.
result Model produces realistic credit spread term structure curves and consistent diffusion over time.
The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to solve this problem. The yield-spreads for both buyer and seller are extracted. Th…
In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering met…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors -- one fast-varying and one slow-varying. Using Four…
Unified framework for growth models with environmental risk and pollution-dependent disasters.
problem Analyzing how rare but catastrophic shocks interact with capital accumulation and pollution in stochastic growth models.
method General Poisson point process formulation leading to non-local HJB equations with closed-form solutions.
result Unified framework captures how environmental degradation amplifies macroeconomic vulnerability and strengthens incentives for abatement.
Locates entanglement in curves using knot intensity distribution.
problem Finding robust methods for locating entanglement in embedded curves.
method Introducing knot intensity distribution as a local quantifier for entanglement contribution.
result Intensity distributions identify regions in knots accommodating topological changes.
In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous mode…
In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset return dynamics in which frequencies of the up and down movements of asset price hav…
The paper models financial data with multivariate jump processes.
problem Capturing the dynamics of financial data with jumps.
method Defined multivariate point processes driven by stochastic jumps, providing stability conditions.
result Nonlinear models fit financial data best, showing jumps cluster during crises.
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordina…
We propose an efficient method for estimating covariate effects in doubly-stochastic spatial models.
problem Computational demands and restrictive assumptions in existing doubly-stochastic spatial models.
method Penalized regression method for estimating covariate effects in doubly-stochastic point processes.
result Consistency and asymptotic normality of the covariate effect estimates achieved despite model misspecification.
Study explains mortgage burnout using Cox hazard models.
problem Understanding burnout in mortgage pools.
method Modeling mortgage prepayment using Cox hazard processes.
result Observed pool hazard is a survival-weighted mean of individual hazards with a selection term.
Existence of a calibrated regime switching local volatility model and new fake Brownian motionsmath.PR
By Gyongy's theorem, a local and stochastic volatility (LSV) model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility function is equal to the ratio of the Dupire local volatility function over the root conditional mean square of the stochastic v…
We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions between the defaultable stock price, its stochastic volatility and the default intens…
This paper measures the intensity of implicit government guarantees using PMC index model.
problem Excessive local government debt due to implicit government guarantees.
method Text mining of policy documents related to municipal investment bonds, PMC index model.
result Recent policies have reduced the intensity of implicit government guarantees.
Developing a semi-analytical approximation for general default intensity models
problem Accurate and efficient pricing of default intensity models
method Path-integral formalism
result Accurate results for the Black-Karasinski model
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
Derives a pricing formula for VIX options using a new stochastic volatility model.
problem Pricing VIX options under a new stochastic volatility model with volatility clustering.
method Derives a semi-analytical pricing formula using the Heston-Hawkes model with an independent compound Hawkes process.
result Derives an explicit expression for VIX^2 as a linear combination of variance and Hawkes intensity.
This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatil…
We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consist…
New test for point processes without strong model assumptions.
problem Testing local independence in point processes without strong model assumptions.
method Expansion similar to Volterra expansions to represent marginalized intensities.
result Approximation of true marginalized intensity arbitrarily well.
Adaptive importance sampling for estimating point process statistics.
problem Estimating the expected value of a statistic of a locally stable point process.
method Adaptive importance sampling with Poisson point processes and cross-entropy minimization.
result The proposed estimator converges to the target value almost surely and is asymptotically normal.
Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transportstat.ME
New method models intensity functions on spheres using normalizing flows.
problem Modeling non-homogeneous Poisson process intensity functions on the sphere.
method Flexible bijective map using normalizing flows to transform intensity functions.
result Normalizing flows provide a flexible way to model intensity functions on spheres.
Local semi-supervised method improves brain tissue classification in child MRI.
problem Inaccurate detection of brain tissue classes due to intensity variations in early developing brains.
method Kernel Fisher Discriminant Analysis (KFDA) combined with SSIM for perceptual image quality assessment.
result Optimal brain partitioning into subdomains with different average intensity values and separating surfaces between brain parts.
Neural network tackles continual learning with neuromodulation and local error signals.
problem Catastrophic forgetting in continuous learning.
method Biologically-inspired neural architecture with local learning and neuromodulation, combined with transfer metalearning.
result Superior performance in continual learning tasks compared to other approaches.
This work extracts stochastic dynamical systems with -stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for -stable Lévy noise.
result Effectiveness of the method confirmed by numerical experiments.
We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model. For this we use the Bellaiche \cite{Bel81} heat kernel expansion combined with Laplace's method to integrate over the volatility variable on a compact set, and (after a gauge transformation) we …
In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero-coupon bonds, vanilla options, and corporate cou…
Developing a climate-aware pricing framework for XL reinsurance and CAT bonds under non-stationary catastrophe risk.
problem Pricing excess-of-loss (XL) reinsurance and catastrophe (CAT) bonds under climate uncertainty.
method Modeling catastrophe arrivals as a Cox process with a temperature-dependent stochastic intensity and aggregate losses following a compound Cox structure.
result Climate dependence materially changes the loss-generation mechanism and affects the valuation of catastrophe-linked contracts.
Small-time expansions for state-dependent local jump-diffusion models with infinite jump activitymath.PR
In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability …
Smoothing graphons improve link prediction in Bayesian SBM without increasing computational complexity.
problem Accurate modeling of exchangeable relational data with flexible and computationally efficient graphons.
method Introducing smoothing procedures to piecewise-constant graphons to create smoothing graphons, which allow continuous intensity values for relations.
result Smoothing graphons improve AUC and precision for link prediction in real-world data sets.
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to the system. In this paper we propose a novel procedure for the detection…
This paper investigates the dynamics of stocks in the S&P500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose, which is a robust index of the dynamics of the market structure and provides information on the int…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the investor and the market value the options by risk-neutral expectations but under diffe…
Starting from the Avellaneda-Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden M…
Difficult image segmentation problems, for instance left atrium MRI, can be addressed by incorporating shape priors to find solutions that are consistent with known objects. Nonetheless, a single multivariate Gaussian is not an adequate model in cases with significant nonlinear shape variation or where the prior distri…
Machine learning classifies topological phases in leaky photonic lattices.
problem Classifying topological phases in leaky photonic lattices using limited data.
method A fully connected neural network trained on bulk intensity measurements.
result Accurate determination of topological properties from intensity distributions.
The intensity of a default time is obtained by assuming that the default indicator process has an absolutely continuous compensator. Here we drop the assumption of absolute continuity with respect to the Lebesgue measure and only assume that the compensator is absolutely continuous with respect to a general -finite …
BSLP is a two-dimensional dynamic model of interacting portfolio-level loss and spread (more exactly, loss intensity) processes. The model is similar to the top-down HJM-like frameworks developed by Schonbucher (2005) and Sidenius-Peterbarg-Andersen (SPA) (2005), however is constructed as a Markovian, short-rate intens…