A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Time-subordinated Brownian motion models improve financial market stochastic distribution.
Order patterns and permutation entropy have become useful tools for studying biomedical, geophysical or climate time series. Here we study day-to-day market data, and Brownian motion which is a good model for their order patterns. A crucial point is that for small lags (1 up to 6 days), pattern frequencies in financial…
Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard f…
We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time . Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations whi…
The paper approximates CARMA models for option pricing.
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…
Modeling price dynamics in AMMs with fees using geometric Brownian motion.
TCNF models SDEs using time deformation of Brownian motion.
We extend martingale transport results to weak martingale transport.
In this paper, we develop a theory of common decomposition for two correlated Brownian motions, in which, by using change of time method, the correlated Brownian motions are represented by a triplet of processes, , where and are independent Brownian motions. We show the equivalent conditions for the tr…
New findings show independent subordination is not relevant for accurate option pricing.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
Study refracted skew Brownian motion, find densities and asymptotics.
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modeled by a Geometric Brownian motion whe…
New SDEs use -Brownian motion, extending mean-field models.
We find a simple expression for the probability density of in terms of its distribution function and the distribution function for the time integral of . The relation is obtained with a change of measure argument where expectations over events determined by the time integral…
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The m…
We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time…
Improved volatility models for option pricing with weak error rates.
A new option pricing model uses a time-varying Hurst exponent for more accurate financial predictions.
Researchers prove long-time existence for two landmark Brownian motion.
Universal approximation for stochastic processes using Brownian motion.
New method calculates geometric Brownian motion with affine drift and its integral.
Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.
We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that o…
Analyzed a generalized voter model with power-law herding intensity, revealing anomalous diffusion and long-range memory.
Optimal probability measure found for constrained stochastic processes.
Study on determinants of unitary Brownian motion and their asymptotic laws.
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…
Dynamic Black-Litterman integrates expert views with portfolio optimization over varying time horizons.
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price path, without making any stochastic assumptions. It is shown that typical price …
Develops a method to estimate the shadow riskless rate from empirical data.
Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. …
The paper prices weather contracts using a complex temperature model.
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference me…
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
The purpose of this note is to give details for an argument of Sullivan to construct eigenfunctions of the Laplacian on a Riemannian manifold using exit times of Brownian motion \cite{sullivanpos}. Let be a complete, simply connected Riemannian manifold of pinched negative sectional curvature. Let $λ_1 = λ_1(X) < 0…
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.
This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be ex…
New model uses generalized fractional Brownian motion for stock price prediction.
Study on Brownian motion on discrete curve spaces, proving stochastic completeness.
Geodesic walks converge to Brownian motion on Finsler manifolds.
New Brownian motion defined in Minkowski normed spaces.
Global approximation for piecewise linear paths via signatures.
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…