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.
New approximations for Asian basket spread options using stochastic Taylor expansions.
New formulas for pricing Asian and basket options using stochastic expansion.
Entropy corrections improve GBM's predictive accuracy for non-log-normal distributions.
Alternative closed-form formula for spread call option prices under log-normal models.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits gro…
In the LIBOR market model, forward interest rates are log-normal under their respective forward measures. This note shows that their distributions under the other forward measures of the tenor structure have approximately log-normal tails.
This work derives an approximate analytical single period solution of the portfolio choice problem for the power utility function. It is possible to do so if we consider that the asset returns follow a multivariate normal distribution. It is shown in the literature that the log-normal distribution seems to be a good pr…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
In this survey, a short introduction in the recent discovery of log-normally distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data…
Establishes a microstructural foundation for a rough log-normal volatility model.
Study on the geometric Dyson Brownian motion of non-square matrix products.
Paper improves basket option pricing for log-normal models.
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
Employing data on the assessed value of land in 1974--2007 Japan, we exhibit a quasistatically varying log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed quasi-balance is adopted together with two approximations. The resultant distribution is power-law with the …
Paper characterizes DLN distribution, its properties, and estimation methods.
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior turns out to depend on the correlation between the components, and the explicit s…
We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The lo…
We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the price of the quanto option. In order to take the skew/smile effect observed in …
Flexible models cluster RNA sequencing data.
A new framework improves VaR recalibration by balancing reliance on imperfect volatility proxies.
In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any …
Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology to economics. Trajectories of GBM are distributed according to the we…
Quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian representation, which greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small…
A new model predicts race places using changeover-times and log-normal distributions.
Study accelerates NAS research with a large dataset of ZC proxies.
Unified framework for analyzing neural networks trained by gradient descent.
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of …
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
Study shows big winner stocks significantly impact passive and active investment strategies.
Derives TAP approximation for Bayesian linear regression.
Study semi-supervised learning with noisy proxy covariates, deriving bounds and showing gains.
The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Completion have become popular methods for Link Prediction due to the low rank nature of mutual node fr…
DFPV improves PCL for confounded bandit policy evaluation.
A framework uses proxies to prioritize treatment without estimating causal effects.
New method recovers latent confounders from high-dimensional proxy variables.
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…
Single proxy variable helps estimate causal effects from confounders.
A scalable method for deep metric learning using chance constraints.
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
A new tree model, GRST, improves option pricing without log-normality assumptions.
This work introduces a geometric approach to probability representation and option pricing.
Develops methods to improve demand counterfactuals from imperfect proxies.
New method handles many noisy proxy controls for causal inference.
Predicting delayed outcomes is an important problem in recommender systems (e.g., if customers will finish reading an ebook). We formalize the problem as an adversarial, delayed online learning problem and consider how a proxy for the delayed outcome (e.g., if customers read a third of the book in 24 hours) can help mi…
A machine learning model may exhibit discrimination when used to make decisions involving people. One potential cause for such outcomes is that the model uses a statistical proxy for a protected demographic attribute. In this paper we formulate a definition of proxy use for the setting of linear regression and present …