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.
Alternative closed-form formula for spread call option prices under log-normal models.
Entropy corrections improve GBM's predictive accuracy for non-log-normal distributions.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
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.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
Establishes a microstructural foundation for a rough log-normal volatility model.
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…
Paper improves basket option pricing for log-normal models.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
Flexible models cluster RNA sequencing data.
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…
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…
Study on the geometric Dyson Brownian motion of non-square matrix products.
New approximations for Asian basket spread options using stochastic Taylor expansions.
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.
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 …
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 …
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…
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 …
Paper characterizes DLN distribution, its properties, and estimation methods.
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…
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…
Tree-based variational inference improves PLN model for hierarchical count data.
We study a model of wealth dynamics [Bouchaud and Mézard 2000, \emph{Physica A} \textbf{282}, 536] which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network. The extreme cases of a fully connected and a ful…
Study shows big winner stocks significantly impact passive and active investment strategies.
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 …
A new tree model, GRST, improves option pricing without log-normality assumptions.
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the …
Generative model identifies temporal count data components with regime-dependent contributions.
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
Onflow optimizes portfolio allocation with gradient flows, robust to transaction fees.
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certai…
Derives TAP approximation for Bayesian linear regression.
We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. …
In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the Lévy Libor model developed by Eberlein and Özkan (2005). This model is an extension to Lévy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is signif…
In this paper we address the question of the size distribution of firms. To this aim, we use the Bloomberg database comprising multinational firms within the years 1995-2003, and analyze the data of the sales and the total assets of the separate financial statement of the Japanese and the US companies, and make a compa…
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…
Study high-dimensional Bayesian linear regression using variational inference.
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…
Bayesian model predicts oncology demand trends with high accuracy.
This work introduces a geometric approach to probability representation and option pricing.
A brief overview of the models and data analyses of income, wealth, consumption distributions by the physicists, are presented here. It has been found empirically that the distributions of income and wealth possess fairly robust features, like the bulk of both the income and wealth distributions seem to reasonably fit …
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently pro…
Paper proposes a new reserving model using machine learning techniques.
3D dust map of the Milky Way improves resolution and accuracy.