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Related papers: Drift in Transaction-Level Asset Price Models

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We consider the pricing of derivatives written on accumulated marks, such as weather derivatives or aggregate loss claims, using a self-exciting marked point process. The jump intensity mean-reverts between events and increases at jump…

Mathematical Finance · Quantitative Finance 2026-03-16 Aqib Ahmed , Heiðar Eyjólfsson

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…

Probability · Mathematics 2015-01-08 Marton Balazs , Miklos Z. Racz , Balint Toth

We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…

Pricing of Securities · Quantitative Finance 2012-07-17 Aleksandar Mijatović , Peter Tankov

We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…

Neurons and Cognition · Quantitative Biology 2016-01-26 Vaibhav Srivastava , Philip Holmes , Patrick Simen

Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context…

adap-org · Physics 2015-06-30 J. Doyne Farmer

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…

Trading and Market Microstructure · Quantitative Finance 2024-06-21 Neil Shephard , Justin J. Yang

Predicting metrics associated with entities' transnational behavior within payment processing networks is essential for system monitoring. Multivariate time series, aggregated from the past transaction history, can provide valuable insights…

Machine Learning · Computer Science 2021-09-23 Chin-Chia Michael Yeh , Zhongfang Zhuang , Junpeng Wang , Yan Zheng , Javid Ebrahimi , Ryan Mercer , Liang Wang , Wei Zhang

Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This…

Trading and Market Microstructure · Quantitative Finance 2025-11-27 Yao Wu

Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…

Statistical Mechanics · Physics 2024-03-01 Guoxing Lin , Shaokun Zheng

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the…

Statistical Finance · Quantitative Finance 2008-12-02 Austin Gerig

In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…

Mathematical Physics · Physics 2026-02-25 Paolo Cifani , Franco Flandoli , Lorenzo Marino

One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…

Pricing of Securities · Quantitative Finance 2013-04-18 Youssef El-Khatib , Abdulnasser Hatemi-J

We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…

Statistical Finance · Quantitative Finance 2010-10-26 Jean Jacod , Viktor Todorov

The intermarket analysis, in particular the lead-lag relationship, plays an important role within financial markets. Therefore a mathematical approach to be able to find interrelations between the price development of two different…

Statistical Finance · Quantitative Finance 2015-04-24 Stanislaus Maier-Paape , Andreas Platen

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…

Statistical Mechanics · Physics 2011-06-21 Tomasz Srokowski

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…

Statistical Finance · Quantitative Finance 2015-05-14 Miguel A. Fuentes , Austin Gerig , Javier Vicente

We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to…

Statistical Mechanics · Physics 2014-01-14 Rama Cont , Jean-Philippe Bouchaud

The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…

Pricing of Securities · Quantitative Finance 2008-12-02 Pavel Levin

The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. Standard models assume fixed objectives, yet organizations from hospitals to power grids…

Computational Finance · Quantitative Finance 2025-09-18 JINHO CHA

Detecting drift in performance of Machine Learning (ML) models is an acknowledged challenge. For ML models to become an integral part of business applications it is essential to detect when an ML model drifts away from acceptable operation.…

Machine Learning · Computer Science 2021-08-12 Samuel Ackerman , Parijat Dube , Eitan Farchi , Orna Raz , Marcel Zalmanovici
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