Related papers: Diffusive behavior and the modeling of characteris…
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of…
We study a variant of cost-aware sequential hypothesis testing in which a single active Decision Maker (DM) selects actions with positive, random costs to identify the true hypothesis under an average error constraint, while minimizing the…
We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time…
In this paper we introduce two new Hawkes processes, namely, compound and regime-switching compound Hawkes processes, to model the price processes in limit order books. We prove Law of Large Numbers and Functional Central Limit Theorems…
Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of…
Using simple particle models of limit order markets, we argue that mid-term over-diffusive price behaviour is inherent to the very nature of these markets. Several rules for rate changes are considered. We obtain analytical results for…
The time it takes the fastest searcher out of $N\gg1$ searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much…
We design TimeBoost: a practical transaction ordering policy for rollup sequencers that takes into account both transaction timestamps and bids; it works by creating a score from timestamps and bids, and orders transactions based on this…
The classical reduced-form and filtration expansion framework in credit risk is extended to the case of multiple, non-ordered defaults, assuming that conditional densities of the default times exist. Intensities and pricing formulas are…
The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an…
In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of…
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…
Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
The first time a searcher finds a target is called a first passage time (FPT). In many physical, chemical, and biological processes, the searcher is "mortal," which means that the searcher might become inactivated (degrade, die, etc.)…
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the…
The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the…
An ability to postpone one's execution without penalty provides an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution…
Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large…
Estimating market impact and transaction costs of large trades (metaorders) is a very important topic in finance. However, using models of price and trade based on public market data provide average price trajectories which are…