Related papers: On binomial order avalanches
This paper is split in three parts: first we use labelled trade data to exhibit how market participants accept or not transactions via limit orders as a function of liquidity imbalance; then we develop a theoretical stochastic control…
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask"…
We consider the randomness of market trade as the origin of price and return stochasticity. We look at time series of trade values and volumes as random variables during the averaging interval {\Delta} and describe the dependences of…
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
We propose a unified mean-field framework that bridges the dynamics of informal financial markets and formal markets governed by Limit Order Books (LOBs). Both settings are modeled as interacting particle systems on a 1D price lattice, with…
This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…
We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal…
This paper develops a strategic model of trade between two regions in which, depending on the relation among output, financial resources and transportation costs, the adjustment of prices towards an equilibrium is studied. We derive…
This paper develops a theoretical mesoscopic model of the limit order book driven by multivariate Hawkes processes, designed to capture temporal self-excitation and the spatial propagation of order flow across price levels. In contrast to…
Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the…
The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different…
Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB)…
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…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the…
Constant price impact functions, much used in financial literature, are shown to give rise to paradoxical outcomes since they do not allow for proper predictability removal: for instance the exploitation of a single large trade whose size…
In two previous papers the author developed a second-order price adjustment (t\^atonnement) process. This paper extends the approach to include both quantity and price adjustments. We demonstrate three results: a analogue to physical…