A String Model of Liquidity in Financial Markets

TL;DR

This paper introduces a dynamic liquidity model using stochastic strings to represent order books, demonstrating no arbitrage conditions, and calibrating the model with real data for option pricing.

Contribution

It presents a novel string-based market model that captures liquidity dynamics and allows for arbitrage-free pricing under stochastic demand surfaces.

Findings

Model ensures no arbitrage with stochastic string noise.

Option prices calibrated to real order book data.

Demand curve parametrizations affect pricing outcomes.

Abstract

We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage in the model when the driving noise is a stochastic string. Under the equivalent martingale measure, the clearing price is a martingale, and options can be priced under the no-arbitrage hypothesis. We consider several parameterized versions of the model, and show some advantages of specifying the demand curve as quantity as a function of price (as opposed to price as a function of quantity). We calibrate our model to real order book data, compute option prices by Monte Carlo simulation, and compare the results to observed data.