Time Consistent Dynamic Limit Order Books Calibrated on Options

TL;DR

This paper develops a framework for dynamic limit order books in incomplete markets using Time Consistent Pricing Procedures, extending fundamental theorems and providing calibration methods based on option prices.

Contribution

It introduces a new approach to calibrate dynamic limit order books on options within an incomplete market using TCPP and extends fundamental theorems to this context.

Findings

Extension of Kreps-Yan fundamental theorem to limit order books

Characterization of TCPP calibrated on options via dual representation

Construction of TCPP using cadlag BMO martingales

Abstract

In an incomplete financial market, the axiomatic of Time Consistent Pricing Procedure (TCPP), recently introduced, is used to assign to any financial asset a dynamic limit order book, taking into account both the dynamics of basic assets and the limit order books for options. Kreps-Yan fundamental theorem is extended to that context. A characterization of TCPP calibrated on options is given in terms of their dual representation. In case of perfectly liquid options, these options can be used as the basic assets to hedge dynamically. A generic family of TCPP calibrated on option prices is constructed, from cadlag BMO martingales.