Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices

TL;DR

This paper develops a theoretical framework for pricing and hedging derivatives in markets with transaction costs using dynamic coherent acceptability indices, extending fundamental asset pricing theorems.

Contribution

It introduces dynamic bid and ask prices based on dynamic coherent risk measures and provides a representation theorem linking prices to probability measures.

Findings

Derived dynamic bid and ask prices in markets with transaction costs.

Proved a version of the Fundamental Theorem of Asset Pricing for this setting.

Computed prices for path-dependent options using the dynamic Gain-Loss Ratio.

Abstract

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.