No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs

TL;DR

This paper establishes a fundamental theorem linking no-arbitrage conditions to risk-neutral measures in discrete-time markets with transaction costs and dividend-paying securities, providing dual representations for pricing derivatives.

Contribution

It extends the fundamental theorem of asset pricing to markets with transaction costs and dividends, including dual pricing representations and an illustrative credit default swap example.

Findings

No-arbitrage condition is equivalent to the existence of a risk-neutral measure.

Derived dual representations for superhedging and subhedging prices.

Applied results to a vanilla credit default swap contract.

Abstract

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk-neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a derivative contract. Our results are illustrated with a vanilla credit default swap contract.