Contingent Claim Valuation under Increasing Profit, Strong Arbitrage, and Arbitrage of the First Kind

TL;DR

This paper analyzes how various forms of arbitrage affect the upper hedging prices of contingent claims in market models, especially when reflecting boundaries and corporate stock actions are involved.

Contribution

It introduces a framework for understanding the impact of increasing profit and arbitrage of the first kind on option pricing in complex market models.

Findings

Arbitrage can lower the upper hedging price of contingent claims.

Reflecting boundaries in asset prices lead to reduced option prices similar to knock-out options.

Corporate stock issuance and repurchase plans can produce increasing profit scenarios.

Abstract

We study the upper hedging price for contingent claims in market models with strong types of arbitrage: increasing profit, strong arbitrage, and arbitrage of the first kind. The existence of arbitrage may make the price smaller than if it did not exist. For example, when the asset price process has a reflecting boundary, which introduces increasing profit in the market model, the option prices are reduced to those of the corresponding options that knock-out at the boundary. Furthermore, we demonstrate that corporate stock price processes with increasing profit are obtained as a result of corporate stock issuance and repurchase plans.