🤖 AI Summary
This study addresses the superhedging pricing of contingent claims in financial markets admitting strong arbitrage opportunities, such as those yielding increasing profit or arbitrage of the first kind. By integrating superhedging theory, boundary behavior analysis of stochastic processes, and a classification framework for arbitrage, the paper systematically demonstrates for the first time that strong arbitrage can lower option prices. It establishes a theoretical link between reflected boundaries in asset price dynamics and corporate mechanisms of equity issuance and repurchase. The main contribution lies in proving that, under asset price models with reflection at the boundary, the superhedging price of a contingent claim coincides with the price of a corresponding knock-out option. Furthermore, it shows that corporate capital structure adjustments naturally generate processes with increasing profit, thereby offering a novel perspective on derivative pricing in markets featuring arbitrage.
📝 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.