Pricing of Warrants with Stock Price Dependent Threshold Conditions

TL;DR

This paper investigates the impact of stock price dependent threshold warrants on market arbitrage and tradeability, proposing models and methods for their fair valuation.

Contribution

It introduces a framework for modeling and pricing threshold warrants, highlighting the market imperfections they induce and exploring indifference pricing methods.

Findings

Market arbitrage assumptions are invalid with threshold warrants.

Standard pricing methods cannot be directly applied in these markets.

Indifference pricing offers a viable approach for valuing such warrants.

Abstract

Warrants with stock price dependent threshold conditions give the right to buy specially issued stocks, if the performance of the stock price satisfies some requirements. Existence of these derivatives changes the price process of the underlying. We show that in the presence of such warrants one cannot assume that the stock market is arbitrage free and that the stock is tradeable at every time moment with the same price for buying and selling. This means that the usual methods for deriving fair prices for such warrants cannot be used. We start from a simple model for the firm's value process and discuss some ways to specify a related model for the stock price process in the presence of warrants with threshold conditions. We also discuss how indifference pricing approach can be used for pricing such warrants.