Stoptions: Representations and Applications

Abstract

We introduce a new derivative security called a stoption.
After paying an upfront premium, the owner of a stoption accrues realized price changes in some underlying security
until the exposure is stopped by the owner.
Upon stopping, the reward is the sum of all of the previous price changes plus a deterministic amount which can vary with the stopping time.
Stoptions are finite-lived and hence must be stopped at or before a fixed maturity date.
We propose a particular discrete-time probabilistic model for the underlying's price changes and then determine the optimal stopping strategy and
stoption premium for that model in closed-form.
We also present an application to DVA (debit valuation adjustment) under full collateralization.

Keywords: tropical arithmetic, path-dependent options

JEL Classification: G13