Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2022-01-28
Number: 22-007/IV
Author-Name: Jean-Claude Hessing
Author-Workplace-Name: Erasmus Universiteit Rotterdam
Author-Name: Rutger-Jan Lange
Author-Workplace-Name: Erasmus Universiteit Rotterdam
Author-Name: Daniel Ralph
Author-Workplace-Name: Cambridge Judge Business School
Title: This article establishes the Poisson optional stopping times (POST) method by Lange et al. (2020) as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker is permitted to “stop”, i.e. exercise the option, only at a set of Poisson arrival times; this can be viewed as a liquidity constraint or “penalty” that limits access to optionality. We use monotonicity arguments in function space to establish that the POST algorithm either (i) finds the solution or (ii) demonstrates that no solution exists. The monotonicity of POST carries over to the discretised setting, where we additionally show geometric convergence and provide convergence bounds. For jump-diffusion processes, dense matrix factorisation may be avoided by using a suitable operator-splitting method for which we prove convergence. We also highlight a connection with linear complementarity problems (LCPs). We use the POST algorithm to value American options and compute early-exercise boundaries for Kou’s jump-diffusion model and Heston’s stochastic volatility model, illustrating the breadth of application and numerical reliability of the method.
Classification-JEL: C61, G13, C44
Keywords: Optimal stopping, Penalty method, HJB equation, Contraction, Fixed Point, Operator Splitting, Implicit Explicit, Linear Complementarity Problem
File-URL: https://papers.tinbergen.nl/22007.pdf
File-Format: application/pdf
File-Size: 572,143 bytes
Handle: RePEc:tin:wpaper:20220070