Beating the Omega Clock: An Optimal Stopping Problem with Random Time-Horizon Under Spectrally Negative Lévy Models

The Annals of Applied Probability, Forthcoming

35 Pages Posted: 14 Jun 2017  

Neofytos Rodosthenous

Queen Mary, University of London

Hongzhong Zhang

Columbia University

Date Written: June 13, 2017

Abstract

We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative L'evy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying L'evy process below a level y, exceeds an independent exponential random variable with mean 1/q. We show that the shape of the value function varies qualitatively with different values of q and y. In particular, we show that for certain values of q and y, some quantitatively different but traditional up-crossing strategies are still optimal, while for other values we may have two disconnected continuation regions, resulting in the optimality of two-sided exit strategies. By deriving the joint distribution of the discounting factor and the underlying process under a random discount rate, we give a complete characterization of all optimal exercising thresholds. Finally, we present an example with a compound Poisson process plus a drifted Brownian motion.

Keywords: L'evy process, optimal stopping, Omega clock, occupation times, random discount rate, impatience

JEL Classification: C41, G12

Suggested Citation

Rodosthenous, Neofytos and Zhang, Hongzhong, Beating the Omega Clock: An Optimal Stopping Problem with Random Time-Horizon Under Spectrally Negative Lévy Models (June 13, 2017). The Annals of Applied Probability, Forthcoming . Available at SSRN: https://ssrn.com/abstract=2985493

Neofytos Rodosthenous

Queen Mary, University of London ( email )

School of Mathematical Sciences
Mile End Road
London, E1 4NS
United Kingdom

Hongzhong Zhang (Contact Author)

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Paper statistics

Downloads
10
Abstract Views
162