On the regularity of American options with regime-switching uncertainty

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Jacka, Saul D.^1,2  Ocejo, Adriana³ 

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] Alan Turing Inst, British Lib, 96 Euston Rd, London NW1 2DB, England

[3] Univ North Carolina Charlotte, Dept Math & Stat, Charlotte, NC 28223 USA

关键词: Regime-switching;    Markov-modulated;    Time-change;    Coupling;    American option;    Initial boundary value problem;   

DOI  :  10.1016/j.spa.2017.06.007

来源: Elsevier

【 摘 要 】

We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free