Robust upper bounds for American put options

• DOI: http://doi.org/10.1002/fut.21961
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 15 February 2018

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Revised: 30 July 2018

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Accepted: 6 August 2018

DOI: 10.1002/fut.21961

RESEARCH ARTICLE

Robust upper bounds for American put options

Ye Du

1

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Shan Xue

2

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Yanchu Liu

3

1

Western Business School, Southwestern

University of Finance and Economics,

Chengdu, China

2

School of Finance, Southwestern

University of Finance and Economics,

Chengdu, China

3

Lingnan (University) College, Sun

Yat‐sen University, Guangzhou, China

Correspondence

Yanchu Liu, Lingnan (University)

College, Sun Yat‐sen University,

510275 Guangzhou, China.

Email: liuych26@mail.sysu.edu.cn

Funding information

National Natural Science Foundation of

China, Grant/Award Numbers: 11501464,

11761141007, 71501196, 71721001;

National Social Science Fund of China,

Grant/Award Number: 17ZDA073;

Innovative Research Team Project of

Guangdong Province of China, Grant/

Award Number: 2016WCXTD001;

Natural Science Foundation of

Guangdong Province of China, Grant/

Award Number: 2014A030312003

Abstract

In this paper, we develop robust and model‐free upper bounds for American put

option prices. Our bounds have all of those appealing features of the upper

bounds for European options provided in DeMarzo et al. (2016, Robust option

pricing: Hannan and Blackwell meet Black and Scholes, Journal of Economic

Theory, 410‐434) but cover more popular derivatives in practice. Numerical and

empirical investigations illustrate the performance of our method.

KEYWORDS

American option pricing, gradient strategies, regret minimization, robust upper bounds

JEL CLASSIFICATION

C73, D81, G13

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INTRODUCTION

Option pricing has been an important topic in finance for decades. Various celebrated model‐based approaches,

such as the Black–Scholes–Merton model (Black & Scholes, 1973), the Heston stochastic volatility model

(Heston, 1993), the jump‐diffusion model (Kou, 2002), among others, have been proposed to price financial

options traded on either exchanges or over‐the‐counter markets (see Broadie and Detemple (2004) for an

excellent survey). Those models have proved successful in generating tractable or numerically efficient pricing

formulas which partially fit certain stylized empirical facts observed in financial markets. Contrarily, the model

risk, as an inevitable issue for any model‐based method, has attracted a great deal of attention among researchers

and practitioners, especially after the financial crisis in 2008. This concern substantially motivates a growing

literature on model‐independent bounds for option prices, which can be deliberately used for evaluating the

accuracy of different models and facilitating general risk management practice. Research progress on bounds for

prices of European‐style options is comprehensively reviewed in Kahalé (2017), who also develops new bounds

delivered numerically through convex programming based on optimal super‐/subreplication strategies. Another

closely related work is Kahalé (2016), in which lower bounds on discretely monitored variance swaps in terms of

a continuum of European call option prices with the same maturity are obtained. These results, however, cannot

cover the early‐exercise feature of American options.

J Futures Markets. 2019;39:3–14. wileyonlinelibrary.com/journal/fut © 2018 Wiley Periodicals, Inc.

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