Lookback option pricing problem of mean-reverting stock model in uncertain environment

Miao Tian; Xiangfeng Yang; Yi Zhang

doi:10.3934/jimo.2020090

Article Contents

2021, Volume 17, Issue 5: 2703-2714. Doi: 10.3934/jimo.2020090

This issue Previous Article Bond pricing formulas for Markov-modulated affine term structure models Next Article A proximal ADMM with the Broyden family for convex optimization problems

Lookback option pricing problem of mean-reverting stock model in uncertain environment

1.
School of Mathematics, Renmin University of China, Beijing 100872, China
2.
School of Information Technology & Management, University of International, Business & Economics, Beijing 100029, China
3.
School of Economics & Management, Beijing University of Chemical, Technology, Beijing 100029, China

^* Corresponding author: Xiangfeng Yang
^* Corresponding author: Xiangfeng Yang

Received: January 31, 2019

Revised: December 31, 2019

Early access: May 2020

Published: September 2021

The second author is supported by the Program for Young Excellent Talents in UIBE (No.18YQ06).

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Abstract

A lookback option is an exotic option that allows investors to look back at the underlying prices occurring over the life of the option, and to exercise the right at assets optimal point. This paper proposes a mean-reverting stock model to investigate the lookback option in an uncertain environment. The lookback call and put options pricing formulas of the stock model are derived, and the corresponding numerical algorithms are designed to compute the prices of these two options.

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Mathematics Subject Classification: Primary: 91G99; Secondary: 91G80.

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Figure 1. Lookback call option price $ f_{call} $ with different parameters

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Figure 2. Lookback put option price $ f_{put} $ with different parameters

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