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JACIII Vol.25 No.5 pp. 539-545
doi: 10.20965/jaciii.2021.p0539
(2021)

Paper:

# Lookback Option Pricing Problems of Uncertain Mean-Reverting Stock Model

## Zhaopeng Liu†

School of Mathematics and Statistics, Suzhou University
East Campus of Suzhou University, Education Park, Suzhou, Anhui 234000, China

Corresponding author

July 13, 2020
Accepted:
March 20, 2021
Published:
September 20, 2021
Keywords:
uncertainty theory, uncertain mean-reverting stock model, floating interest rate, lookback options
Abstract

A lookback option is a path-dependent option, offering a payoff that depends on the maximum or minimum value of the underlying asset price over the life of the option. This paper presents a new mean-reverting uncertain stock model with a floating interest rate to study the lookback option price, in which the processing of the interest rate is assumed to be the uncertain counterpart of the Cox–Ingersoll–Ross (CIR) model. The CIR model can reflect the fluctuations in the interest rate and ensure that such rate is positive. Subsequently, lookback option pricing formulas are derived through the α-path method and some mathematical properties of the uncertain option pricing formulas are discussed. In addition, several numerical examples are given to illustrate the effectiveness of the proposed model.

Z. Liu, “Lookback Option Pricing Problems of Uncertain Mean-Reverting Stock Model,” J. Adv. Comput. Intell. Intell. Inform., Vol.25 No.5, pp. 539-545, 2021.
Data files:
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Last updated on Sep. 21, 2023