Open AccessLookback Option Pricing Problems of Uncertain Mean-Reverting Stock Model
Author(s) -
Zhaopeng Liu
Publication year - 2021
Publication title -
journal of advanced computational intelligence and intelligent informatics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.172
H-Index - 20
eISSN - 1343-0130
pISSN - 1883-8014
DOI - 10.20965/jaciii.2021.p0539
Subject(s) - mean reversion , valuation of options , short rate model , interest rate , rendleman–bartter model , computer science , stochastic game , econometrics , uncertainty theory , stock (firearms) , economics , mathematical optimization , mathematical economics , mathematics , finance , mechanical engineering , engineering
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.