Option Pricing Formulas in a New Uncertain Mean-Reverting Stock Model with Floating Interest Rate

Zhaopeng Liu,Filippo Cacace

doi:10.1155/2020/3764589

Abstract

Options play a very important role in the financial market, and option pricing has become one of the focus issues discussed by the scholars. This paper proposes a new uncertain mean-reverting stock model with floating interest rate, where the interest rate is assumed to be the uncertain Cox-Ingersoll-Ross (CIR) model. The European option and American option pricing formulas are derived via the α -path method. In addition, some mathematical properties of the uncertain option pricing formulas are discussed. Subsequently, several numerical examples are given to illustrate the effectiveness of the proposed model.

Highlights

Previous studies of option pricing are based on the assumption that the underlying asset price follows the stochastic differential equation [1,2,3,4]
We proposed a new uncertain stock model with floating interest rate. e European option and American option pricing formulas are investigated under the assumption that the underlying stock price follows an uncertain mean-reverting stock model, and the interest rate follows an uncertain CIR model
DXt a2 − b2Xt􏼁dt + σ2dC2t, where a1 represents the rate of adjustment of rt, b1 represents the average interest rate, σ1 represents the interest rate diffusion, a1, b1, σ1, a2, b2, σ2 are constants, and C1t and C2t are independent canonical Liu processes

Summary

Introduction

Previous studies of option pricing are based on the assumption that the underlying asset price follows the stochastic differential equation [1,2,3,4]. Liu [6] proposed the uncertain stock model and deduced the European option pricing formulas. Peng and Yao [8] proposed an uncertain stock model with mean-reverting process. Yin et al [11] gave the lookback option pricing formulas of uncertain exponential Ornstein-Uhlenbeck model, and Wang and Chen [12] derived Asian options pricing formulas in an uncertain stock model with floating interest rate. Zhang et al [13] investigated the pricing problem of lookback options for uncertain financial market, and so on. E European option and American option pricing formulas are investigated under the assumption that the underlying stock price follows an uncertain mean-reverting stock model, and the interest rate follows an uncertain CIR model We proposed a new uncertain stock model with floating interest rate. e European option and American option pricing formulas are investigated under the assumption that the underlying stock price follows an uncertain mean-reverting stock model, and the interest rate follows an uncertain CIR model

Preliminaries

European Option Pricing Formulas

Uncertain Mean-Reverting Stock Model with Floating Interest Rate

American Option Pricing Formulas

Conclusions