European Spread Option Pricing with the Floating Interest Rate for Uncertain Financial Market

Lidong Zhang,Xiangbo Meng,Yanmei Sun

doi:10.1155/2020/2015845

Lidong Zhang, Xiangbo Meng + Show 1 more

Open Access

https://doi.org/10.1155/2020/2015845

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Abstract

In this paper, we investigate the pricing problems of European spread options with the floating interest rate. In this model, uncertain differential equation and stochastic differential equation are used to describe the fluctuation of stock price and the floating interest rate, respectively. We derive the pricing formulas for spread options including the European spread call option and the European spread put option. Finally, numerical algorithms are provided to illustrate our results.

Highlights

Since financial derivatives have the function of hedging and risk aversion, they are widely used in the financial market
To describe uncertain dynamic systems, Liu [6] introduced the concept of uncertain processes and proposed uncertain differential equations driven by canonical Liu process
Liu [7] proposed an uncertain stock model in which stock price was described by an uncertain differential equation

Summary

Introduction

Since financial derivatives have the function of hedging and risk aversion, they are widely used in the financial market. Liu [7] proposed an uncertain stock model in which stock price was described by an uncertain differential equation. Us, basing uncertainty theory and probability theory (socalled chance theory), we study the pricing of spread options with a stochastic interest rate under uncertain environment. Liu [22] proposed the operation law of uncertain variables and calculated the inverse uncertainty distribution of strictly monotone function of uncertain variables. Ξn be independent uncertain variables with uncertainty distributions. For an uncertain variable ξ with an uncertainty distribution Φ(x), if its expected value exists, Liu [5] showed that. (iii) Every increment Cs+t − Cs is a normal uncertain variable with expected value 0 and variance t2, whose uncertainty distribution is Definition 9 (see Yao and Chen [23]). Respectively. en, M􏼈Xt ≤ Xαt , ∀t􏼉 α, M􏼈Xt > Xαt , ∀t􏼉 1 − α

Chance eory

European Spread Option Pricing Formulas

Conclusions