European option pricing model with generalized Ornstein\u2013Uhlenbeck process under stochastic earning yield and stochastic dividend yield

N Phewchean,Y Wu

doi:10.1186/s13662-019-2210-5

Abstract

This paper aims to examine and establish the models for European option pricing which include parameters of stochastic dividend yield and stochastic earning yield. We generalize the Ornstein–Uhlenbeck process and define it as generalized Ornstein–Uhlenbeck process. We have learned that the firm stocks, according to Black–Scholes–Merton structure, obey the geometric Brownian motion process. Under a stochastic earning yield, the dividend yield complies with the generalized Ornstein–Uhlenbeck process. The firm dividend randomly deviates from the earning yield flow because of the presence of stochastic components of dynamic Wiener process of generalized Ornstein–Uhlenbeck. In this study, we model the stock price with stochastic earning yield, and stochastic dividend yield to be taking account stochastic market price of risk parameter which is mean-reverting as well. We developed explicit formulae for European call option pricing calculations. From numerical simulation, we could evaluate the performance of our new model that could be compared with other notable option pricing models by using actual option price data. The outcomes prove that our new model performance is best when compared with others.

Highlights

When making an investment decision, traders seek confidence in profit making
In Black–Scholes–Merton structure, many parameters are used to determine option price, such as dividend yield, volatility, interest rates, and time maturity [1]. This option pricing model leaves out some parameters and does not reflect real world finance situation
Generalized process of Ornstein–Uhlenbeck is defined in order to explain option pricing models when stochastic earning yield is an element of stochastic dividend yield

Summary

Introduction

When making an investment decision, traders seek confidence in profit making. They consider a derivative financial instrument: an option. Generalized process of Ornstein–Uhlenbeck is defined in order to explain option pricing models when stochastic earning yield is an element of stochastic dividend yield. Option valuation models have utilized the Ornstein–Uhlenbeck process which is an important main component for any economic study of valuation with stochastic property [2, 5, 8] Such a model is commonly used to describe the stochastic behavior of many crucial variables in the real world of financial market such as interest rates, dividends, volatility, currency exchange rates, and commodity prices [9]. With all four definitions provided, we will illustrate the construction of the pricing models, under market price of risks, that includes proposed parameters, stochastic earning yield, and stochastic dividend yield. As we consider the P/E ratio to be related to the model of option pricing in this paper, the dividend yield is a component to determine the P/E ratio

Earning Per Share

We can mathematically express the total earning yield ψ

Call options Put options