Asian rainbow option pricing formulas of uncertain stock model

Gao, Rong; Wu, Wei; Liu, Jie

doi:10.1007/s00500-021-05922-y

Cited by 15 publications

(3 citation statements)

References 27 publications

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“…In this framework, the underlying assets' prices are considered stochastic processes that follow uncertain differential equations driven by independent Liu processes which are uncertain processes with stationary and independent increments. Some numerical examples are provided to illustrate how to compute the prices of the corresponding options using the derived pricing formula [10].…”

Section: Related Researchmentioning

confidence: 99%

An Analysis of Optimized Asian Options

Chen¹,

Lu²,

Zhang³

2022

Advances in Economics, Business and Management Research

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Nowadays, the option is an indispensable financial tool in the current financial market. Moreover, the Asian option, as one of the most famous and widely used exotic options, plays a significant role in it. This paper aims to propose a new type of Asian option, which is jointly designed by the authors and makes an improvement based on the regular Asian option better to meet the demands of the current financial market. This paper provides an explicit definition and comprehensive explanation of this new Asian option and explores its unique functions in the financial market compared with the normal Asian option. Furthermore, to verify the effectiveness of the proposed option, this paper selects representative real stock prices and makes some reasonable assumptions. After using Stata to process the data, the performance of the new Asian option is analyzed, and a numerical comparison between the proposed option and the normal Asian option is made. And the effectiveness of the proposed option in mitigating risk is validated. This paper expounds on the proposed option in detail so that readers can develop a deep understanding of it. It also provides some reference for the option issuers to issue new options.

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Section: Related Researchmentioning

confidence: 99%

An Analysis of Optimized Asian Options

Chen¹,

Lu²,

Zhang³

2022

Advances in Economics, Business and Management Research

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“…Hence Gao et al [7] studied multi-asset option pricing in an uncertain financial market with jump risk. And Gao et al [6] discussed Asian rainbow option for the uncertain multi-stock model. But the European rainbow option pricing problem has not been studied.…”

Section: Introductionmentioning

confidence: 99%

Pricing rainbow option for uncertain financial market

Gao

2022

RAIRO-Oper. Res.

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Rainbow option refers to the option whose payoff depends on at least two underlying risky assets, which is justifiably one of the most significant tool to hedge risk brought by the uncertainty from ﬁnancial market. Hence, option pricing problem is always an issue with great attention. In this paper, we assume that the multiple dynamic stock prices obey uncertain differential equations without sharing dividends in the framework of uncertainty theory. Then we discuss the rainbow option pricing problem for multiple stocks in a financial market with uncertain information, give the concepts and derive pricing formulas for five scenarios including maximum call, minimum call, maximum put, minimum put, and put on 2 and call on 1. Moreover, some corresponding examples are respectively taken to illustrate the pricing formulas in five cases.

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“…Additionally, some researchers studied numerical solution for an uncertain differential equation, such as Gao [14]. Then, uncertain differential equation has been applied to uncertain fiance [15,16], uncertain optimal control [17].…”

Section: Introductionmentioning

confidence: 99%

Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations

Gao

2022

Mathematics

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Multi-dimensional uncertain differential equation is a tool to model an uncertain multi-dimensional dynamic system. Furthermore, stability has a significant role in the field of differential equations because it can be describe the effect of the initial value on the solution of the differential equation. Hence, the concept of almost sure stability is presented concerning multi-dimensional uncertain differential equation in this paper. Moreover, a stability theorem, that is a condition, is derived to judge whether a multi-dimensional uncertain differential equation is almost surely stable or not. Additionally, the paper takes a counterexample to show that the given condition is not necessary for a multi-dimensional uncertain differential equation being almost surely stable.

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Asian rainbow option pricing formulas of uncertain stock model

Cited by 15 publications

References 27 publications

An Analysis of Optimized Asian Options

An Analysis of Optimized Asian Options

Pricing rainbow option for uncertain financial market

Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations

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