Asian-barrier option pricing formulas of uncertain financial market

Yang, Xiangfeng; Zhang, Zhiqiang; Gao, Xuexu

doi:10.1016/j.chaos.2019.03.037

Cited by 52 publications

(27 citation statements)

References 17 publications

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“…Following uncertain stock model, the pricing formulas of Asian barrier option and American barrier option were deduced by Yang et al. ( 2019 ) and Gao et al. ( 2019 ), respectively.…”

Section: Introductionmentioning

confidence: 99%

Asian rainbow option pricing formulas of uncertain stock model

Gao

Liu

2021

Soft Comput

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Asian rainbow option is option on the minimum or the maximum of several average prices. In modern financial market, Asian rainbow option is an effective instrument for asset allocation and risk management. The investor with Asian rainbow option enjoys an entitlement to select a max or min from multiple assets with an exercise price at maturity date. The investor has to defray fee to acquire this right, which raises the option pricing issue. This paper mainly explores the pricing of Asian rainbow option in the uncertain financial environment, in which the underlying assets prices are treated as uncertain processes. Here, the pricing formulas of Asian rainbow option are derived under the condition that stock prices obey uncertain differential equations driven by independent Liu processes. Furthermore, some numerical examples are designed to compute the prices of these options.

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“…Following uncertain stock model, the pricing formulas of Asian barrier option and American barrier option were deduced by Yang et al. ( 2019 ) and Gao et al. ( 2019 ), respectively.…”

Section: Introductionmentioning

confidence: 99%

Asian rainbow option pricing formulas of uncertain stock model

Gao

Liu

2021

Soft Comput

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“…Yao and Zhou 20 studied the reliability in an insurance risk process via criteria such as ruin index, ruin time, and deficit. On account of the system reliability of financial products, different kinds of barrier option pricing formulas were derived by Yang et al, 21 Tian et al, 22 and Gao et al 23 In the engineering field, Li et al 24 introduced the uncertainty theory to account for such uncertainty due to small samples and build up a framework of accelerated degradation testing modeling to aid the reliability and lifetime evaluations for highly reliable products. Yu et al 25 proposed an interest‐rate model with jumps in uncertain financial markets.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of the uncertain fractional‐order dynamic system with state constraint

Jin

Xia

Gao

2021

Math Methods in App Sciences

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Uncertain fractional‐order differential equations driven by the Liu process are of significance to depict the heredity and memory features of uncertain dynamical systems. This paper primarily analyses the reliability of the uncertain fractional‐order dynamic system with a state constraint. First, consider the possibility that the real dynamical system is actually limited; the state constraint is absorbed to the ordinary uncertain fractional‐order dynamical system. The concept of reliability of uncertain system is presented innovatively, which are ulteriorly formulated through the existing first‐hitting time theorem. Second, based on the proposed reliability and under a given sufficient condition, a novel uncertain fractional‐order dynamic system with a state constraint is modeled mathematically; corresponding minimum operation ability of the uncertain system is also given. Lastly, the uncertain fractional‐order dynamic system with a state constraint is applied to different physical and financial dynamical models. Analytic expressions of reliability indexes are derived to demonstrate the reasonableness of our model. Meanwhile, expected time response and American barrier option prices are calculated by using the predictor–corrector scheme. The sensitivity analysis is also presented for the numerical examples.

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“…Sheng and Shi [13] and Gao et al [14] calculated the prices of Asian options and lookback options, respectively. ese works were generalized by Hassanzadeh and Mehrdoust [15] and Yang et al [16]. e UDEs were also used to model the interest rate in the uncertain environment by Chen and Gao [17], in which the zero-coupon bond is priced in an analytic form.…”

Section: Introductionmentioning

confidence: 99%

Interest-Rate Products Pricing Problems with Uncertain Jump Processes

Sun

Liu

2021

Discrete Dynamics in Nature and Society

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Uncertain differential equations (UDEs) with jumps are an essential tool to model the dynamic uncertain systems with dramatic changes. The interest rates, impacted heavily by human uncertainty, are assumed to follow UDEs with jumps in ideal markets. Based on this assumption, two derivatives, namely, interest-rate caps (IRCs) and interest-rate floors (IRFs), are investigated. Some formulas are presented to calculate their prices, which are of too complex forms for calculation in practice. For this reason, numerical algorithms are designed by using the formulas in order to compute the prices of these structured products. Numerical experiments are performed to illustrate the effectiveness and efficiency, which also show the prices of IRCs are strictly increasing with respect to the diffusion parameter while the prices of IRFs are strictly decreasing with respect to the diffusion parameter.

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Asian-barrier option pricing formulas of uncertain financial market

Cited by 52 publications

References 17 publications

Asian rainbow option pricing formulas of uncertain stock model

Asian rainbow option pricing formulas of uncertain stock model

Reliability analysis of the uncertain fractional‐order dynamic system with state constraint

Interest-Rate Products Pricing Problems with Uncertain Jump Processes

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