Incomplete markets, Knightian uncertainty and high-water marks

Liu, Fengjun; Niu, Yingjie; Zou, Zhentao

doi:10.1016/j.orl.2020.02.005

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…Under the assumption of the jump process, (1 + U i ) follows a log-normal distribution with mean μ and volatility σ. The value of the enterprise stock (15), enterprise bond (16), and default probability (11) under Knightian uncertainty have the following expressions…”

Section: A Particular Casementioning

confidence: 99%

“…Huang and Wang [14] also paid attention to the option pricing under Knightian uncertainty driven by the Lévy process, and established the upper and lower bounds model of European options. Liu et al [15] extended the pricing of the hedge fund compensation to the Knightianian uncertainty market and obtained the conclusion that an increase in the level of Knightian uncertainty would cause the erosion of the value of the fees and the claim. Furthermore, based on uncertainty theory proposed by Liu [16] in 2007, Liu [16] and Chen [17] proved European and American option pricing formulas, respectively.…”

Section: Introductionmentioning

confidence: 99%

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A Structural Credit Risk Model Driven by the Lévy Process under Knightian Uncertainty

2022

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The classic credit risk structured model assumes that risky asset values obey geometric Brownian motion. In reality, however, risky asset values are often not a continuous and symmetrical process, but rather they appear to jump and have asymmetric characteristics, such as higher peaks and fat tails. On the other hand, there are real Knight uncertainty risks in financial markets that cannot be measured by a single probability measure. This work examined a structural credit risk model in the Lévy market under Knight uncertainty. Using the Lévy–Laplace exponent, we established dynamic pricing models and obtained intervals of prices for default probability, stock values, and bond values of enterprise, respectively. In particular, we also proved the explicit solutions for the three value processes above when the jump process is assumed to follow a log-normal distribution. Finally, the important impacts of Knightian uncertainty on the pricing of default probability and stock values of enterprise were studied through numerical analysis. The results showed that the default probability of enterprise, the stock values, and bond values were no longer a certain value, but an interval under Knightian uncertainty. In addition, the interval changed continuously with the increase in Knightian uncertainty. This result better reflected the impact of different market sentiments on the equilibrium value of assets, and expanded decision-making flexibility for investors.

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Section: A Particular Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Structural Credit Risk Model Driven by the Lévy Process under Knightian Uncertainty

2022

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“…The study further deployed the upper and lower bounds’ model for the European option. In the study conducted by Liu et al ( 2020 ), the authors expanded the hedge fund compensation price up to Knightian uncertainty market. The study arrived at the conclusion that when the Knight uncertainty value increases, then it erodes the values of both, the fees as well as the claim.…”

Section: Introductionmentioning

confidence: 99%

Structural credit risk model driven by Lévy process under knight uncertainty

Tang

Zhong

Zhang³

et al. 2023

Ann Oper Res

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As per the projections of conventional credit risk structured model, the risky asset values tend to adhere to the geometric Brownian motion. On the contrary, the risky asset values remain a non-continuous and dynamic ones and jump based on the conditions. Is not possible to measure the real Knight Uncertainty risks in financial markets with the help of a single probability measure. In this background, the current research work analyzes a structural credit risk model that belongs to Levy market under Knight Uncertainty. With the help of Lévy-Laplace exponent, the authors developed a dynamic pricing model in this study and acquired the price intervals for default probability, stock value and the bond value of enterprise. To be specific, the study intended to establish explicit solutions for three value processes, discussed earlier, with an assumption that the jump process follows a log-normal distribution. At the end, the study also conducted numerical analysis to understand the crucial role played by Knight Uncertainty upon the pricing of default probability and the stock value of the enterprise.

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Robust risk-taking under a sustainable constraint

Luo

Yan

et al. 2022

Operations Research Letters

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Incomplete markets, Knightian uncertainty and high-water marks

Cited by 5 publications

References 17 publications

A Structural Credit Risk Model Driven by the Lévy Process under Knightian Uncertainty

A Structural Credit Risk Model Driven by the Lévy Process under Knightian Uncertainty

Structural credit risk model driven by Lévy process under knight uncertainty

Robust risk-taking under a sustainable constraint

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