Valuation of stock loan under uncertain stock model with floating interest rate

A lookback option is a path-dependent option, offering a payoff that depends on the maximum or minimum value of the underlying asset price over the life of the option. This paper presents a new mean-reverting uncertain stock model with a floating interest rate to study the lookback option price, in which the processing of the interest rate is assumed to be the uncertain counterpart of the Cox–Ingersoll–Ross (CIR) model. The CIR model can reflect the fluctuations in the interest rate and ensure that such rate is positive. Subsequently, lookback option pricing formulas are derived through the α-path method and some mathematical properties of the uncertain option pricing formulas are discussed. In addition, several numerical examples are given to illustrate the effectiveness of the proposed model.

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Knock-in options of an uncertain stock model with floating interest rate

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.110324 ◽

2020 ◽

Vol 141 ◽

pp. 110324

Author(s):

Lifen Jia ◽

Wei Chen

Keyword(s):

Interest Rate ◽

Stock Model

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No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate

Fuzzy Optimization and Decision Making ◽

10.1007/s10700-016-9246-8 ◽

2016 ◽

Vol 16 (2) ◽

pp. 221-234 ◽

Cited By ~ 2

Author(s):

Xiaoyu Ji ◽

Hua Ke

Keyword(s):

Interest Rate ◽

No Arbitrage ◽

Stock Model

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Option Pricing Formulas in a New Uncertain Mean-Reverting Stock Model with Floating Interest Rate

Discrete Dynamics in Nature and Society ◽

10.1155/2020/3764589 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Zhaopeng Liu

Keyword(s):

Interest Rate ◽

Option Pricing ◽

Financial Market ◽

American Option Pricing ◽

European Option ◽

Numerical Examples ◽

Mathematical Properties ◽

Proposed Model ◽

Stock Model ◽

The Interest Rate

Options play a very important role in the financial market, and option pricing has become one of the focus issues discussed by the scholars. This paper proposes a new uncertain mean-reverting stock model with floating interest rate, where the interest rate is assumed to be the uncertain Cox-Ingersoll-Ross (CIR) model. The European option and American option pricing formulas are derived via the α -path method. In addition, some mathematical properties of the uncertain option pricing formulas are discussed. Subsequently, several numerical examples are given to illustrate the effectiveness of the proposed model.

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