Valuation of Currency Option Based on Uncertain Fractional Differential Equation

Uncertain fractional differential equations (UFDEs) are excellent tools for describing complicated dynamic systems. This study analyzes the valuation problems of currency options based on UFDE under the optimistic value criterion. Firstly, a new uncertain fractional currency model is formulated to d...

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Bibliographic Details
Published inFractal and fractional Vol. 8; no. 8; p. 478
Main Authors Wang, Weiwei, Ralescu, Dan A, Xue, Xiaojuan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2024
Subjects
Analysis
Brownian motion
Criteria
currency option
Currency options
Differential equations
Expected values
Foreign exchange
Foreign exchange markets
Foreign exchange rates
Fractional calculus
fractional-order differential equation
Interest rates
Investments
Investors
Numerical analysis
optimistic value
Prices and rates
Random variables
Securities markets
Securities prices
Simulation methods
Stochastic models
uncertain hypothesis test
uncertainty theory
Valuation
Volatility
Germany
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Summary:Uncertain fractional differential equations (UFDEs) are excellent tools for describing complicated dynamic systems. This study analyzes the valuation problems of currency options based on UFDE under the optimistic value criterion. Firstly, a new uncertain fractional currency model is formulated to describe the dynamics of the foreign exchange rate. Then, the pricing formulae of European, American, and Asian currency options are obtained under the optimistic value criterion. Numerical simulations are performed to discuss the properties of the option prices with respect to some parameters. Finally, a real-world example is provided to show that the uncertain fractional currency model is superior to the classical stochastic model.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8080478