The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method
In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1942762 |
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| Summary: | In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution. |
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| ISSN: | 1687-9120 1687-9139 |