Exponential Time Integration and  Second‐Order Difference Scheme for a Generalized Black‐Scholes Equation

Cen, Zhongdi; Le, Anbo; Xu, Aiqiang

doi:10.1155/2012/796814

Cited by 8 publications

(11 citation statements)

References 20 publications

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“…This approximation is similar to the one in [21] with central difference on non uniform grid. We approximate the convection term using the standard upwinding technique as following…”

mentioning

confidence: 58%

“…In recent years, the computational complexity of mathematical models employed in financial mathematics has witnessed a tremendous growth (see [22,21,15] and references therein). The aims of this paper is to solve numerically our delayed nonlinear model for firm market value along with the corresponding RPDEs, using real data from firms.…”

Section: Introductionmentioning

confidence: 99%

“…The function x → max(x, 0) is not smooth, it important to approximate it by a smooth function. The approximation in [21] is a fourth-order smooth function denoted π and defined by…”

mentioning

confidence: 99%

See 2 more Smart Citations

A Stochastic Delay Model for Pricing Debt and Equity: Numerical Techniques and Applications

Kemajou¹,

Tambue²,

Mohammed³

2013

Preprint

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In the accompanied paper [14], a delayed nonlinear model for pricing corporate liabilities was developed. Using self-financed strategy and duplication we were able to derive two Random Partial Differential Equations (RPDEs) describing the evolution of debt and equity values of the corporate in the last delay period interval. In this paper, we provide numerical techniques to solve our delayed nonlinear model along with the corresponding RPDEs modeling the debt and equity values of the corporate.Using financial data from some firms, we compare numerical solutions from both our nonlinear model and classical Merton model [7] to the real corporate data. From this comparison, it comes up that in corporate finance the past dependence of the firm value process may be an important feature and therefore should not be ignored.

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“…This approximation is similar to the one in [21] with central difference on non uniform grid. We approximate the convection term using the standard upwinding technique as following…”

mentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Stochastic Delay Model for Pricing Debt and Equity: Numerical Techniques and Applications

Kemajou¹,

Tambue²,

Mohammed³

2013

Preprint

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“…It is obviously that the decrease of the collocation points can improve the efficiency of the algorithm. The performance of Mei's interval wavelet [4] relates to the external interpolation points ( ), and the choice scheme of was not given in [3]. It was pointed out in [23] that the bigger usually introduces bigger condition number which can decrease the precision greatly.…”

Section: Black-scholes Equation and Its Interval Wavelet Approximationmentioning

confidence: 99%

“…In contrast with the traditional Black-Scholes equation, it is almost impossible to find the analytical solution of the nonlinear Black-Scholes equations. Most of the numerical schemes focus on the finite difference methods [2,3]. As the matter of fact, the wavelet precise integration method (WPIM) is a simple and effective method for linear partial differential equations proposed by Mei et al [4].…”

Section: Introductionmentioning

confidence: 99%

Construction of Interval Shannon Wavelet and Its Application in Solving Nonlinear Black-Scholes Equation

Liu

2014

Mathematical Problems in Engineering

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Interval wavelet numerical method for nonlinear PDEs can improve the calculation precision compared with the common wavelet. A new interval Shannon wavelet is constructed with the general variational principle. Compared with the existing interval wavelet, both the gradient and the smoothness near the boundary of the approximated function are taken into account. Using the new interval Shannon wavelet, a multiscale interpolation wavelet operator was constructed in this paper, which can transform the nonlinear partial differential equations into matrix differential equations; this can be solved by the coupling technique of the wavelet precise integration method (WPIM) and the variational iteration method (VIM). At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical results show that this method can decrease the boundary effect greatly and improve the numerical precision in the whole definition domain compared with Yan’s method.

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A novel higher-order efficient computational method for pricing European and Asian options

Bansal,

Natesan

2024

Numer Algor

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Exponential Time Integration and Second‐Order Difference Scheme for a Generalized Black‐Scholes Equation

Cited by 8 publications

References 20 publications

A Stochastic Delay Model for Pricing Debt and Equity: Numerical Techniques and Applications

A Stochastic Delay Model for Pricing Debt and Equity: Numerical Techniques and Applications

Construction of Interval Shannon Wavelet and Its Application in Solving Nonlinear Black-Scholes Equation

A novel higher-order efficient computational method for pricing European and Asian options

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