Finite volume method for the Black-Scholes equation transformed on finite interval

Valkov, Radoslav L.

doi:10.1063/1.4766769

Cited by 1 publication

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“…Note that the analysis in Case 1 can not be applied here because the flux degenerates at x = 0. To solve this difficulty, following [2,6,18,21], we will reconsider the flux ODE with an extra degree of freedom in the following form…”

Section: Space Discretizationmentioning

confidence: 99%

“…Let us introduce the finite element space V h by specifying it's basis {φ i } N i=0 . Following [6,18] we introduce the functions…”

Section: Space Discretizationmentioning

confidence: 99%

“…Furthermore, using the flux approximations (11), (12), (18), obtained in Cases 1, 2 and 3 respectively, we define by ρ h (u) an approximation to ρ(u)| Ii := ρ i (u), i = 0, . .…”

Section: Space Discretizationmentioning

confidence: 99%

“…Some results, concerning the case of the transformed Black-Scholes equation above, are reported in [18].…”

Section: Introductionmentioning

confidence: 99%

“…Numerical experiments are discussed in the last section. Some results, concerning the case of the transformed Black-Scholes equation above, are reported in [18].…”

Section: Introductionmentioning

confidence: 99%

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Fitted finite volume method for a generalized Black–Scholes equation transformed on finite interval

Valkov

2013

Numer Algor

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A generalized Black-Scholes equation is considered on the semiaxis. It is transformed on the interval (0, 1) in order to make the computational domain finite. The new parabolic operator degenerates at the both ends of the interval and we are forced to use the Gärding inequality rather than the classical coercivity. A fitted finite volume element space approximation is constructed. It is proved that the time θ-weighted full discretization is uniquely solvable and positivity-preserving. Numerical experiments, performed to illustrate the usefulness of the method, are presented.

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Section: Space Discretizationmentioning

confidence: 99%

“…Let us introduce the finite element space V h by specifying it's basis {φ i } N i=0 . Following [6,18] we introduce the functions…”

Section: Space Discretizationmentioning

confidence: 99%

“…Furthermore, using the flux approximations (11), (12), (18), obtained in Cases 1, 2 and 3 respectively, we define by ρ h (u) an approximation to ρ(u)| Ii := ρ i (u), i = 0, . .…”

Section: Space Discretizationmentioning

confidence: 99%

“…Some results, concerning the case of the transformed Black-Scholes equation above, are reported in [18].…”

Section: Introductionmentioning

confidence: 99%

“…Numerical experiments are discussed in the last section. Some results, concerning the case of the transformed Black-Scholes equation above, are reported in [18].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fitted finite volume method for a generalized Black–Scholes equation transformed on finite interval

Valkov

2013

Numer Algor

View full text Add to dashboard Cite

show abstract

Finite volume method for the Black-Scholes equation transformed on finite interval

Cited by 1 publication

References 0 publications

Fitted finite volume method for a generalized Black–Scholes equation transformed on finite interval

Fitted finite volume method for a generalized Black–Scholes equation transformed on finite interval

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