Robust and accurate method for the black-scholes equations with payoff-consistent extrapolation

Yongho Choi, Darae Jeong, Junseok Kim, Young Rock Kim, Seunggyu Lee, Seungsuk Seo, Minhyun Yoo

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the pay-off profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.

Original languageEnglish
Pages (from-to)297-311
Number of pages15
JournalCommunications of the Korean Mathematical Society
Volume30
Issue number3
DOIs
Publication statusPublished - 2015

Fingerprint

Black-Scholes Equation
Extrapolation
Boundary conditions
Numerical Solution
Numerical Scheme
Dirichlet Boundary Conditions
Pricing
High-dimensional
Verify
Robustness
Derivative
Numerical Results
Term
Derivatives
Demonstrate
Costs

Keywords

  • Extrapolation
  • High correlation
  • Linear boundary condition
  • Multi-dimensional black-scholes equations
  • Operator splitting method

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Robust and accurate method for the black-scholes equations with payoff-consistent extrapolation. / Choi, Yongho; Jeong, Darae; Kim, Junseok; Kim, Young Rock; Lee, Seunggyu; Seo, Seungsuk; Yoo, Minhyun.

In: Communications of the Korean Mathematical Society, Vol. 30, No. 3, 2015, p. 297-311.

Research output: Contribution to journalArticle

Choi, Yongho ; Jeong, Darae ; Kim, Junseok ; Kim, Young Rock ; Lee, Seunggyu ; Seo, Seungsuk ; Yoo, Minhyun. / Robust and accurate method for the black-scholes equations with payoff-consistent extrapolation. In: Communications of the Korean Mathematical Society. 2015 ; Vol. 30, No. 3. pp. 297-311.
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AU - Choi, Yongho

AU - Jeong, Darae

AU - Kim, Junseok

AU - Kim, Young Rock

AU - Lee, Seunggyu

AU - Seo, Seungsuk

AU - Yoo, Minhyun

PY - 2015

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N2 - We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the pay-off profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.

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