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We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consis\-tent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the payoff 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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참고문헌 (16)
참고문헌 신청
Z. Cen / 2013 / Finite difference scheme with a moving mesh for pricing Asian options / Appl. Math. Comput 219(16):8667~8675
D. J. Duffy / 2006 / Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach / John Wiley and Sons
A. Esser / 2003 / General valuation principles for arbitrary payoffs and applications to power options under stochastic volatility / Financ. Markets and Portfolio Manage 17(3):351~372
A. Golbabai / 2013 / A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options / Comput. Econ :1~21
E. G. Haug / 1998 / The Complete Guide to Option Pricing Formulas / McGraw-Hill
D. J. Duffy / 2006 / Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach / John Wiley and Sons
A. Esser / 2003 / General valuation principles for arbitrary payoffs and applications to power options under stochastic volatility / Financ. Markets and Portfolio Manage 17(3):351~372
A. Golbabai / 2013 / A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options / Comput. Econ :1~21
E. G. Haug / 1998 / The Complete Guide to Option Pricing Formulas / McGraw-Hill
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