Finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition
하이브리드 경계조건을 이용하여 2차원 블랙숄츠방정식을 유한차분법으로 푸는 방법
- 주제(키워드) Black–Scholes partial differential equation , finite difference method
- 발행기관 고려대학교 대학원
- 지도교수 김준석
- 발행년도 2019
- 학위수여년월 2019. 2
- 유형 Text
- 학위구분 석사
- 학과 대학원 수학과
- 세부전공 응용수학 전공
- 원문페이지 47 p
- 실제URI http://www.dcollection.net/handler/korea/000000083198
- UCI I804:11009-000000083198
- DOI 10.23186/korea.000000083198.11009.0000928
- 본문언어 영어
- 제출원본 000045978678
초록/요약
In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black–Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries such that at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain by one grid so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary value profiles.
more목차
Abstract
Contents i
List of Figures iii
List of Tables v
1 Black-Scholes partial differential equation 1
2 Introduction 5
3 Numerical solution 7
4 Numerical experiments 13
4.0.1 European call option of two-asset 13
4.0.2 Two-asset cash-or-nothing option 17
5 Conclusion 27
6 MATLAB code for closed-form solutions 29
Bibliography 41
