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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.19 No.1
- 발행연도
- 2015.3
- 수록면
- 1 - 21 (21page)
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This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly.
By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable.
We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r ＞ d, r ≤ d, long-time or short-time maturity T.
By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable.
We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r ＞ d, r ≤ d, long-time or short-time maturity T.
목차
ABSTRACT
1. INTRODUCTION
2. THE IMPLICIT SYSTEM FOR OPTION PRICE AND FREE BOUNDARY
3. NUMERICAL ALGORITHMS
4. NUMERICAL EXPERIMENTS
5. CONCLUSIONS
REFERENCES
참고문헌 (12)
참고문헌 신청
1. [단행본] - L. BADEA / 2000 / A new formulation for the valuation of American options, I: Solution uniqueness, Analysis and Scientific Computing
2. [학술지(정기간행물)] - F. BLACK / 1973 / The pricing of options and corporate liabilities / Journal of Political Economy 81 : 637 ~ 654
3. [학술지(정기간행물)] - J. C. COX / 1979 / Option Pricing: A Simplified Approach / Journal of Financial Economics 7 : 229 ~ 264
4. [단행본] - J. C. HULL / 1998 / Introductioin to Futures and Options Markets / Prentice-Hall
5. [학술지(정기간행물)] - F. JAMSHIDIAN / 1992 / An Analysis of American Options / Review of Futures Markets 11 : 72 ~ 80
2. [학술지(정기간행물)] - F. BLACK / 1973 / The pricing of options and corporate liabilities / Journal of Political Economy 81 : 637 ~ 654
3. [학술지(정기간행물)] - J. C. COX / 1979 / Option Pricing: A Simplified Approach / Journal of Financial Economics 7 : 229 ~ 264
4. [단행본] - J. C. HULL / 1998 / Introductioin to Futures and Options Markets / Prentice-Hall
5. [학술지(정기간행물)] - F. JAMSHIDIAN / 1992 / An Analysis of American Options / Review of Futures Markets 11 : 72 ~ 80
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UCI(KEPA) : I410-ECN-0101-2016-410-001252696