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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.12 No.4
- 발행연도
- 2008.12
- 수록면
- 271 - 287 (17page)
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This paper deals with American call and put options. Determining the fair price and the free boundary of an American option is a very difficult problem since they depends on each other. This paper presents numerical algorithms of finite element method based on the three-level scheme to compute both the price and the free boundary. One algorithm is designed for American call options and the other one for American put options. These algorithms are formulated on the system of the Jamshidian equation for the option price and the free boundary. Here. the Jamshidi an equation is of a kind of the nonhomogeneous Black-Scholes equations. We prove the existence and uniqueness of the numerical solution by the Lax-Milgram lemma and carried out extensive numerical experiments to compare with various methods.
목차
ABSTRACT
1. INTRODUCTION
2. THE SYSTEM OF JAMSHIDIAN EQUATION AND FREE BOUNDARY
3. WEAK FORMUALTION
4. FULLY DISCRETE METHODS
5. NUMERICAL RESULTS
6. CONCLUSION
REFERENCES
참고문헌 (15)
참고문헌 신청
F. Black / 1973 / The pricing of options and corporate liabilities / Journal of Political Economy 81:637~654
D. Lamberton / 1996 / Introduction to Stochastic Calculus Applied to Finance / Chapman and Hall, New York
R.C. Merton / 1973 / Theory of rational option pricing / Bell Journal of Economics and Management Science 4:141~183
F. Jamshidian / 1992 / An Analysis of American Options / Review of Futures Markets 11:72~80
V.A. Kholodnyi / 1997 / A Nonlinear partial differential equation for American options in the entire domain of the state variable / Nonlinear Analysis Theory Methods and Applications 30:5059~5070
D. Lamberton / 1996 / Introduction to Stochastic Calculus Applied to Finance / Chapman and Hall, New York
R.C. Merton / 1973 / Theory of rational option pricing / Bell Journal of Economics and Management Science 4:141~183
F. Jamshidian / 1992 / An Analysis of American Options / Review of Futures Markets 11:72~80
V.A. Kholodnyi / 1997 / A Nonlinear partial differential equation for American options in the entire domain of the state variable / Nonlinear Analysis Theory Methods and Applications 30:5059~5070
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UCI(KEPA) : I410-ECN-0101-2009-410-015704208