경로에 의존하는 미국형 옵션의 해석적 가치 평가

학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 강명주.American options are type of options that can be exercised anytime during their life. Therefore, the valuation of such options is usually classified as optimal stopping problems or free boundary problems. I derive the analytic pricing formulas and integral equations of American chained options, Russian options with finite time horizon, American floating strike lookback options, and American maximum quanto options. To verify the derived pricing formula and the integral equation satisfied by the free boundary are correct, we numerically solve the derived integral equations using recursive integration method or simple iterative method.Chapter 1 Introduction 1 Chapter 2 Chained knock-in barrier option 3 2.1 Preliminaries 4 2.2 Analytic Valuation of Chained American Barrier Options 6 2.2.1 Crossing a single barrier 6 2.2.2 Crossing two barriers 10 2.3 Numerical results 14 2.4 Summary 19 Chapter 3 Russian option with finite time horizon 22 3.1 Model Formulation: Free Boundary Problem 23 3.2 Inhomogeneous Black-Scholes Partial Differential Equation:Mixed Boundary Problem 26 3.3 Integral Equation of Russian Options with Finite Time Horizon:Premium Decomposition 34 3.3.1 Case of r 6= q 35 3.3.2 Case of r = q 37 3.4 Valuing Russian Options: Perpetual Case 42 3.5 Numerical Results 47 3.5.1 Recursive Integration Method for Russian Option with Finite Time Horizon 47 3.5.2 Results : Qualitative analysis 51 3.5.3 Results : Comparison with Other Methods 51 3.6 Summary 59 Chapter 4 American floating strike lookback option 60 4.1 Model formulation 62 4.2 Inhomogeneous Black-Scholes equation with Neumann boundary condition 65 4.3 Integral equation representation of American floating strike lookback option 71 4.4 Perpetual American floating strike lookback option 78 4.5 Summary 85 Chapter 5 American maximum exchange rate quanto lookback option 87 5.1 Model Formulation : Free boundary problem 89 5.2 Derivation of analytic solution for two-dimensional inhomogeneous Black-Scholes PDE 93 5.2.1 Two-dimensional Inhomogeneous Black-Scholes parabolic PDE on Unrestricted Domain 93 5.2.2 Two-dimensional inhomogeneous Black-Scholes parabolic PDE : Dirichlet Boundary Conditions 95 5.2.3 Two-dimensional inhomogeneous Black-Scholes parabolic PDE : Mixed Boundary Conditions 98 5.3 Analytic Pricing of American Maximum Exchange-Rate Quanto Lookback Options 105 5.3.1 European Maximum Exchange Rate Quanto Lookback Options 106 5.3.2 American Maximum Exchange Rate Quanto Lookback Options 109 5.4 Numerical Results 114 5.4.1 An iterative method 114 5.4.2 Forward shooting grid method for two-state model 116 5.4.3 Implications 118 5.5 Summary 126 Appendix A Basic Properties of Mellin Transforms 133 A.1 Properties of Mellin transform 133 A.2 Properties of double Mellin transform 135 Appendix B Some useful lemmas 137 Abstract (in Korean) 138Docto