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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊德良(Der-Liang Young) | |
dc.contributor.author | Chia-Peng Sun | en |
dc.contributor.author | 孫嘉蓬 | zh_TW |
dc.date.accessioned | 2021-06-12T18:32:25Z | - |
dc.date.available | 2016-08-16 | |
dc.date.copyright | 2011-08-16 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-08-08 | |
dc.identifier.citation | [1] Ahn, D. H.; Gao, B.; Figlewski, S. (1999): Pricing Discrete Barrier Options with the Adaptive Mesh Model. The Journal of Derivatives, Vol. 6, No. 4, pp. 33–44.
[2] Ait-Sahalia, Y.; Lo, A. W. (1998): Nonparametric Estimation of State-price Densities Implicit in Financial Asset Prices. The Journal of Finance, Vol. 53, Iss. 2, pp. 499–547. [3] Albert, M.; Fink, J.; Fink, K. (2008): Adaptive Mesh Modeling and Barrier Option Pricing Under a Jump-Diffusion Process. Journal of Financial Research, Vol. 31, No. 4, pp. 381-408. [4] Almendral, A.; Oosterlee, C. W. (2005): Numerical Valuation of Options with Jumps in the Underlying. Applied Numerical Mathematics, Vol. 53, pp. 1-18. [5] Almendral, A.; Oosterlee, C. W. (2007): On American Options Under the Variance Gamma Process. Applied Mathematical Finance, Vol. 14, No. 2, pp. 131-152. [6] Amin, K. I.; Jarrow, R. A. (1992): Pricing Options on Risky Assets in a Stochastic Interest Rate Economy. Mathematical Finance, Vol. 2, Iss. 4, pp. 217-237. [7] Amin, K. I.; Ng, V. K. (1993) Option Valuation with Systematic Stochastic Volatility. Journal of Finance, Vol. 48, pp. 881-910. [8] Amin, K. I. (1993): Jump-Diffusion Option Valuation in Discrete Time. Journal of Finance, Vol. 48, pp. 1833-1863. [9] Andersen, L.; Andreasen, J. (2000): Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing. Review of Derivatives Research, Vol. 4, pp. 231-262. [10] Avellaneda, M.; Levy, A.; Paras, A. (1995): Pricing and Hedging Derivative Securities in Markets with Uncertain Volatilities. Applied Mathematical Finance, Vol. 2, pp. 73–88. [11] Avellaneda, M.; Paras, A. (1994): Dynamic Hedging portfolios for Derivative Securities in the Presence of Large Transaction Costs. Applied Mathematical Finance, Vol. 1, pp. 165–194. [12] Averbukh, V. (1997): Pricing American Options Using Monte Carlo Simulation. Ph.D. dissertation, Cornell University, NY, USA. [13] Babbs, S. (2000): Binomial Valuation of Lookback Options. Journal of Economics Dynamics and Control, Vol. 24, Iss. 11-12, pp. 1499-1525. [14] Bailey, W.; Stulz, R. M. (1989): The Pricing of Stock Index Options in a General Equilibrium Model. Journal of Financial and Quantitative Analysis, Vol. 24, pp. 1-12. [15] Bakshi, G.; Cao, C.; Chen, Z. (1997): Empirical Performance of Alternative Option Pricing Models. The Journal of Finance, Vol. 5, pp. 2003-2049. [16] Bakshi, G., Cao, C., and Chen, Z. (2000): Pricing and Hedging Long-term Options. Journal of Econometrics, Vol. 94, Iss. 1-2, pp. 277-318. [17] Bakshi, G., and Chen, Z. (1997): An Alternative Valuation Model for Contingent Claims. Journal of Financial Economics, Vol. 44, pp. 123-165. [18] Bakshi, G., and Chen, Z. (1997): Equilibrium Valuation of Foreign Exchange Claims. Journal of Finance, Vol. 52, pp. 799-826. [19] Bates, D. S. (1991): The Crash of 87: Was It Expected? The Evidence from Options Markets. Journal of Finance, Vol. 46, pp. 1009-1044. [20] Bates, D. S. (1996): Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Options. Review of Financial Studies, Vol. 9, pp. 69-108. [21] Bates, D. S. (2000): Post-87 Crash Fears in S&P 500 Futures Option Market. Journal of Econometrics, Vol. 94, Iss. 1-2, pp. 181-238. [22] Bellman, R. E.; Kashef, B. G.; Casti, J. (1972): Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equations. Journal of Computational Physics, Vol. 10, pp. 40–52. [23] Bellman, R. E., Kashef, B. G. and Vasudevan, R. (1974): The Inverse Problem of Estimating Heart Parameters from Cardiograms. Mathematical Biosciences, Vol. 19, pp. 321-230. [24] Bert C. W., Malik M. (1996): Differential Quadrature Method in Computational Mechanics, A Review. Applied Mechanics Reviews, Vol. 49, Iss.1, pp.1–28. [25] Bert C. W., Wang X., Striz A. G. (1993): Differential Quadrature for Static and Free Vibration Analyses of Anisotropic Plates. International Journal of Solids and Structures, Vol. 30, Iss. 13, pp. 1737-1744. [26] Black, F.; Scholes, M. (1973): The Pricing of Options and Corporate Liabilities. The Journal of Political Economy, Vol. 81, pp. 637–654. [27] Boyle, P.P., (1977): Options: A Monte Carlo approach. Journal of Financial Economics, Vol. 4, Issue 3, pp. 323-338. [28] Boyle, P.P., (1986): Option Valuation Using a Three-Jump Process. International Options Journal, Vol. 3, pp. 7-12. [29] Briani, M.; Natalini, R.; Russo, G. (2007): Implicit-Explicit Numerical Schemes for Jump-Diffusion Processes. Calcolo, Vol. 44, No. 1, pp. 33-57. [30] Broadie, M.; Yamamoto, Y. (2003): Application of the Fast Gauss Transform to Option Pricing. Management Science, Vol. 49, No. 8, pp. 1071-1088. [31] Broadie M.; Detemple J. (1996): American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods. The Review of Financial Studies, Vol. 9, No. 4, pp. 1211-1250. [32] Carr, P.; Mayo, A. (2007): On the Numerical Evaluation of Option Prices in Jump Diffusion Processes. The European Journal of Finance, Vol. 13, No. 4, pp. 353-372. [33] Chang C. T.; C. S. Tsai; T. T. Lin (1993): The Modified Differential Quadratures and Their Applications. Chemical Engineering Communications, Vol. 123, pp. 135–164. [34] Chen C.N. (2000): Solution of Anisotropic Nonuniform Plate Problems by the Differential Quadrature Finite Difference Method. Computational Mechanics, Vol. 27, pp. 273-280. [35] Chen W.; Zhong T.; Liang S. (1997): On the DQ analysis of Geometrically Nonlinear Vibration of Immovably Simply Supported Beams. Journal of Sound and Vibration, Vol. 206, Iss.5, pp.745–748. [36] Cheuk, T. H. F.; Vorst, C. T. F. (1996): Complex Barrier Options. The Journal of Derivatives, Vol. 4, No. 1, pp. 8-22. [37] Civan, F.; Sliepcevich C. M. (1983): Application of Differential Quadrature to Transport Processes. Journal of Mathematical Analysis and Applications, Vol. 93, Issue 1, pp. 206-221. [38] Civan, F.; Sliepcevich C. M. (1984) Differential Quadrature for Multi-dimensional Problems. Journal of Mathematical Analysis and Applications, Vol. 101, Issue 2, pp. 423-443. [39] Clarke, N.; Parrott, K. (1999): Multigrid for American Option Pricing with Stochastic Volatility. Applied Mathematical Finance, Vol. 6, pp. 177–195. [40] Clift, S. S.; Forsyth, P. A. (2008): Numerical Solution of Two-Asset Jump Diffusion Models for Option Valuation. Applied Numerical Mathematics, Vol. 58, pp. 743-782. [41] Coleman, T. F.; Li, Y.; Verma, A. (1999): Reconstructing the Unknown Local Volatility Function. Journal of Computational Finance, Vol. 2, pp. 77–100. [42] Cont, R.; Voltchkova, E. (2005): A Finite-Difference Scheme for Option Pricing in Jump Diffusion and Exponential Levy Processes. SIAM Journal on Numerical Analysis, Vol. 43, No. 4, pp. 596-1626. [43] Cooney, M. (2000): Report on the Accuracy and Efficiency of the Fitted Methods for Solving the Black-Scholes equation for European and American Options. Working report, Datasim Education Ltd, Dublin. [44] Cox, J; Ross, S. (1976): The Valuation of Options for Alternative Stochastic Processes. Journal of Financial Economics, Vol. 3, pp. 145-166. [45] Cox, J.; Ross, S.; Rubinstein, M. (1979): Option Pricing: a Simplified Approach. Journal of Financial Economics, Vol. 7, pp. 229–263. [46] Ding, H.; Shu, C.; Yeo, K.S.; Xu, D. (2006): Numerical Computation of Three-Dimensional Incompressible Viscous Flows in the Primitive Variable Form by Local Multiquadric Differential Quadrature Method. Computer Methods in Applied Mechanics and Engineering, Vol. 195, pp. 516–533. [47] During, B.; Fournie, M.; Jungel, A. (2004): Convergence of a High-Order Compact Finite Difference Scheme for a Nonlinear B;ack-Scholes Equation. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 38, pp. 359-369. [48] Duffy, D. J. (1980): Uniformly Convergent Difference Schemes for Problems with a Small Parameter in the Leading Derivative, PhD thesis, Trinity College, Dublin, Ireland. [49] Duffy, D. J. (2006): Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. John Wiley & Sons, Ltd. [50] Duffie, D., Pan, J., Singleton, K. (2000): Transform Analysis and Asset Pricing for Affine Jump-diffusions. Econometrica, Vol. 68, pp. 1343-1376. [51] Eraker, B.; Johnnes, M.; Polson, N. (2003): The Impact of Jumps in Volatility and Returns. Journal of Finance, Vol. 58, No. 3, pp. 1269-1300. [52] Feng, L.; Linesky, V. (2008): Pricing Options in Jump-Diffusion Models: an Extrapolation Approach. Operations Research, Vol. 56, No. 2, pp. 304-325. [53] Figlewski, S.; Gao, B. (1999): The Adaptive Mesh Model: a New Approach to Efficient Option Pricing. Journal of Financial Economics, Vol. 53, pp. 313–351. [54] Fonseca, J. D.; Grasselli, M.; Tebaldi, C. (2007): Option Pricing When Correlations are Stochastic: an Analytical Framework. Review of Derivatives Research, Vol. 10, No. 2, pp. 151-180. [55] Forsyth, P. A.; Vetzal, K. R.; Zvan, R. (1999): A Finite Element Approach to the Pricing of Discrete Lookbacks with Stochastic Volatility. Applied Mathematical Finance, Vol. 6, pp. 87–106. [56] Frey, R.; Stremme, A. (1997): Market Volatility and Feedback Effects from Dynamic Hedging. Mathematical Finance, Vol. 7, pp. 351-374. [57] Geman, H.; Yor, M. (1996): Pricing and Hedging Double-barrier Options: a Probabilistic. Mathematical Finance, Vol. 6, No. 4, pp. 365-378. [58] Geske, R.; Shastri, K. (1985): Valuation by Approximation: a Comparison of Option Valuation Techniques. Journal of Financial and Quantitative Analysis, Vol. 20, pp. 45–771. [59] Gilli, M.; Kellezi, E.; Pauletto, G. (2002): Solving Finite Difference Schemes Arising in Trivariate Option Pricing. Journal of Economic Dynamics & Control, Vol. 26, pp. 1499-1515. [60] Greengard, L.; Strain, J. (1991): The Fast Gauss Transform. SIAM Journal on Scientific and Statistical Computing, Vol. 12, pp. 79-94. [61] Gutierrez, R. H.; Laura, P. A. A.; Rossi, R.E. (1994): The Method of Differential Quadrature and its Application to the Approximate Solution of Ocean Engineering problems. Ocean Engineering, Vol. 21, Iss. 1, pp. 57-66. [62] Gutierrez, R. H.; Laura P. A. A.; Sanzi H.C.; Elvira, G. (1995): Vibrations of a Rectangular Plate of Non-uniform Thickness Partially Embedded in a Winker Medium. Journal of Sound and Vibration, Vol. 185, Iss. 5, pp. 910-914. [63] Gutierrez, R. H.; Laura, P. A. A. (1999): Use of the Differential Quadrature Method when dealing with Transverse Vibrations of a Rectangular Plate subjected to a Non-uniform Stress Distribution Field. Journal of Sound and Vibration, Vol. 220, Iss. 4, pp. 765-769. [64] d’Halluin, Y.; Forsyth, P. A.; Labahn, G (2004): A Penalty Method for American options with Jump Diffusion Processes. Numerische Mathematik, Vol. 97, pp. 321-352. [65] d’Halluin, Y.; Forsyth, P. A.; Labahn, G (2005): A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion. SIAM Journal on Scientific Computing, Vol. 27, pp. 315-345. [66] d’Halluin, Y.; Forsyth, P. A.; Vetzal, K. R. (2005): Robust Numerical Methods for Contingent Claims under Jump Diffusion Processes. IMA Journal of Numerical Analysis, Vol. 25, pp. 87-112. [67] Haug, E. (1998): The Complete Guide to Option Pricing Formulas. McGraw-Hill, New York. [68] Heider, P (2010): Numerical Methods for Non-Linear Black-Scholes Equations. Applied Mathematical Finance, Vol. 17, pp. 59-81. [69] Heston, S. (1993): A Closed Form Solution for Options with Stochastic Volatility and Applications to Bond and Currency Options. Reviews of Financial Studies, Vol. 6, pp. 327–343. [70] Hoggard, T.; Whalley, A. E.; Wilmott, P. (1994): Hedging Option Portfolios in the Presence of Transaction Costs. Advanced Futures and Options Research, Vol. 7, pp. 21–35. [71] Hon, Y. C.; Mao, X. Z. (1999): A Radial Basis Function Method for Solving Options Pricing Model. The Journal of Financial Engineering, Vol. 8, pp. 31–49. [72] Huang, C. S.; Hung, C. H.; Wang, S. (2006): A Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities. Computing, Vol. 77, pp. 297–320. [73] Hull, J.; White, A. (1987): The Pricing of Options on Assets with Stochastic Volatilities. Journal of Finance, Vol. 42, No.2, pp. 281–300. [74] Johnson, H. (1987): Options in the maximum or the Minimum of Several assets. The Journal of Financial and Quantitative Analysis, Vol. 22, No. 3, pp. 277-283. [75] Kou, S. G. (2002) A jump-diffusion model for option pricing. Management Science, Vol. 48, pp.1086-1101. [76] Kou, S. G., Wang, H. (2003) First Passage Time of a Jump Diffusion Process. Advances in Applied Probability, Vol. 35, pp.504-531. [77] Kou, S. G., Wang, H. (2004): Option Pricing under a Double Exponential Jump Diffusion Model. Management Science, Vol. 50, pp. 1178-1192. [78] Kou, S. G., Petrella, G., Wang, H. (2005): Pricing Path-dependent Options with Jump Risk via Laplace Transforms. Kyoto Economic Review, Vol. 74, pp. 1-23. [79] Kunitomo, N.; Ikeda, M. (1992): Pricing Options with Curved Boundaries. Mathematical finance, Vol. 2, No. 4, pp. 275-298. [80] Laura, P.A.A.; Gutierrez, R.H. (1993): Analysis of Vibrating Timoshenko Beams using the Method of Differential Quadrature. Shock and Vibration, Vol. 1, pp. 89-93. [81] Laura, P.A.A.; Gutierrez, R.H. (1993): Analysis of Vibrating Circular Plates of Nonuniform Thickness by the Method of Differential Quadrature. Ocean Engineering, Vol. 22, Iss. 1, pp. 97-100. [82] Leland, H. E. (1985): Option Pricing and Replication with Transaction Costs. Journal of Finance, Vol. 40, pp. 1283-1301. [83] Lewis, A. L. (2001): A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy processes. Technical Report, Envision Financial Systems and OptionCity.net, Augest. [84] Lewis, A. L. (2002): Fear of Jumps. Wilmott Magazine, pp. 60-67. [85] Liu, C. S.; Atluri, S. N. (2008): A Novel Time Integration Method for Solving A Large System of Non-Linear Algebraic Equations. Computer Modeling in Engineering & Sciences, Vol. 31, No. 2, pp. 71-84. [86] Liu, C. S.; Yeih, W. C.; Atluri, S. N. (2009): On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales. Computer Modeling in Engineering & Sciences, Vol. 44, No. 3, pp. 281-312. [87] Lo, D. C.; Young, D. L.; Murugesan, K. (2005): GDQ method for Natural Convection in a Square Cavity using Velocity-Vorticity formulation. Numerical Heat Transfer, Part B, Vol. 47, pp. 321-341. [88] Lo, D. C.; Young, D. L.; Murugesan, K. (2005): GDQ method for Natural Convection in a Cubic Cavity using Velocity-Vorticity formulation. Numerical Heat Transfer, Part B, Vol. 48, pp. 363-386. [89] Lo, D. C.; Young, D. L.; Murugesan, K.; Tsai, C. C.; Gou, M. H. (2007): Velocity-vorticity formulation for 3D Natural Convection in an Inclined Cavity by DQ method. International Journal of Heat and Mass Transfer, Vol. 50, pp. 479-491. [90] Longstaff, F. A.; Schwartz, E. S. (2001): Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies, Vol. 14, No. 1, pp. 113-–147. [91] Lyons, T. J. (1995): Uncertain Volatility and the Risk-free Synthesis of Derivatives. Applied Mathematical Finance, Vol. 2, pp. 117–133. [92] Ma, H.; Qin Q. H. (2008): An Interpolation-Based Local Differential Quadrature Method to Solve Partial Differential Equations Using Irregularly Distributed Nodes. Communications in Numerical Methods in Engineering, Vol. 24, pp. 573–584. [93] Madan, D. B.; Carr, P. P.; Chang, E. C. (1998): The Variance Gamma Process and Option Pricing. Review of Finance, Vol. 2, Iss.1. pp. 79-105. [94] Medvedev, A.; Scaillet, O. (2010): Pricing American Options under Stochastic Volatility and Stochastic Interest Rates. Journal of Financial Economics. Vol. 98, Iss. 1, pp. 145-159. [95] Melino, A.; Turnbull, S. (1990): Pricing Foreign Currency Options with Stochastic Volatility. Journal of Econometrics, Vol. 45, pp. 239-265. [96] Melino, A.; Turnbull, S. (1995): Misspecification and the Pricing and Hedging of Long-term Foreign Currency Options. Journal of International Money and Finance, Vol. 14, pp. 373-393. [97] Merton, R. C. (1973) Theory of rational option pricing. The Bell Journal of Economics and Management, Vol. 4, pp. 141-183. [98] Merton, R. C. (1976) Option Pricing when Underlying Stock Returns are Discontinuous. The Journal of Financial Economics, Vol. 3, pp. 125–144. [99] Metwally, S.; Atiya, A. (2002): Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options. The Journal of Derivatives, Vol. 10, No. 1, pp. 43-54. [100] Mingle J. O. (1977): The Method of Differential Quadrature for Transient Nonlinear Diffusion. Journal of Mathematical Analysis and Applications, Vol. 60, Issue 3, pp.559-569. [101] Moradi S.; Taheri, F. (1998): Differential Quadrature Approach for Delamination Buckling Analysis of Composites with Shear Deformation. AIAA Journal, Vol. 36, Iss. 10, pp. 1865-1873. [102] Mun, J. (2002): Real Options Analysis. John Wiley & Sons, New Jersey. [103] Page, F. H. Jr.; Sanders, A. B. (1986): A General Derivation of the Jump Process Option Pricing Formula. Journal of Financial and Quantitative Analysis, Vol. 21, No. 4, pp. 437-446. [104] Pan, J. (2001): The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study. Journal of Financial Economics, Vol. 63, pp. 3-50. [105] Pilipović, D (1998) Energy Risk. McGraw-Hill, New York. [106] Pooley, D. M.; Forsyth, P. A. and Vetzal, K. R. (2003): Numerical Convergence Properties of Option Pricing PDEs with Uncertain Volatility. IMA Journal of Numerical Analysis, Vol. 23, pp. 241-267. [107] Quan, J. R.; Chang, C. T. (1989): New Insights in Solving Distribution System Equations by the Quadrature Methods – I. Computers & Chemical Engineering, Vol. 13, pp. 779-788. [108] Quan, J. R.; Chang, C. T. (1989): New Insights in Solving Distribution System Equations by the Quadrature Methods – II. Computers & Chemical Engineering, Vol. 13, pp. 1017-1024. [109] Rannacher, R. (1984): Finite Element Solution of Diffusion Problems with Irregular data. Numerische Mathematik, Vol. 43, No. 2, pp. 309-327. [110] Rubinstein, M. (1985): Nonparametric Tests of Alternative Option Pricing Models using all Reported Trades and Quotes on the 30 Most Active CBOE Options Classes from August 23, 1976 through August 31, 1978. Journal of Finance, Vol. 49, pp. 771-818. [111] Rubinstein, M. (1994): Implied Binomial Trees. Journal of Finance, Vol. 40, pp. 455-480 [112] Saad, Y.; Schultz, M. H. (1986): GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing, Vol. 7, pp. 856-869. [113] Sadeghian, H.; Rezazadeh, G.; Osterberg, P. M. (2007): Application of the Generalized Differential Quadrature Method to the Study of Pull-In Phenomena of MEMS Switches. Journal of Microelectromechanical Systems, Vol. 16, No. 6, pp. 1334-1340. [114] Scott, L. (1987): Option Pricing when the Variance Changes Randomly: Theory, Estimators, and Applications. Journal of Financial and Quantitative Analysis, Vol. 22, pp. 419-438. [115] Scott, L. (1997): Pricing Stock Options in a Jump-diffusion Model with Stochastic Volatility and Interest Rates: Application of Fourier Inversion Methods. Mathematical Finance, Vol. 7, Iss. 4, pp. 413-426. [116] Shan, Y. Y.; Shu, C.; Lu, Z. L. (2008): Application of Local MQ-DQ Method to Solve 3D Incompressible Viscous Flows with Curved Boundary. Computer Modeling in Engineering & Sciences, Vol. 25, No. 2, pp. 99-113. [117] Shen, L. H.; Young, D. L.; Lo, D. C.; Sun, C.P. (2009): Local Differential Quadrature Method for 2D Flow and Forced Convection problems in Irregular Domains. Numerical Heat Transfer, Part B Fundamentals, Vol. 55, pp. 118–134. [118] Shina, Y. J.; Kwonb, K. M.; Yunc, J. H. (2008): Vibration Analysis of a Circular Arch with Variable Cross-Section Using Differential Transformation and Generalized Differential Quadrature. Journal of Sound and Vibration, Vol. 309, No. 1-2, pp. 9-19. [119] Shu, C. (1991): Generalized Differential-Integral Quadrature and Application to the Simulation of Incompressible Viscous Flows Including Parallel Computation. Ph.D. thesis, University of Glasgow, Scotland, UK. [120] Shu, C. (2000): Differential Quadrature and Its Applications in Engineering. Springer, Berlin, Germany. [121] Shu C; Chen, W. (1999): On Optimal Selection of Interior Points for Applying Discretized Boundary Conditions in DQ Vibration Analysis of Beams and Plates. Journal of Sound and Vibration, Vol. 222, Iss. 2, pp.239–57. [122] Shu, C.; Richards, B. E. (1990): High Resolution of Natural Convection in a Square Cavity by Generalized Differential Quadrature. Proc. of 3rd Conf. on Adv. in Numer. Methods in Eng.: Theory and Appl., Swansea, U.K., Vol. 7, pp. 978–985. [123] Shu, C.; Richards, B.E. (1992): Application of Generalized Differential Quadrature to Solve 2-Dimensional Incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids, Vol. 15, No. 7, pp. 791–795. [124] Shu C.; Ding, H.; Yeo, K.S. (2003): Local Radial Basis Function-based Differential Quadrature Method and its Application to solve Two-dimensional Incompressible Navier-Stokes Equations. Computer Methods in Applied Mechanics and Engineering, Vol. 192, pp. 941-954. [125] Shu, C.; Ding, H.; Yeo, K. S. (2005): Computation of Incompressible Navier-Stokes Equations by Local RBF-Based Differential Quadrature Method. Computer Modeling in Engineering & Sciences, Vol. 7, No. 2, pp. 195–205. [126] Shu, C; Ding, H.; Zhao, N. (2006): Numerical Comparison of Least Square-Based Finite-Difference (LSFD) and Radial Basis Function-Based Finite-Difference (RBFFD) Methods. Computers & Mathematics with Applications, Vol. 51, pp. 1297-1310. [127] Sircar, K. R.; Papanicolaou, G. (1998): General Black-Scholes Models Accounting for Increased Market Volatility from Hedging Strategies. Applied Mathematical Finance, Vol. 5, pp.45-82. [128] Stein, E.; Stein, J. (1991): Stock Price Distributions with Stochastic Volatility. Review of Financial Studies, Vol. 4, pp. 727-752. [129] Stulz, R.W. (1982): Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Application. Journal of Financial Economics, Vol. 10, pp. 161-185. [130] Striz, A. G.; Jang, S. K.; Bert, C. W. (1988): Nonlinear Bending Analysis of Thin Circular Plates by Differential Quadrature. Thin Wall Structures, Vol. 6, Iss. 1, pp. 51-62. [131] Sun, C. P.; Young, D. L. (2008): Solving Option Pricing Model by Local Differential Quadrature Method. ICCES’08, March 19–22, Honolulu, Hawaii, USA. [132] Tavella, D.; Randall, C. (2000): Pricing Financial Instruments: The Finite Difference Method. New York: Wiley. [133] Tezer-Sezgin, M. (2003): Solution of Magnetohydrodynamic Flow in a Rectangular Duct by Differential Quadrature Method. Computers & Fluids, Vol. 33, Iss. 4, pp. 533-547. [134] Topper, J. (1998): Finite Element Modeling of Exotic Options. Discussion paper, University of Hannover. [135] Topper, J. (2005): Financial Engineering with Finite Elements. John Wiley & Sons, Chichster, UK. [136] Tsai, C. C.; Young, D. L.; Chiang, J. H.; Lo, D. C. (2006): The Method of Fundamental Solutions for Solving Option Pricing Model. Applied Mathematics and Computation, Vol. 181, pp. 390–401. [137] Wiggins, J. (1987): Option Values under Stochastic Volatilities. Journal of Financial Economics, Vol. 19, pp. 35-372. [138] Wilmott, P.; Dewynne, J. N.; Howison, S. D. (1993): Option Pricing: Mathematical Models and Computation. Oxford Financial Press, Oxford, UK. [139] Wilmott, P. (1998): Derivatives, New York: Wiley [140] Wilmott, P.; Schӧnbucher, P. J. (2000): The Feedback Effect of Hedging in Illiquid Markets. SIAM Journal on Applied Mathematics, 61, pp. 232-272. [141] Wu, L.; Kwok, Y. K. (1997): A Front-Fixing Finite Difference Method for the Valuation of American Options. Journal of Financial Engineering, Vol. 6, pp. 83–97. [142] Young, D. L.; Sun, C. P.; Shen, L. H. (2009): Pricing Options with Stochastic Volatilities by the Local Differential Quadrature Method. Computer Modeling in Engineering & Sciences, Vol. 46, No. 2, pp. 129–150. [143] Zhang, X. L. (1997): Numerical Analysis of American Option Pricing In A Jump-Diffusion Model. Mathematics of Operations Research, Vol. 22, No. 3, pp. 668-690. [144] Zhang Q.D.; Khoo B.C.; Yeo K.S. (1997): A Numerical Study of the Effect of Free Surface and Water Depth on the Stability of Wake: Use of GDQ formulation. International Journal for Numerical Methods in Fluids, Vol. 24, pp. 1079-1090. [145] Zhou, C.S. (2001): The Term Structure of Credit Spreads with Jump Risk. Journal of Banking & Finance, Vol. 25, Iss. 11, pp. 2015-2040 [146] Zong, Z.; Lam, K. Y. (2002): A Localized Differential Quadrature (LDQ) Method and its Application to the 2D Wave Equation. Computational Mechanics, Vol. 29, pp. 382–391. [147] Zvan, R.; Forsyth, P. A.; Vetzal, K. R. (2003): Negative Coefficients in Two-Factor Option Pricing Models. Journal of Computational Finance, Vol. 7, No. 1, pp. 37-73. [148] Zvan, R.; Vetzal, K. R.; Forsyth, P. A. (2000): PDE Methods for Pricing Barrier Options. Journal of Economic Dynamics and Control, Vol. 24, pp. 2563–2590. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27996 | - |
dc.description.abstract | 本文主要闡述以局部微分積分數值方法求解選擇權評價問題之過程以及結果。在Black, Scholes以及Merton於1973年提出之模式帶來之重大貢獻後,為了使其假設更接近真實金融市場或是更廣泛應用選擇權理論於特定商品的需求,眾多改良自Black-Scholes模式的選擇權評價模式隨之被提出。一般而言,這些模式依照其針對標的資產價格之動態過程假設之數學形式大致可分為兩種。第一種模式僅假設標的資產價格之動態過程滿足布朗運動, 可歸類為「擴散模式」;另一種則假設標的資產價格之動態過程包括布朗運動以及隨機跳躍,可歸類為「跳躍─擴散模式」。本研究主要目標則為提供一無論於「擴散模式」或「跳躍─擴散模式」下進行選擇權評價時皆能有效運行之數值模式。為求有效提升本問題數值運算效益,故本研究採用針對收益函數之一階偏微分導數不連續位置進行加密佈點之網格,並使用適用於該類網格之局部微分積分法進行數值計算。針對「跳躍─擴散模式」,由於其統御方程式較「擴散模式」多一非局部積分項,本研究亦提供一能在非均勻佈點網格上有效求解該積分之數值流程。數值案例皆為典型且常見之選擇權評價問題,包括歐式、美式、回顧型以及障礙型選擇權。經過與參考資料比較結果後,發現本研究建議之方法流程於「擴散模式」及「跳躍─擴散模式」皆擁有良好穩定性以及表現,並且適用於各類典型常見之選擇權評價問題,故可得此方法可成功應用於選擇權評價問題之結論。 | zh_TW |
dc.description.abstract | This study demonstrates the numerical procedure of solving option-pricing problems by the local differential quadrature (LDQ) method. After the remarkable contribution of Black, Scholes and Merton in 1973, many option-pricing models are developed for relaxing the restrictions of the Black-Scholes (BS) model or extending the theory to much wider applications. In general, these models can be divided into two kinds based on the assumption of the dynamic process for the underlying assets. Ones are diffusion models in which the dynamics of the underlying-asset price follow the Brownian process; the others are jump-diffusion models with the random jumps considered in the dynamics. Our work aims to develop a numerical process for solving both the diffusion and jump-diffusion models efficiently. Because of the non-differentiability of the payoff functions, non-uniformly distributed nodes are applied, and thus the LDQ method is used due to its advantage for arbitrary grid nodes. For the jump-diffusion models, we also provide an efficient scheme for computing the non-local integral of the governing equations on the non-uniform nodal girds. Numerical experiments include typical option-pricing problems, such as European, American, lookback, binary and barrier options. According to the comparison with the reference data, our results show that the proposed method has robustness and good performance for both diffusion and jump-diffusion type option-pricing models. In brief, one can conclude that it is a successful application. | en |
dc.description.provenance | Made available in DSpace on 2021-06-12T18:32:25Z (GMT). No. of bitstreams: 1 ntu-100-F93521319-1.pdf: 3060737 bytes, checksum: 94e21b5e439d0e689d4ba5c1aa52fb7f (MD5) Previous issue date: 2011 | en |
dc.description.tableofcontents | Chapter 1 Introduction.....................................1
1.1 The Option Pricing Models..........................2 1.2 Solutions..........................................5 1.3 The differential quadrature method................10 1.4 The localized differential quadrature method......13 1.5 Organization of the dissertation..................15 Chapter 2 Numerical Solutions of the Black-Scholes Model..19 2.1 The Generalized Black-Scholes model...............20 2.2 Numerical method and discretization...............22 2.3 Numerical experiments.............................27 2.4 Conclusions.......................................37 Chapter 3 Numerical Solutions of Heston’s Stochastic-Volatility Model..........................................39 3.1 Introduction......................................40 3.2 Formulation.......................................41 3.3 Numerical discretization..........................47 3.4 Numerical experiments.............................48 3.5 Conclusions.......................................62 Chapter 4 Numerical Solutions of the Non-Linear Black-Scholes Models............................................63 4.1 The Extended Black-Scholes models.................64 4.2 Numerical procedure...............................66 4.3 Numerical experiments.............................68 4.4 Conclusions.......................................74 Chapter 5 Numerical Solutions of Jump-Diffusion Models....77 5.1 Introduction......................................78 5.2 The basic models..................................80 5.3 Numerical discretization..........................83 5.4 Numerical experiments.............................85 5.5 Conclusions.......................................91 Chapter 6 An Alternative Numerical Scheme for Jump-Diffusion Models....................................................93 6.1 Introduction......................................94 6.2 The basic models..................................97 6.3 Alternative methods for calculating integral.....101 6.4 Numerical experiments............................104 6.5 Conclusions......................................122 Chapter 7 Pricing Barrier Options........................125 7.1 Introduction.....................................126 7.2 Barrier options and boundary conditions..........127 7.3 Numerical experiments............................131 7.4 Conclusions......................................142 Chapter 8 An Example in the Real Market..................145 8.1 The example......................................146 8.2 The adaptability of the models...................147 8.3 Conclusions......................................152 Chapter 9 Conclusions and Suggestions....................153 9.1 Summaries and conclusions........................154 9.2 Suggestions......................................158 References...............................................163 | |
dc.language.iso | en | |
dc.title | 應用局部微分積分法求解選擇權評價問題 | zh_TW |
dc.title | Pricing Options by the Local Differential Quadrature Method | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 蔡加正,呂育道,陳清祥,石百達,張始偉 | |
dc.subject.keyword | 局部微分積分法,Black-Scholes 模式,跳躍─擴散模式,歐式選擇權,美式選擇權,回顧選擇權,障礙型選擇權, | zh_TW |
dc.subject.keyword | local differential quadrature,the Black-Scholes model,jump-diffusion model,European option,American option,lookback option,barrier option, | en |
dc.relation.page | 187 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2011-08-08 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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