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系統識別號 U0026-0812200911531816
論文名稱(中文) 雙邊信用價差障礙選擇權之評價-混合型方法之應用
論文名稱(英文) Valuation of Double-Barrier Credit Spread Option - The Hybrid Approach
校院名稱 成功大學
系所名稱(中) 財務金融研究所
系所名稱(英) Graduate Institute of Finance & Banking
學年度 94
學期 2
出版年 95
研究生(中文) 陳玉寶
研究生(英文) Yu-Bao Chen
學號 r8693104
學位類別 碩士
語文別 英文
論文頁數 47頁
口試委員 指導教授-王明隆
口試委員-劉裕宏
口試委員-陳寒濤
中文關鍵字 有限差分  拉普拉斯轉換  障礙選擇權  信用價差 
英文關鍵字 the Laplace transformation  Credit spread  Barriers  the Finite difference method 
學科別分類
中文摘要 本篇研究使用拉普拉斯轉換(Laplace transform)和有限差分法(finite difference method)來評價雙邊障礙信用價差選擇權(double-barrier credit spread option)。傳統的顯然有限差分法(Explicit Finite difference)雖簡單易懂,卻存在穩定性(Stability)的問題,卽較難收歛至精確的數值解(numerical solution);隱然有限差分法(Implicit finite difference)雖會收歛到精確數值解,但當我們將時間變數間距(Time step)縮小時,其計算過程卻相當耗時。使用上述組合型方法(Hybrid method)的優點在於經過拉普拉斯轉換之後,排除了時間變數,因此,傳統之有限差分法運算耗時及不易收歛到精確數值解的問題都可獲得改善。本篇研究將以此組合型方法所求得轉換後之數值解,經由數值逆拉普拉斯轉換(numerical inversion of Laplace transform)後,即可求得在原來時間領域(Time domain)下任ㄧ時點的選擇權價格,整個計算的過程將更快速且穩定。






英文摘要 This paper uses the combination of the Laplace transformation and the finite difference method to value the double-barrier credit spread option. The major advantage of the combination method over the finite difference method is that the Laplace transformation will eliminate the time steps, thus, an accurate and precise numerical solution will be obtained quickly. The hybrid method can provide practitioners with a more efficient and applicable way to solve the PDE (partial differential equation) within various boundary constraints. Therefore, the method will be a highly powerful approach to price exotic options with complex features.






論文目次 Contents
I. Introduction 1

II. Literature Review 5
A. The valuation of credit spread option 5
B. The valuation of barrier option 7
1. Closed-form solution 7
2. Lattice Model 8
3. Monte Carlo Method 9
4. Double Barrier Options 10
C. The finite difference method 11
D. The hybrid method 12

III. Methodology 13
A. Introduce the governing equation, initial and boundary conditions 14
B. Take the Laplace transform 16
C. The finite difference method 17
D. To approximate the PDE with central difference method 19
E. Numerical inversion of the Laplace transform 22

IV.Numerical Examples 25
A.The convergence in different partitions for standard European credit spread option 26
B.The convergence in different partitions for Double-Barrier Credit Spread Option 28
C. The double-barrier credit spread knock-out call value for different credit spread with rebate , 29
D. The double-barrier credit spread knock-out call value for different credit spread with rebate , 30
E. The double-barrier credit spread knock-out call value for different strike yield spread with rebate , 31
F. The double-barrier credit spread knock-out call value for different strike yield spread with rebate , 32
G.The double-barrier credit spread knock-out call value for different volatilities with rebate , 33
H. The double-barrier credit spread knock-out call value for different volatilities with rebate , 34
I. The double barrier knock-out call value for different risk-free rate with rebate , 35
J. The double barrier knock-out call value for different risk-free rate with rebate , 36
K. The double-barrier credit spread knock-out call value for different barrier levels with rebate , 37
L. The double barrier credit spread knock-out call value for different rebates 38
M. The double barrier knock-out call value for different time to maturity with rebate , 39
N. The double barrier knock-out call value for difference time to maturity with rebate , 40

Ⅴ. Conclusions and further research 41
A.Conclusions 42
B.Further research 43

References 44


























參考文獻 References
[1] Black F. and M. Scholes, 1973,“The Pricing of Options and Corporate Liabilities,” The Journal of Political Economy 81, 637
[2] Boyle, P. P., and S. H. Lau, 1994,“Bumping Up Against the Barrier with the Binomial Method,” Journal of Derivatives 1, 6-14
[3] Brennan M. J., and E. S. Schwartz. 1978,“Finite Difference Method and Jump Processes Arising in the Pricing of Contingent Claims,” Journal of Financial and Quantitative Analysis, 13, 461-474
[4] Brennan M. J., and E. S. Schwartz. 1976,“The valuation of American Put options,” Journal of Finance
[5] Cox, J. C., S. A. Ross, and M. Rubinstein, 1979, “Option Pricing: A Simplified
Approach,” Journal of Financial Economics 7, 229-264
[6] Cheuk, T. H. F., and T. C. F. Vorst, 1996, “Complex Barrier Options,” Journal of
Derivatives 4, 8-22
[7] Geske R., and K. Shastri. 1985,“Valuation of Approximation: a Comparison of Alternative Approaches,” Journal of Financial and Quantitative Analysis, 20, 45-72
[8] G. Honig and U. Hirdes, 1984,“A method for the numerical inversion of Laplace transforms,” J. Comput. Appl. Math. 9, 113-132
[9] Geman, H., and M. Yor, 1996, “Pricing and hedging double-barrier options: A probabilistic approach,” Mathematical Finance, Vol. 6, 365-378
[10] Haug E. G., 1997, “The Complete Guide to Option Pricing Formulus,”
McGraw-Hill, New York, 1997.
[11] Haug E. G., 1998,“Option Pricing Formulas,” McGraw-Hill, New York
[12] Heynen, P. and H. Kat, “Partial Barrier Option, 1994,” Journal of Financial
Engineering 3, 253-274
[13] Howard K., 1995, ”An Introduction to Credit Derivatives, ” Derivatives Quarterly, Vol. 2, 28-37,
[14] Hsueh, 2001, “Analysis of American Discrete Barrier Option with Stochastic
Rebate,” Journal of Financial Studies 9, 27-46
[15] Hull, J. and A. White. 1994, “Numerical Procedures for Implementing Term Structure Models I: Single-Factor Models.” Journal of Derivatives, 2 , 7-16
[16] Hull, J. and A. White. 1994, “Numerical Procedures for Implementing Term Structure Models II: Two-Factor Models.” Journal of Derivatives, 2 , 37-48
[17] H. T. Chen and C. K. Chen, 1988, “Hybrid Laplace transform/finite element method for Two-dimensional transient heat conduction problem,” Computer Methods in Applied Mechanics and engineering, 31-36
[18] H.T Chen and C.K. Chen, 1988, “Hybrid Laplace transform/finite difference method for transient heat conduction problems,” International Journal for Numerical Methods in Engineering, Vol. 26, 1433-1447
[19] Joao B. C., V. Helmut and C. Reinaldo, “On The Pricing Of Credit Spread Options: A Two Factor HW-BK Algorithm,” International Journal of Theoretical and Applied Finance, Vol.6 No.5 491-505
[20] Kennth R. Vetzal, 1998, “An improved finite difference approach to fitting the initial term structure,” The Journal of Fixed Income, 62-81
[21] Kunitomo, N., M. Ikeda, 1992, “Pricing options with curved boundaries,” Mathematical Finance 2, 275-298
[22] Longstaff F.A., and E.S. Schwartz, 1995, “Valuing Credit Derivatives,” The Journal of Fixed Income, Vol 5, 6-12

[23] Merton, R. C., 1973, “Theory of Rational Option Pricing,” Bell Journal of
Economics and Management Science 4, 141-183

[24] Pelsser, A., 2000, “Pricing double barrier options using Laplace transforms”, Finance and Stochastics 4, 95-104
[25] Rubinstein, M., and E. Reiner,1991,” Breaking Down the Barriers,” RISK 4, 28-35
[26] Rich, D., 1994, “The Mathematical Foundations of Barrier Option-Pricing Theory,” Advances in Futures and Options Research 7,267-311
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