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研究生:陳冠群
研究生(外文):Chen Kuan Chun
論文名稱:隨機波動模型下美式選擇權之評價
論文名稱(外文):American Option Pricing Under Stochastic Volatility
指導教授:梁雪富梁雪富引用關係
學位類別:碩士
校院名稱:南台科技大學
系所名稱:財務金融系
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:57
中文關鍵詞:隨機波動權美式選擇有限差分分法自由邊界快速傅利葉轉換
外文關鍵詞:Stochastic Volatility (SV)American OptionFinite Different Method (FDM)Free BoundaryFast Fourier Transform (FFT)Crank-Nicolson Method
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本文的主要目的在於使用有限差分法來求得選擇權的價格,同時亦對有限差分法所求得的結果做測試,而在選擇權的評價上則採用Heston (1993)的隨機波動模型。比較結果顯示無論是歐式選擇權或是美式選擇權,本文所架構的有限差分法皆能有效地提供精確的答案。
在美式選擇權求解的同時,能夠架構出自由邊界,本文亦對自由邊界進行探討,且說明當模型估計的參數不確定時,美式選擇權評價可能出現的問題。
The main objective of this dissertation is to investigate the effectiveness of finite difference method (FDM) for pricing different options under Heston stochastic volatility model (1993). FDM is firstly used for pricing European and American options and its results compared with published works to validate the correctness of its implementation; then, acting on Heston model parameters, a sensitivity analysis of American options free boundaries, is performed. This free boundary analysis helps to explain the risk of parametric uncertainty.
TABLE OF CONTENT

CHAPTER 1 NTRODUCTIONAND MOTIVATION 5
CHAPTER 2 LITERATURE REVIEW 10
2.1 PROGRESS OF OPTION PRICING MODELS 12
2.2 EMPIRICAL FINDINGS OF STOCHASTIC VOLATILITY 16
2.3 COMPARIONS OF AMERICAN OPTION PRICING METHODS 19
CHAPTER 3 METHODOLOGY 22
3.1 BRIEF REVIEW OF FINITE DIFFERENCE METHOD 24
3.2 ILLUSTRATION OF FDM IN BS FRAMEWORK 26
3.3 FDM WITH STOCHASTIC VOLAITLITY 30
3.4 BOUNDARY OF THE SYSTEM 34
CHAPTER 4 EXPERIMENTAL RESULT 39
4.1 MODEL SPECIFICATION 41
4.2 EUROPEAN OPTION 42
4.2.1 Comparing FDM and FFT 43
4.2.2 Error Test between FDM and FFT 44
4.3 AMERICAN OPTION 47
4.3.1 Implementation method for American put Option 47
4.3.2 Methods Comparison 49
4.4 THE FREE BOUNDARY ANALYSIS 53
CHAPTER 5 CONCLUSION AND FUTHER EXTENSION 58
APPENDIX 60
CHAPTER A.3: METHODOLOGY AND NUMERICAL METHODS 60
A.3.1 HESTON PDE DERIVATION 60
A.3.2 FINITE DIFFERENCE METHOD AND MATHEMATICAL FRAMEWORK 66
A.3.3 CONSISTENCY, STABILITY AND CONVERGENCE 69
A.3.4 BOUNDARY CONDITIONS FOR AMERICAN OPTIONS 70

CHAPTER A.4: IMPLEMENTATION 74
A.4.1 CHARACTERISTIC FUNCTION AND FAST FOURIER TRANSFORM 74
A.4.1.1. Characteristic Function (CF) 74
A.4.1.2. Fast Fourier transform (FFT) 75
A.4.2 ADJUSTING BOUNDARY RANGE IN AMERICAN OPTION 76
REFERENCE LIST 78
MATLAB CODE 82
1. PARAMETERS 82
2. EUROPEAN OPTION 83
3. FFT 87
4. AMERICAN OPTION 91
[1]ACHDOU Y., FRANCHI B., TCHOU, N.A. (2005). A partial differential equation connected to option pricing with stochastic volatility: regularity results and discretization. Mathematics of Computations, 74 (2005), 1291-1322.
[2]ACHDOU Y., PIRONNEAU, O. (2005). Computational Methods for Option Pricing. Vol. 30 of Frontiers in Applied Mathematics, SIAM, Philadelphia, PA.
[3]BAKSHI, G., CAO, C., CHEN, Z. (1997). Empirical performance of alternative option pricing models, Journal of Finance, 52, 2004-2049.
[4]BATES, D. (1991). The crash of 87: Was it expected? The evidence from options markets, Journal of Finance 46, 1009-1044.
[5]BATES, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutschemark options, Review of Financial Studies 9, 69-108.
[6]BATES, D.S. (2003). Empirical option pricing: a retrospection. Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
[7]BAXTER M., RENNIE, A. (1996). Financial Calculus: An Introduction to Option Pricing, Cambridge.
[8]BLACK F., SCHOLES M. (1973). The pricing of Options and Corporate Liabilities, Journal of Political Economy, 81:635-654.
[9]BRANDIMARTE, P. (2006). Numerical Methods in Finance And Economics: A MATLAB-Based Introduction, Wiley.
[10]BRENNAN M.J., SCHWARTZ, E.S. (1978). Finite difference methods and jump processes arising in the pricing of contingent claims: A synthesis. Journal of Financial and Quantitative Analysis, 13, 461-474, September.
[11]BRENNER S.C., SCOTT L.R. (2005). The mathematical theory of Finite Element Methods. Springer Verlag, 2005.
[12]BRIANI, M. (2003). Numerical methods for option pricing in jump-diffusion markets, Ph.D. Thesis, Università degli Studi di Roma “La Sapienza”.
[13]BARONE-ADESI, G., AND R. WHALEY, 1987. Efficient Analytic Approximation of American Option Values, Journal of Finance 42, 301.-320
[14]BOYLE, P., M. BROADIE, AND P. GLASSERMAN, 1997. Monte Carlo methods for security pricing, Journal of Economic Dynamics & Control 21, 1267-1322.
[15]CARR, P., R. JARROW, AND R. MYNENI, 1992, Alternative characterizations ofAmerican put options, Mathematical Finance 2, 87-106.
[16]CARR, P., MADAN D. (1998). Option Valuation using the fast Fourier transform, Journal of Computational Finance, 2, 61-73.
[17]CLARKE, N., PARROTT, K. (1996). The multigrid solution of two-factor American put options, Tech. Rep. 96-16, Oxford Computing Laboratory, Oxford.
[18]CLARKE, N., PARROTT, K. (1999). Multigrid for American option pricing with stochastic volatility. Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(3), pages 177-195, September.
[19]CONT., R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, Vol. 1, No. 2 (March 2001) 223-236.
[20]COX, J., ROSS S., RUBINSTEIN M. (1979). Option pricing: a simplified approach, Journal of Economics, January.
[21]COX, J., INGERSOLL, J.E., ROSS, S.A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica, Vol. 53, No. 2., pp. 385-407.
[22]CREPEY S. (2007). Computational finance. Notes. Évry University.
[23]Chourdakis Kyriakos’ unpblised Lecturer Notes, 2007
[24] http://www.univ-evry.fr/pdf/ufr_sfa/maths/me_crepey.pdf
[25]DUFFIE, D., PAN J., SINGLETON, K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions, Econometrica, 68, 6, pp. 1343-1376.
[26]DUFFY, D. J. (2006). Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach, Wiley.
[27]DUPIRE, B. (1994). Pricing with a smile, Risk, 7, pp. 18-20.
[28]GESKE R., SHASTRI, K. (1985). Valuation by approximation: a comparison of alternative option valuation techniques. Journal of Financial and Quantitative Analysis, 20, pp. 45-71.
[29]HESTON, S. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43.
[30]HUANG J., M. G. SUBRAHMANYAM, AND G. G. YU, 1996. Pricing and Hedging
American Options: A Recursive Integration Method, The Review of Financial
[31]HULL, J. C. (2006). Options, futures, & other derivatives, Prentice Hall, 6th edition.
[32]HULL, J.C., WHITE, A. D. (1987). The Pricing of Options on Assets with Stochastic Volatilities. Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
[33]HULL, J. C., WHITE, A. D. (1990). Valuing Derivative Securities Using the Explicit Finite Difference Method. The Journal of Financial and Quantitative Analysis, Vol. 25, No. 1. (Mar., 1990), pp. 87-100.
[34]IBANEZ A., 2003. Robust pricing of the American put option: A note on Richardson extrapolation and the early exercise premium, Management Science 49, 1210-1228
[35]IKONEN S., TOIVANEN, J. (2004). Operator Splitting Methods for American Option Pricing, Applied Mathematics Letters, Volume 17, Issue 7, pp. 809-814.
[36]LONGSTAFF, F. A. , SCHWARTZ, E. S. (2001). Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
[37]MERTON, R.C. (1973). Theory of rational option pricing, Bell Journal of Economics and Management Science, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
[38]MOODLEY, N. (2005). The Heston Model: A Practical Approach with Matlab Code. Ph.D. proposal. University of The Witwatersrand, Johannesburg. Link: http://www.cam.wits.ac.za/mfinance/projects/nimalinmoodley.pdf
[39]NANDI, S. (1998). How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market. Journal of Banking and Finance, Vol. 22.
[40]RÜBENKÖNIG, O. (2007). The Finite Volume Method (FVM). http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Lectures%20and%20Tips/Simulation%20I/FVM_introDocu.html.
[41]RUBINSTEIN, M. (1985). Nonparametric tests of alternative option price 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, 40, 455-480.
[42]SCHWARTZ, E.S. (1977). The Valuation of Warrants: Implementing a New Approach. Journal of Financial Economics, 4, 79-93.
[43]Schwartz E. and Brennan, M., 1977, The valuation of American put options,
Journal of Finance 32, 449-462.

[44]STEIN, E. M., STEIN, J. C. (1991). Stock Price Distributions with Stochastic Volatility: An Analytic Approach, Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(4), pages 727-52.
[45]SUKHA, S. (2001). Finite-Difference Methods for Pricing the American Put Option. PhD Proposal. University of the Witwatersrand.
[46]TZAVALIS E., WANG, S. (2003). Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary, Working Papers 488, Queen Mary, University of London, Dept. of Economics.
[47]WILMOTT, P., DEWYNNE J., HOWISON, S. (1994). Option Pricing – Mathematical Models and Computation, Oxford Financial Press.
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