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Title在Heston架構下評價VIX選擇權與實證分析
Pricing VIX Options under the Heston Framework and Empirical Analysis
Creator李多達
Lido, Daouda
Contributor林士貴
Lin, Shih Kuei
李多達
Lido, Daouda
Key WordsHeston Model
VIX Options
Stochastic Volatility
Mean-reversion
Volatility Smile
Calibration
Option Pricing
Date2013
Date Issued25-Aug-2014 15:17:21 (UTC+8)
Summary在Heston架構下評價VIX選擇權與實證分析
In this thesis, we give a quasi-thorough review of the different VIX options pricing models in the literature, before developing the Heston stochastic volatility model as it pertains to pricing VIX options. Our empirical tests and results show that the Heston model is able to quite capture empirical characteristics of the VIX, although the model does exhibit some inconsistencies with regards to the stability of the parameters over time. Instead of invalidating the model, this shows that the Heston model setup is acceptable as an alternative to pricing VIX options until the advent of a better model.
參考文獻 Bibliography
     
     1. Bakshi, G., C. Cao and Z. Chen (1997). "Empirical performance of alternative option pricing models." The Journal of Finance 52(5): 2003-2049.
     2. Black, F. and M. Scholes (1973). "The pricing of options and corporate liabilities." The journal of political economy: 637-654.
     3. Carr, P. and R. Lee (2007). "Realized volatility and variance: Options via swaps." Risk 20(5): 76-83.
     4. Carr, P. and R. Lee (2008). Robust replication of volatility derivatives. PRMIA award for Best Paper in Derivatives, MFA 2008 Annual Meeting.
     5. Carr, P. and R. Lee (2009). "Volatility derivatives." Annu. Rev. Financ. Econ. 1(1): 319-339.
     6. Christoffersen, P., S. Heston and K. Jacobs (2009). "The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well." Management Science 55(12): 1914-1932.
     7. Cox, J. C., J. E. Ingersoll Jr and S. A. Ross (1985). "A theory of the term structure of interest rates." Econometrica: Journal of the Econometric Society: 385-407.
     8. Detemple, J. and C. Osakwe (2000). "The valuation of volatility options." European Finance Review 4(1): 21-50.
     9. Detlefsen, K. and W. K. Härdle (2006). Calibration risk for exotic options, SFB 649 discussion paper.
     10. Feller, W. (1951). "Two singular diffusion problems." Annals of mathematics: 173-182.
     11. Gatheral, J. (2006). The volatility surface: a practitioner`s guide, John Wiley & Sons.
     12. Goard, J. and M. Mazur (2013). "Stochastic Volatility Models and the Pricing of Vix Options." Mathematical Finance 23(3): 439-458.
     13. Grünbichler, A. and F. A. Longstaff (1996). "Valuing futures and options on volatility." Journal of Banking & Finance 20(6): 985-1001.
     14. Heston, S. L. (1993). "A closed-form solution for options with stochastic volatility with applications to bond and currency options." Review of financial studies 6(2): 327-343.
     15. Lin, Y. N. and C. H. Chang (2009). "VIX option pricing." Journal of Futures Markets 29(6): 523-543.
     16. Moodley, N. (2005). "The Heston model: A practical approach with Matlab code." Bachelor Thesis, University of the Witwatersrand, Johannesburg, math. nyu. edu.
     17. Psychoyios, D. and G. Skiadopoulos (2006). "Volatility options: Hedging effectiveness, pricing, and model error." Journal of Futures Markets 26(1): 1-31.
     18. Simon, D. P. and J. Campasano (2012). "The VIX Futures Basis: Evidence and Trading Strategies." The Journal of Derivatives 21(3): 54-69.
     19. Wang, Z. and R. T. Daigler (2011). "The performance of VIX option pricing models: Empirical evidence beyond simulation." Journal of Futures Markets 31(3): 251-281.
     20. Whaley, R. E. (1993). "Derivatives on market volatility: Hedging tools long overdue." The journal of Derivatives 1(1): 71-84.
     21. Whaley, R. E. (2009). "Understanding the VIX." The Journal of Portfolio Management 35(3): 98-105.
     22. Zhang, J. E. and Y. Zhu (2006). "VIX futures." Journal of Futures Markets 26(6): 521-531.
Description碩士
國立政治大學
金融研究所
100352032
102
資料來源 http://thesis.lib.nccu.edu.tw/record/#G1003520322
Typethesis
dc.contributor.advisor 林士貴zh_TW
dc.contributor.advisor Lin, Shih Kueien_US
dc.contributor.author (Authors) 李多達zh_TW
dc.contributor.author (Authors) Lido, Daoudaen_US
dc.creator (作者) 李多達zh_TW
dc.creator (作者) Lido, Daoudaen_US
dc.date (日期) 2013en_US
dc.date.accessioned 25-Aug-2014 15:17:21 (UTC+8)-
dc.date.available 25-Aug-2014 15:17:21 (UTC+8)-
dc.date.issued (上傳時間) 25-Aug-2014 15:17:21 (UTC+8)-
dc.identifier (Other Identifiers) G1003520322en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/69200-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 100352032zh_TW
dc.description (描述) 102zh_TW
dc.description.abstract (摘要) 在Heston架構下評價VIX選擇權與實證分析zh_TW
dc.description.abstract (摘要) In this thesis, we give a quasi-thorough review of the different VIX options pricing models in the literature, before developing the Heston stochastic volatility model as it pertains to pricing VIX options. Our empirical tests and results show that the Heston model is able to quite capture empirical characteristics of the VIX, although the model does exhibit some inconsistencies with regards to the stability of the parameters over time. Instead of invalidating the model, this shows that the Heston model setup is acceptable as an alternative to pricing VIX options until the advent of a better model.en_US
dc.description.tableofcontents Table of Content: Pricing VIX Options under Heston Framework and Empirical Analysis
     
     I. Introduction 4
     II. Motivation 5
      1. Historical Background 7
      1.1. Volatility Swaps 7
      1.2. Variance Swaps 7
      2. VIX Index 8
      2.1. VIX Calculation Formula 9
      2.2. VIX Futures 10
      2.3. VIX Options 11
     III. VIX Modeling review 11
     VI. The Model 19
      1. The Heston Model: Stochastic Volatility 19
      2. Solution to the Heston Model 20
     V. Methodology & Data 21
      1. Data 21
      2. Model Calibration 22
     VI. Empirical Results 23
      1. Parameter Estimates 23
      2. Parameter Variation Over Time 25
      3. The Effects Of Changing Parameters 28
     VII. Conclusion 30
     A. Bibliography 32
     B. Appendix 34		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1003520322en_US
dc.subject (關鍵詞) Heston Modelen_US
dc.subject (關鍵詞) VIX Optionsen_US
dc.subject (關鍵詞) Stochastic Volatilityen_US
dc.subject (關鍵詞) Mean-reversionen_US
dc.subject (關鍵詞) Volatility Smileen_US
dc.subject (關鍵詞) Calibrationen_US
dc.subject (關鍵詞) Option Pricingen_US
dc.title (題名) 在Heston架構下評價VIX選擇權與實證分析zh_TW
dc.title (題名) Pricing VIX Options under the Heston Framework and Empirical Analysisen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Bibliography
     
     1. Bakshi, G., C. Cao and Z. Chen (1997). "Empirical performance of alternative option pricing models." The Journal of Finance 52(5): 2003-2049.
     2. Black, F. and M. Scholes (1973). "The pricing of options and corporate liabilities." The journal of political economy: 637-654.
     3. Carr, P. and R. Lee (2007). "Realized volatility and variance: Options via swaps." Risk 20(5): 76-83.
     4. Carr, P. and R. Lee (2008). Robust replication of volatility derivatives. PRMIA award for Best Paper in Derivatives, MFA 2008 Annual Meeting.
     5. Carr, P. and R. Lee (2009). "Volatility derivatives." Annu. Rev. Financ. Econ. 1(1): 319-339.
     6. Christoffersen, P., S. Heston and K. Jacobs (2009). "The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well." Management Science 55(12): 1914-1932.
     7. Cox, J. C., J. E. Ingersoll Jr and S. A. Ross (1985). "A theory of the term structure of interest rates." Econometrica: Journal of the Econometric Society: 385-407.
     8. Detemple, J. and C. Osakwe (2000). "The valuation of volatility options." European Finance Review 4(1): 21-50.
     9. Detlefsen, K. and W. K. Härdle (2006). Calibration risk for exotic options, SFB 649 discussion paper.
     10. Feller, W. (1951). "Two singular diffusion problems." Annals of mathematics: 173-182.
     11. Gatheral, J. (2006). The volatility surface: a practitioner`s guide, John Wiley & Sons.
     12. Goard, J. and M. Mazur (2013). "Stochastic Volatility Models and the Pricing of Vix Options." Mathematical Finance 23(3): 439-458.
     13. Grünbichler, A. and F. A. Longstaff (1996). "Valuing futures and options on volatility." Journal of Banking & Finance 20(6): 985-1001.
     14. Heston, S. L. (1993). "A closed-form solution for options with stochastic volatility with applications to bond and currency options." Review of financial studies 6(2): 327-343.
     15. Lin, Y. N. and C. H. Chang (2009). "VIX option pricing." Journal of Futures Markets 29(6): 523-543.
     16. Moodley, N. (2005). "The Heston model: A practical approach with Matlab code." Bachelor Thesis, University of the Witwatersrand, Johannesburg, math. nyu. edu.
     17. Psychoyios, D. and G. Skiadopoulos (2006). "Volatility options: Hedging effectiveness, pricing, and model error." Journal of Futures Markets 26(1): 1-31.
     18. Simon, D. P. and J. Campasano (2012). "The VIX Futures Basis: Evidence and Trading Strategies." The Journal of Derivatives 21(3): 54-69.
     19. Wang, Z. and R. T. Daigler (2011). "The performance of VIX option pricing models: Empirical evidence beyond simulation." Journal of Futures Markets 31(3): 251-281.
     20. Whaley, R. E. (1993). "Derivatives on market volatility: Hedging tools long overdue." The journal of Derivatives 1(1): 71-84.
     21. Whaley, R. E. (2009). "Understanding the VIX." The Journal of Portfolio Management 35(3): 98-105.
     22. Zhang, J. E. and Y. Zhu (2006). "VIX futures." Journal of Futures Markets 26(6): 521-531.		zh_TW