title page
Abstract
Contents
1. Introduction 9
2. Previously Established Option Pricing Models 10
3. Data Description 12
4. Parameter estimation and fitness test 17
4.1. Parameter estimation method 17
4.2. Implied Parameters and In-Sample Pricing Fit 18
i/I) Call options data set estimation 20
ii) Put options data set estimation 22
iii) Mixed options data set estimation 23
4.3. Model Estimation Error 24
4.4. Model fitness test 27
4.5. Out-of-Sample Pricing Performance 28
4.6. Delta Hedge Performance 30
5. Conclusion 32
Appendix 33
요약문 35
References 36
감사의 글 76
Table 1. Sample(Sampe) size for 'Call options', 'Put options', and 'Mixed options' 57
Table 2. Sample properties of KOSPI 200 Index call options put options price 57
Table 3. Sample properties of KOSPI 200 Index call options and put options implied volatility 57
Table 4. Options estimated each half year with BS model. 58
Table 5. Model parameter estimation using Call options data set 59
Table 6. Model parameter estimation using Put options data set 62
Table 7. Model parameter estimation using Mixed options data set 65
Table 8. Out-of-Sample Pricing Errors (one day ahead) call 68
Table 9. Out-of-Sample Pricing Errors (one day ahead) put 69
Table 10. Out-of-Sample Pricing Errors (one day ahead) Mixed 70
Table 11. Out-of-Sample Pricing Errors (one week ahead) call 71
Table 12. Out-of-Sample Pricing Errors (one week ahead) put 72
Table 13. Out-of-sample Pricing Errors (one week ahead) Mixed 73
Table 14. Hedge performance (one day ahead) 74
Table 15. Hedge performance (three day ahead) 75
Fig 1. Observed tic price of call options and put options with the same maturity and strike price for 2000. January, 6th. The solid line is max(S(t)-K,(t)) and put options are used to retain no arbitrage call options price using put-call parity.(이미지참조) 39
Fig 2a. Implied volatility of call options (o) and put options (x) with the same maturity and strike price for 2000, January, 6th.(이미지참조) 39
Fig 2b. Time series of the call options and put options, nearest to moneyness 1, implied volatility for six month sub periods. Half of the sub periods show that put options has higher implied volatility compared to call options. Disjoint implied volatility movement is noticable 40
Fig 3. Implied volatility calculated using the BS model for every Call option within the no-arbitrage bound. Data period is from January 2000, to December 2002. 41
Fig 4. Implied volatility calculated using the BS model for every Put option within the no-arbitrage bound. Data period is from January 2000, to December 2002. 42
Fig 5. Implied volatility calculated using the BS model for every Mixed option within the no-arbitrage bound. Data period is from January 2000, to December 2002. 43
Fig 6. In sample Call options pricing error using the same day parameter estimation for each models. Pricing error = observed market price - calculated price using the same day data set estimated parameters 44
Fig 7. In sample Put option pricing error using the same day parameter estimation for each models. Pricing error = observed market price - calculated price using the same day data set estimated parameters 45
Fig 8. In sample Mixed option pricing error using the same day parameter estimation for each model. Pricing error = observed market price - calculated price using the same day data set estimated parameters 46
Fig 9. In sample implied volatility using the BS model (solid line) and SV, SVo8, SVJ, SVJV, SVSI, and DPS model price implied volatility (broken line) for call options with less than 15 days to maturity 47
Fig 10. In sample implied volatility using the BS model (solid line) and SV, SVo8, SVJ, SVJV, SVSI, and DPS model price implied volatility (broken line) for put options with less than 15 days to maturity 48
Fig 11. In sample implied volatility using the BS model (solid line) and SV, SVo8, SVJ, SVJV, SVSI, and DPS model price implied volatility (broken line) for mixed options with less than 15 days to maturity 49
Fig 12. In sample implied volatility using the BS model (solid line) and SV, SVo8, SVJ, SVJV, SVSI, and DPS model price implied volatility (broken line) for call options with more than 15 days to maturity and less than 30 days to maturity 50
Fig 13. In sample implied volatility using the BS model (solid line) and SV, SVo8, SVJ, SVJV, SVSI, and DPS model price implied volatility (broken line) for put options with more than 15 days to maturity and less than 30 days to maturity 51
Fig 14. In sample implied volatility using the BS model (solid line) and SV, SVo8, SVJ, SVJV, SVSI, and DPS model price implied volatility (broken line) for mixed options with more than 15 days to maturity and less than 30 days to maturity 52
Fig 15. Individual model fitting of implied volatility at the abnormal day January 5th, 2000. The BS model implied volatility (dot) and the SV, SVo8, SVJ, SVJV, SVSI, and DPS model options price induced implied volatility (solid line) 53
Fig 16. Model fitness test using Call options. Spot volatility for each model which equates todays options price using the previous days estimated parameters. The solid line is the implied volatility by the BS model. Implied volatility is plotted by moneyness and separated by time to maturity left (TTM).... 54
Fig 17. Model fitness test using put options. Spot volatility for each model which equates todays options price using the previous days estimated parameters. The solid line is the implied volatility by the BS model. Implied volatility is plotted by moneyness and separated by time to maturity left (TTM).... 55
Fig 18. Model fitness test using Mixed options. Spot volatility for each model which equates todays options price using the previous days estimated parameters. The solid line is the implied volatility by the BS model. Implied volatility is plotted by moneyness and separated by time to maturity left (TTM).... 56