本文是以BS模型和 Merton模型來配適存續期間在民國89年到民國90年4月的11檔上市認購權證的市價，並比較兩模型每日避險的損益狀況。
過去不少與避險有關的文獻，均是採用模擬的方法做為研究，本文考量市場的實際狀況，以實證方法比較各避險區間的避險效果，並比較是否長的避險區間之風險與報酬會一致地高於短的避險區間之風險與報酬。
結果顯示，當股票的波動率處於高水準時，兩模型的配適能力並沒有顯著差別，且避險效果也沒有顯著的不同。另外發現，較長的避險區間，其報酬與風險並不會一致地高於較短的避險區間之報酬與風險，但這可能與模型或避險區間的選擇無關，而與股價行為有關。

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目錄
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機與目的 3
1.3 研究限制 4
1.4 研究架構 5
第二章 文獻回顧 6
2.1 股價模型的相關文獻 6
2.1.1 擴散過程（Diffusion Process） 6
2.1.2 跳躍過程（Jump Process） 7
2.2 非連續避險的相關文獻 8
2.2.1 無交易成本假設下的非連續避險 9
2.2.2 有交易成本假設下的非連續避險 10
第三章 模型描述 11
3.1 BS模型 11
3.1.1 股價模型假設 11
3.1.2 BS選擇權定價模型 13
3.2 MERTON模型 14
3.2.1 股價模型假設 14
3.2.2 Merton選擇權定價模型 15
3.3 避險定義、階段與策略 19
3.3.1 避險定義 19
3.3.2 避險階段 20
3.3.3 避險策略 21
3.4 避險誤差 22
第四章 研究方法 26
4.1 資料的選取與來源 26
4.2 參數估計 27
4.2.1 決定估計期間 27
4.2.2 決定無風險利率 28
4.2.3 BS模型參數估計的方法與結果 29
4.2.4 Merton模型參數估計的方法與結果 30
4.3 價格計算 35
4.3.1 BS價格計算 35
4.3.2 Merton價格計算 35
4.4 衡量指標 36
4.4.1 模型配適度的衡量指標 36
4.4.2 避險效果的衡量指標 37
第五章 實證結果 38
5.1 實證結果一：權證市價與BS價格、MERTON價格之比較 38
5.2 實證結果二：間斷避險策略比較 47
5.2.1 以市價衡量的BS避險比率之避險效果 47
5.2.2 以市價衡量的Merton避險比率之避險效果 50
5.2.3 BS避險比率與Merton避險比率之比較 53
5.2.4 以理論價衡量的BS及Merton避險比率之避險效果 54
第六章 結論與後續研究建議 64
6.1 結論 64
6.2 後續研究建議 66
參考文獻 67
國內文獻 67
國外文獻 67
表目錄
表 4-1 認購權證發行資料 26
表 4-2 長期峰態估計 28
表 4-3 無風險利率 28
表 4-4 第一期兩模型參數估計值 32
表 4-5 第二期兩模型參數估計值 33
表 4-6 第三期兩模型參數估計值 33
表 4-7 第四期兩模型參數估計值 33
表 5-1 兩模型之配適誤差比較 38
表 5-2 兩模型之配適誤差比較 39
表 5-3 兩模型價格差異之比較 45
表 5-4 BS避險報酬及風險 48
表 5-5 BS避險報酬SHARPE指標 49
表 5-6 MERTON避險報酬及風險 51
表 5-7 MERTON避險報酬SHARPE指標 52
表 5-8 BS避險報酬及風險 57
表 5-9 BS避險報酬SHARPE指標 58
表 5-10 MERTON避險報酬及風險 59
表 5-11 MERTON避險報酬SHARPE指標 60
表 5-12 中信04的BS避險報酬及風險 63
圖目錄
圖 5-1 元大15的兩模型配適誤差之差異 41
圖 5-2 權證市價與BS價格、MERTON價格之比較圖 42
圖 5-3 中信04之BS模型避險誤差：市價衡量 V.S. 理論價衡量 55

參考文獻
國內文獻
1. 王麗妙，1999，以跳躍-擴散模型評價單一型認購權證之實證研究，國立高雄第一科技大學金融營運所，碩士論文
2. 李存修暨台大財務金融研究所，1999，台股認購權證個案集，智勝文化事業有限公司
3. 林筠，1994，期貨與選擇權避險效果評估指標，Working Paper No.9302
4. 劉岳玲，1998，認購權證發行券商避險策略之研究，國立中山大學財物管理研究所，碩士論文

國外文獻
1. Akgiray, V. and G. Booth, 1986, "Stock Price Processes with Discontinuous Time Paths: An Empirical Examination.", Financial Review,vol.21,pp.163-184.
2. Ball,A.C. and W. N. Torous,1983, "A Simplified Jump Process for Common Stock Returns." Journal of Financial and Quantitative Analysis,vol.16, pp.53-65.
3. Ball,A.C. and W. N. Torous,1985a, "On Jumps in Stock Returns", Journal of Financial and Quantitative Analysis, vol.10, pp.337-351.
4. Ball,A.C. and W. N. Torous,1985b, "On Jump in Common Stock Prices and Their Impact on Call Option Pricing." Journal of finance,vol.40,pp.155-173.
5. Beckers,S.,1981,"A Note on Estimating the Parameters of the Diffusion-Jump Model of Stock Returns." Journal of Financial and Quantitative Analysis, vol.16,pp.127-139,March.
6. Black,F., and M.Scholes.”The Valuation of Option Contracts and a Test of Market Efficiency.” Journal of Finance,27(May 1972),pp.399-417.
7. Black,F. and M.Scholes,1973, "The Pricing of Options and Corporate Liabilities." Journal of Political Economy,vol.18, pp.637-659,May-June.
8. Boyle,P.P., and D.Emanuel. “Discretely Adjusted Option Hedges.” Journal of Financial Economics,8(1980),pp.259-282.
9. Boyle,P.P., and T. Vorst. ”Option Replication in Discrete Time with Transaction Costs.” Journal of Finance,47(1992),pp.271-293.
10. Chang,W.Carolyn,1995, "A No-Arbitrage Martingale Analysis for Jump-Diffusion Valuation." Journal of Financial Research, pp.351-381, Fall.
11. Cox,J.C. and S. Ross. "The Pricing of Options for Jump Processes." Working Paper No. 2-75. University of Pennsylvania, Rodney L. White Center for Financial Research April 1975.
12. Cox,J.C. and S. Ross,1976, "The Valuation of Options for Alternative Stochastic Processes." Journal of Financial Economics, vol.3, pp.145-166,Jan-March.
13. Fama,Eugene F.,1965,"The Behavior of Stock Market Prices." Journal of Business, vol.38,pp.34-105,Jan.
14. Feinstone,L.,1985,"Minute by Minute: Efficiency,Normally and Randomness in Intradaily Asset Prices." Unpublished manuscript.
15. Figlewski,S.“Options Arbitrage in Imperfect Markets” Journal of Finance,44 (December 1989),pp.1289-1311.
16. Galai,D. “The Compoenets of the Return from Hedging Options Against Stocks” Journal of Business,56(January 1983),pp.45-54.
17. Jones,E.P,1984, "Option Arbitrage and Strategy with Large Price Changes." Journal of Financial Economics, vol.13, pp.91-113, March.
18. Jarrow,R.A. and E.R. Rosenfeld,1984, "Jump Risks and the Intertemporal Capital Asset Pricing Model.", Journal of Business,vol.57,pp.337-351.
19. Kabanov, Yuri M., Safarian, Mher M, 1997 "On Leland's strategy of option pricing with transactions costs." Finance and Stochastics, vol. 1, issue 3, pp.239 -250
20. Kremer,J.W. and R. L. Roenfeldt,1992, "Warrant Pricing: Jump-Diffusion vs. Black-Scholes." Journal of Financial and Quantitative Analysis, vol.28,pp.255-272, June.
21. Lauterbach,B.and P.Schultz,1990, "Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives." Journal of Finance,vol.45,pp.1181-1209,Sep.
22. Leland, H. E., 1985, "Option Pricing and Replication with Transaction Costs." Journal of Finance 40, pp.1283-1301.
23. Hull,C.John,Options,Futures,And Other Derivatives,Prentice Hall International Editions,2000,Fourth Edition.
24. Mandlebrot,B,1963, "The Variation of Certain Speculative Prices." Journal of Business,vol.36,pp.394-419, Oct.
25. Merton,R.C,1973, "Theory of Rational Option Pricing." Bell Journal of Economics and Management Science,vol.4,pp.141-183.
26. Merton,R.C,1976, "Option Pricing When the Underlying Stock Returns Are Discontinuous." Journal of Financial Economics, vol.3,pp.125-144,Jan.-March.
27. Noreen,E. and M.Wolfson,1981,"Equilibrium Warrant Pricing Models and Accounting for Executive Stock Options." Journal of Accounting Research,vol.19,pp.384-398, Autumn.
28. Naik,V. and M.Lee,1990, "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns." The Review of Financial Studies,vol.3,pp.493-521.
29. Oldfield,G., R. Rogalski and R.Jarrow,1977, "An Autoregressive jump process for common stock returns." Journal of Financial Economics, vol.5,pp.389-418,Dec.
30. Press,J.S. "A Compound Events Model of Security Prices, 1967," Journal of Business, vol.40, pp.317-335, July.
31. Rosenberg,B.,1972, "The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security prices." Working Paper No.11, Graduate School of Business, Univ. of CA, Berkeley.
32. Rosenfeld,E.,1982, "Stochastic Processes of Common Stock Returns: An Empirical Investigation." Working Paper 82-34, Graduate School of Business Administration, Harvard Univ.
33. Rubinstein,M.,1985, "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978." Journal of Finance,vol.41,pp.455-480,June.
34. Samuelson,P.A,1965, "Rational Theory of Warrants Pricing." Industrial Management Review, vol.6, pp.13-31,Spring.
35. Schwartz,E.S,1977, "The Valuation of Warrants: Implementing a New Approach." Journal of Financial Economics,vol.4, pp.79-93,Jan.
36. Shastri,K. and Wethyavivorn K,1987, "The Valuation of Currency Options for Alternate Stochastic Processes." Journal of Financial Research,vol.39,pp.283-293,Summer.
37. Sterk,W.,1983, "Comparative Performance on the Black-Scholes and Roll-Geske-Whaley Option Pricing Models." Journal of Financial and Quantitative Analysis,vol.18,pp.345-355, Sep.
38. Wei,Jason Z,1995,"Empirical Tests of the Pricing of Nikkei Put Warrants." The Financial Review,vol.30,pp.211-241,May.
39. Whalley,A.E.,and P.Wilmott. 1997 "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs." Mathematical Finance,7, pp.307-324.