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標題: 無母數迴歸在選擇權訂價模型之探討
A study on using Nonparametric Regressions in Option Pricing Models
作者: 邱晏瑜
Chiou, Yan-Yu
關鍵字: Black-Scholes 選擇權訂價模型;Black-Scholes option pricing model;無母數迴歸;選擇權評價;維度的困擾;模型設定錯誤;波動度微笑;nonparametric regression;option pricing;curse of dimensionality;model misspecification;volatility smile
出版社: 財務金融系所
引用: 參考文獻 林福來(2003), “無母數迴歸分析中顯著性檢定之研究”, 博士論文, 國立中正大學國際經濟研究所。 陳松男(2008), 《金融工程學(三版)》, 新陸書局。 陳浚泓(2003), “B-S 模式與隨機波動性定價模式之比較: 台灣股價指數選擇權之實證”,碩士論文, 成功大學企業管理所。 A‥ıt-Sahalia. and Lo, Y. (1998), “Nonparametric estimation of state-price density implicit asset prices,”, The Journal of Finance, 53(2), 499–547. A‥ıt-Sahalia, Y. and Duarte, J. (2003), “Nonparametric option pricing under shape rsstrictions,”, Journal of Econometrics, 116, 9–47. Barlow, R.E., Bartholomew, D.J., Bremner, J.m., and Brunk, H.D. (1972), Statistical Inference under Order Restrictions,, New York: Wiley. Black, F. and Scholes, M. (1973), “The pricing of option and corporate liabilities,”, Jouurnal of Political Economy, 81(4), 637–645. Breeden, D. and Litzenberger, R. (2008), “Prices of state-contingent claims implicit in options price,”, Journal of Business, 51, 621–651. Brike, M. and Dette, H. (2007), “Estimatig a convex function in nonparametric regression,”, Scandinavian Journal of Statistics, 34, 384–404. Brike, M. and Plize, K. (2009), “Nonparametric option pricing with no-arbitrage constraints,”, Journal of Financial Econometrics, 7(2), 53–76. Cox, John. C. and Ross, Stephen A. (1976), “The valuation of options for alternative stochastic processes,”, Journal of Financial Economics, 3, 145–166. Dette, H., Neumeyer, N., and Pilz, K.F. (2006), “A simple nonparametric estimator of a strictly monotone regression function,”, Bernoulli, 12, 469–490. Duan, Jin-Chuan (1995), “The garch option pricing model,”, Mathematical Finance, 5(1), 13–32. Dumas, Bernard, Fleming, Jeff, and Whaley, Robert E. (1998), “Implied volatillity functions empirical tests,”, The Journal of Finance, 53(6), 2059–2106. 57 Fan, Jianqing and Mancini, Loriano (2009), “Option pricing with model-guided nonparametric methods,”, Journal of the American Statistical Association, 104, 1351–1372. Fan, Jianqing and Yao, Qiwei (2003), Nonparametric and Parametric Methods,, Springer. Hayfield, T. and Racine, J. S. (2008), “Nonparametric econometrics: The np package,”, Journal of Statistical Software, 27. Heston, Steven L. (1993), “A closed-form silition for options with stochastic volatility with applications to bond and corrency option,”, Review of Financial Studies, 6, 327–343. Heston, Steven L. and Nandi, Saikat (2000), “A closed-form garch option valuation model,”, Review of Financial Studies, 13(3), 585–625. Hull, John . and White, Alan (1987), “The pricing of options on assets with stochastic volatilities,”, The Journal of Finance, 42, 281–300. Hull, John C. (2008), Options,Futures, And Other Derivatives , 7nd edition,, NJ: Upper Saddle River. Merton, Robert C. (1973), “Theory of rational option pricing,”, The Bell Journal of Economics and Mangement Science, 4(1), 141–183. (1976), “Option pricing when underlying stock returns are discontinuous,”, Journal of Financial Economics, 3, 125 – 144. Nadaraya, E. A. (1964), “On estimating regression,”, Theory of Probability and its Applications, 9, 141–142. Watson, G. S. (1964), “Smooth regression analysis,”, Sankhya: The Indian Journal of Statistics: Series A, 359–372.
隨著選擇權市場日漸擴大, 愈多參與者進入市場, 不論其交易目的為何, 準確且客觀
的參考價格是必要的。關於選擇權訂價, 繼Black and Scholes (1973)發表Black-Scholes
選擇權訂價模型之後, 許多學者投入財務工程領域中的選擇權定價。但Black-Scholes 選
型設定錯誤(Model misspecification) 的問題。而將無母數迴歸應用於選擇權評價時, 由
於無母數迴歸是純粹以資料配適選擇權價格, 因此可避免模型設定錯誤的問題。但使用無
母數迴歸進行評價時, 主要會面臨以下課題:
(1) 由於多維度的無母數迴歸將會面臨維度的困擾, 因此將無母數迴歸應用於選擇權評價
時, 需考慮維度的縮減。
(2) 由於無母數迴歸純粹以資料配適選擇權價格, 加入特定函數型式以導入財務理論, 是
研究, 本文樣本取自台灣經濟新報(Taiwan Economic Journal,TEJ),樣本期間橫跨2010年;
並將樣本分為全樣本與子樣本, 而在實證結果指出
(1) 三維度無母數迴歸模型, 不論在總樣本或是子樣本中即使不以Additive model 進行
修正, 在價平, 價內與不區分價性皆有著最佳的表現。
(2) 單維度無母數迴歸模型在價外時有著最佳的表現; 但單維度模型預測能力優於高維度
模型, 在迴歸分析中是一特異的現象。
(3) 本論文參考A‥ıt-Sahalia. and Lo (1998)與Fan and Mancini (2009)將波動度微笑納
入模型中, 以此建立三個半母數模型, 但表現皆遜於無母數迴歸模型。

As the financial markets expand, more and more participants enter into the
markets. No matter what their trading purposes are, precise and objective reference
prices are definitely essential. Since Black and Scholes (1973) developed the
famous Black-Scholes model, numerous scholars have dedicated themselves to the
option pricing models in the field of financial engineering. Apart from the structural
option pricing models, such as Black-Schole model, which may lead to model
misspecifications, the non-parametric option pricing models price the options purely
based on the observed pricing data. However, there are main problems in the applications
of nonparametric models to option pricings, which are:
(1) Multi-dimension nonparametric regressions face curse of dimensionality as pricing
options is of need to reduce the dimensions.
(2) There are specific functions for option pricing in financial theories. Hence, it is
necessary to consider financial information when applying nonparametric models.
This study aims to provide various non-parametric regression models ways to solve
the problems mentioned above, and specifically studies the Taiwan index option.
The samples used in this study are taken from the Taiwan Economic Journal, and
include data from 2010. The samples are sorted into full samples and subsamples,
(1) Three-dimensional nonparametric regression models yield the best results at the
money, in the money, and all sample , regardless of full sample or subsample, and
even without the additive model.
(2) One-dimensional nonparametric regression models yield the best results out the
money, and also predict better than multi-dimensional regression models, which is
a special case in regression models.
(3) This study references A‥ıt-Sahalia. and Lo (1998) and Fan and Mancini (2009),
which place the volatility smile in the model, thus creating three semi-parametric
models, but all yield results worse than that of the non-parametric models.
其他識別: U0005-3006201323190300
Appears in Collections:財務金融學系所

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