# 臺灣博碩士論文加值系統

(3.95.131.146) 您好！臺灣時間：2021/07/26 04:17

:::

### 詳目顯示

:

• 被引用:0
• 點閱:140
• 評分:
• 下載:0
• 書目收藏:0
 本文提出了一個固定機率-隨機波動度的隱含波動二元樹的建構方法。此方法改善了先前其他學者曾提出方法的缺點。相較於Derman-Kani 隱含波動二元樹與Li 隱含波動二元樹，以此方法建構隱含波動樹時，具有相當的穩定性。在Derman-Kani 隱含波動二元樹中有不良機率的問題，亦即在二元樹建構的同時，會出現機率大於1 或小於0 的狀況；在Li 隱含波動二元樹中，雖改良了不良機率發生的情形，但當隱含波動微笑曲線陡峭時，在建構樹的過程中，股價仍會發生違反無套利原則的狀況。然而，本文所提出的新方法，不僅改善了上述二者的缺點，在二元樹的建構概念上相當的簡單易懂，選擇權評價的結果也相當穩定。
 This thesis proposes a constant probability-stochastic volatility implied binomial tree. Our method improves upon some weaknesses of previous works. Compared with the Derman-Kani tree (1994) and the Li tree (2000), our method is considerably more stable. In our method, neither the nvalid transition probability problem occurs, like in the Derman-Kani tree, nor the results of option pricing diverge when the slope of volatility with respect to the strike price is steep, as in the Li tree. Incorporating theknown local volatility function, our method constructs the implied binomial tree directly by forward induction. The option value is calculated from the stock prices in the terminal nodes of the tree backward. As a whole, for the proposed constant probability-stochastic volatility implied binomial tree, its construction is direct, and itsimplementation is straightforward.
 Chapter 1 Introduction ...................... 11.1 Introduction............................. 11.2 Motivations and Contributions ........... 21.3 Organization of this Thesis ............. 3Chapter 2 Literature Review.................. 42.1 Implied Volatility Surface .............. 42.2 Local Volatility Surface ................ 42.3 Causes of Strike Structure of Volatility. 52.4 Volatility Modeling ..................... 62.5 Implied Trees ........................... 7Chapter 3 The Derman-Kani Tree ...............93.1 The Derman-Kani Algorithm................ 93.2 Invalid Transition Probabilities........ 123.3 Replacement of Nodes that Violate the No-Arbitrage Principle... 14Chapter 4 Problems with the Li Tree......... 154.1 The Li Algorithm ....................... 154.2 Problem of Stock Prices which Violate the No-Arbitrage Principle............. 18Chapter 5 An Alternative Method in Constructing Implied Tree .....235.1 Building a Recombining Binomial Tree ... 235.2 Assumptions and Settings ............... 255.3 Building a Constant Probability-Stochastic Volatility Recombining Tree.......... 255.4 Numerical Illustration ................. 28Chapter 6 Conclusions ...................... 32Appendix A.................................. 33Appendix B.................................. 37References.................................. 39
 [1] Ait-Sahalia, Yacine, and Andre W. Lo. “Nonparametric Risk Management and Implied Risk Aversion.” Journal of Econometrics, 94 (2000), pp. 9－51.[2] Barle, S and N.Cakici. “How to Grow A Smiling Tree.” The Journal of Financial Engineering, 7 (1996), pp. 127－146.[3] Barndorff-Nielsen, O.E. and N. Shepherd. “Incorporation of a Leverage Effect in a Stochastic Volatility model.” Working Paper (1999), The Centre forMathematical Physics and Stochastics, University of Aarhus.[4] Bates, D. “Post-87 Crash Fears in the S&P500 Futures Option Market.” Journal of Econometrics, 94 (2000), pp. 181－238.[5] Black, F. and M.J. Scholes. “The Pricing of Options on Corporate Liabilities.”Journal of Political Economy, 81(1973), pp. 637－654.[6] Bollen, N. and R. Whaley. “Does the Net Buying Pressure Affect the Shape of Implied Volatility Functions?” Journal of Finance, 59 (2004), pp. 711－753[7] Brown, G. and Toft, K. B. “Constructing Binomial Trees from Multiplied Implied Probability Distributions,” Journal of Derivatives 7 (1999), pp. 83－100.[8] Campbell, J. Y. and A. S. Kyle. “Smart Money, Noise Trading and Stock Price Behavior,” Review of Economic Studies, 60 (1999), pp. 1－34.[9] Corrado, C.J. and Su, T. “Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices,” The European Journalof Finance, 3 (1997), pp. 73－85.[10] Cox, J., S. Ross, and M. Rubinstein. “Option Pricing: A Simplified Approach,”Journal of Financial Economics, 7 (1979), pp. 229－263.[11] Derman, E., Kani, I. “The Volatility Smile and Its Implied Tree,” Quantitative Strategies Research Notes (1994). New York: Goldman Sachs.[12] Derman, E., Kani, I. & Chriss, N. “Implied Trinomial Trees of the Volatility Smile,” Journal of Derivatives, 4 (1996), pp. 7－12.[13] Dupire, B. “Arbitrage Pricing with Stochastic olatility,” Proceedings of AFFI Conference in Paris, June 1992.[14] Dupire, B. “Pricing with A Smile,” Risk, 8 (1994), pp. 76－81.[15] Heston. “A Closed-Form Solution for Options with Stochastic Volatilities with Applications to Bond and Currency Options,” The Review of Financial Studies, 6(1993), pp. 327－343[16] Hull, J. and A. White. “The Pricing of Options on Assets with Stochastic Volatilities,” Journal of Finance, 42 (1987), pp. 281－300.[17] Hull, J.C., Options, Futures, and Other Derivative Securities, Sixth edition (2007), Prentice Hall, New Jersey.[18] Jackwerth, J. C. and M. Rubinstein, “Recovering Probability Distributions from Option Prices,” Journal of Finance, 51 (1996), pp. 1611－1631.[19] Jackwerth, J. “Generalized Binomial Trees,” Journal of Derivatives, 5 (1997), pp.7－17.[20] Jackwerth, J. “Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review,” Journal of Derivatives, 7 (1999), pp. 66－82.[21] Jackwerth. “Recovering Risk Aversion from Option Prices and Realized Returns,” The Review of Financial Studies, 13 (2000), pp. 433－451.[22] Jarrow, R. and Rudd, A. “Approximate Option Valuation for Arbitrary Stochastic Processes,” Journal of Financial Economics, 10 (1982), pp. 347－369.[23] Li, Yanmin. “A New Algorithm for Constructing Implied Binomial Trees: Does the Implied Model Fit Any Volatility Smile,” Journal of Financial Engineering,4 (2000), pp. 69－95.[24] Lim, K. and D. Zhi, 2002. “Pricing Options Using Implied Trees: Evidence from FTSE-100 Options,” Journal of Futures Markets, 22, pp. 601－626.[25] London, J. Modeling Derivatives in C++ (2004), John Wiley & Sons, pp. 274－323.[26] Mahieu and Schotman. “An Empirical Application of Stochastic Volatility Models,” Journal of Applied Economy, 13 (1998), pp. 330－360.[27] Melick, W. R. and Thomas, C. P. “Recovering an Asset''s Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis,” The Journal of Financial and Quantitative Analysis, 32 (1997), pp. 91－115.[28] Nelson, D. “Conditional Heteroskedasticity in Asset Returns: A new Approach,”Econometrica, 59 (1991), pp. 347－370.[29] Nicolato, E. and E. Venardos. “Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck Type,” Mathematical Finance, 13 (2003), pp. 445－466.[30] Pena, I. & G. Rubio & G. Serna. “Why Do We Smile? On the Determinants of the Implied Volatility Function," Journal of Banking and Finance, 23 (1999), pp.1151－1179.[31] Platen, E., Schweitzer, M. “On Feedback Effects form Hedging Derivatives,”Mathematical Finance, 8 (1998), pp. 67－84.[32] Pritsker, M. “Evaluating Value at Risk Methodologies: Accuracy versus Computational Time,” Journal of Financial Services Research, 12 (1997), pp.201－242.[33] Rubinstein, M. “Implied Binomial Trees,” Journal of Finance, 49 (1997), pp.771－818.[34] Stein, E. M., and J. C. Stein. “Stock Price Distributions with Stochastic Volatility: An Analytic Approach,” Review of Financial Studies, 4 (1991), pp. 727－752.
 國圖紙本論文
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 1 衍生性商品數值評價─樹狀圖法

 無相關期刊

 1 臺指選擇權的評價－一般化極端值模型與B-S模型的比較 2 以樹狀模型評價保證最低提領給付保險附約 3 利用具相關性之二元樹模型做信用組合違約模擬 4 動態隱含波動度模型：以台指選擇權為例 5 台指選擇權隱含波動度之資訊含量 6 選擇權隱含波動率對未來波動率之資訊內涵 7 利用隱含樹狀模型評價波動率及變異數交換 8 由隱含波動率曲面預測未來實際波動率 9 臺指選擇權隱含波動率變動因素之探討 10 無模型隱含波動度及其資訊內涵─以外匯選擇權為例 11 選擇權隱含波動度與現貨市場波動度之領先落後關係 12 誰導致台指選擇權隱含波動率偏斜 13 VIX選擇權隱含價差與未來VIX指數變動之關係 14 利用股價與選擇權的數據來估計GARCH選擇權定價模型 15 「二次逼近法」在評價衍生性商品的應用―以台指選擇權為例

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室