博碩士論文 972205003 詳細資訊




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姓名 張正鉉(Cheng-Syuan Chang)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 SABR模型下使用遠期及選擇權資料的參數估計
(Estimation under SABR Model using both Forward and Option Data)
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摘要(中) 本篇論文中我們使用SABR模型做為標的資產模型,藉由Black -Scholes歐式選擇權定價公式,SABR模型下對於Black-Scholes公式的隱含波動度具有封閉解的形式,接著我們考慮二種情況下的參數估計:首先考慮遠期契約價格以及波動度可觀測的情況,接著我們考慮波動度不可觀測的情況下,使用選擇權資料取代不可觀測的波動度,並以Aït-Sahalia提出變數變換的方式求得近似概似函數。最後以最大概似估計法求得參數的估計值,並以蒙地卡羅模擬比較整體性的結果。
摘要(英) We model the underlying asset with SABR model. According to the Black-Scholes formula, the implied volatility under the SABR model has a closed-form formula. Then we consider about the estimation as the volatility is observable or not. When the volatility is unobservable, the volatility state is replaced by proxies based on the implied volatility. Finally we obtain the estimator by applying the maximum likelihood estimator, and use the Monte Carlo simulation to complete the research.
關鍵字(中) ★ SABR模型
★ 波動度
★ 最大概似估計法
★ 蒙地卡羅模擬
關鍵字(英) ★ SABR model
★ Volatility
★ Maximum likelihood estim
論文目次 中文摘要…………………………………………………………………………i
英文摘要…………………………………………………………………………ii
誌謝 …………………………………………………………………………iii
目錄 …………………………………………………………………………iv
表目錄 …………………………………………………………………………v
符號說明…………………………………………………………………………vi
第一章 緒論……………………………………………………………………1
1.1 研究動機與目的………………………………………………………1
1.2 論文架構………………………………………………………………3
第二章 文獻回顧………………………………………………………………4
2.1 Black-Scholes歐式選擇權評價公式……………………………… 5
2.2 SABR模型………………………………………………………………7
第三章 研究方法………………………………………………………………9
3.1 波動度可直接觀察時,概似函數之介紹……………………………9
3-2 波動度不可直接觀察時,概似函數之介紹…………………………10
第四章 模擬結果………………………………………………………………12
第五章 結論……………………………………………………………………20
參考文獻…………………………………………………………………………21
參考文獻 [1]Aït-Sahalia, Y., 1999. Transition densities for interest rate and other nonlinear diffusions. Journal of Finance 54,1361–1395.
[2]Aït-Sahalia, Y., 2001. Closed-form likelihood expansions for multivariate diffusions. Working Paper, Princeton University.
[3]Aït-Sahalia, Yacine, Kimmel, Bob, 2007. Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics 83,413–452.
[4]Aït-Sahalia, Y., Lo, A., 1998. Nonparametric estimation of state-price-densities implicit in financial asset prices. Journal ofFinance 53, 499–547.
[5]Bakshi, G., Cao, C., Chen, Z., 2000. Do call prices and the underlying stock always move in the same direction? Review of Financial Studies 13, 549–584.
[6]Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the American Statistical Association, pp.171–181.
[7]Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities.Journal of Political Economy 81,637–654.
[8]Heston, S., 1993. A closed-form solution for options with stochastic volatility with applications to bonds and currency options. Review of Financial Studies 6, 327–343.
[9]Ledoit, O., Santa-Clara, P., Yan, S., 2002. Relative pricing of options with stochastic volatility. Working Paper,University of California at Los Angeles.
[10]Merton, R.C., 1973. The theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–183.
[11]Pan, J., 2002. The jump-risk premia implicit in options: evidence from an integrated time-series study. Journal of Financial Economics 63, 3–50.
[12]Stein, E.M., Stein, J.C., 1991. Stock price distributions with stochastic volatility: an analytic approach. Review of Financial Studies 4, 727–752.
[13]G. Vlaming. Pricing options with the SABR model. Master Thesis, University of Utrecht, The Netherlands., 2008.
指導教授 傅承德(Cheng-Der Fuh) 審核日期 2011-7-6
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