Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/32597


Title: 位移與混合型離散過程對波動度模型之解析與實證
Displaced and Mixture Diffusions for Analytically-Tractable Smile Models
Authors: 林豪勵
Lin, Hao Li
Contributors: 陳松男
Chen, Son Nan
林豪勵
Lin, Hao Li
Keywords: 資產價格的動態過程
風險中立機率測度
選擇權評價公式
波動度傾斜
波動度微笑
非線性規劃
參數校準
asset-price dynamics
risk-neutral density
option pricing formula
volatility skew
volatility smile
nonlinear programming
calibration of parameters
Date: 2008
Issue Date: 2009-09-17 13:49:09 (UTC+8)
Abstract: Brigo與Mercurio提出了三種新的資產價格過程,分別是位移CEV過程、位移對數常態過程與混合對數常態過程。在這三種過程中,資產價格的波動度不再是一個固定的常數,而是時間與資產價格的明確函數。而由這三種過程所推導出來的歐式選擇權評價公式,將會導致隱含波動度曲線呈現傾斜曲線或是微笑曲線,且提供了參數讓我們能夠配適市場的波動度結構。本文利用台指買權來實證Brigo與Mercurio所提出的三種歐式選擇權評價公式,我們發現校準結果以混合對數常態過程優於位移CEV過程,而位移CEV過程則稍優於位移對數常態過程。因此,在實務校準時,我們建議以混合對數常態過程為台指買權的評價模型,以達到較佳的校準結果。
Brigo and Mercurio proposed three types of asset-price dynamics which are shifted-CEV process, shifted-lognormal process and mixture-of-lognormals process respectively. In these three processes, the volatility of the asset price is no more a constant but a deterministic function of time and asset price. The European option pricing formulas derived from these three processes lead respectively to skew and smile in the term structure of implied volatilities. Also, the pricing formula provides several parameters for fitting the market volatility term structure. The thesis applies Taiwan’s call option to verifying these three pricing formulas proposed by Brigo and Mercurio. We find that the calibration result of mixture-of-lognormals process is better than the result of shifted-CEV process and the calibration result of shifted-CEV process is a little better than the result of shifted-lognormal process. Therefore, we recommend applying the pricing formula derived from mixture-of-lognormals process to getting a better calibration.
Reference: Black, F. and Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, pp. 637–654.
Brigo, D. and Mercurio, F., D. 2001. Displaced and mixture diffusions for analytically-tractable smile models. In: German, H., Madan, D.B., Pliska, S.R. and Vorst, A.C.F., Editors, 2001. Mathematical Finance Bachelier Congress 2000, Springer, Berlin.
Brigo, D. and Mercurio, F., 2002. Lognormal-mixture dynamics and calibration to market volatility smiles. International Journal of Theoretical and Applied Finance 5 4, pp. 427–446
Cox, J., 1975. Notes on option pricing I: Constant elasticity of variance diffusions. Working paper, Stanford University.
Cox, J. C. and Ross, S. A., 1976. The valuation of options for alternative stochastic processes. Journal of Financial Economics 3, pp. 145–166.
Jackwerth, J. C. and Rubinstein, M., 1996. Recovering probability distributions from option prices. Journal of Finance 51, pp. 1611–1631.
Rubinstein, M., 1994. Implied binomial trees. Journal of Finance 49, pp. 771–818.
Description: 碩士
國立政治大學
應用數學研究所
95751004
97
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0095751004
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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