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研究生:陳昭君
研究生(外文):Chen, Chao-Chun
論文名稱:資產報酬自我相關下之選擇權評價理論
論文名稱(外文):The Valuation of European Options When Asset Returns Are Autocorrelated
指導教授:廖四郎廖四郎引用關係
指導教授(外文):Liao, Szu-Lang
學位類別:博士
校院名稱:國立政治大學
系所名稱:金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:55
中文關鍵詞:選擇權評價報酬自我相關風險中立評價理論
外文關鍵詞:Option PricingAutocorrelated ReturnsMartingale Asset Pricing
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有鑑於資產報酬常具有自我相關的特性,本文探討當標的資產報酬服從一階移動平均過程之選擇權(MA(1)-type option)評價。研究結果顯示,除了總變異因子(total volatility input)不同外,MA(1)-type option 的評價公式與 Black and Scholes 模型極為相似。而根據數值分析的結果,即使資產報酬間自我相關的程度薄弱,由一階移動平均過程產生之自我相關仍會對選擇權價值造成顯著影韾。
This paper derives the closed-form formula for a European option on an asset with returns following a continuous-time type of first-order moving average process, which is named as an MA(1)-type option. The pricing formula of these options is similar to that of Black and Scholes except for the total volitility input. Specifically, the total volatility input of MA(1)-type options is the conditional standard deviation of continuous-compounded returns over the option's remaining life, whereas the total volatility input of Black and Scholes is indeed the diffusion coefficient of a geometric Brownian motion times the square root of an option's time to maturity. Based on the result of numerical analyses, the impact of autocorrelation induced by the MA(1)-type process is significant to option values even when the autocorrelation between asset returns is weak.
1 Introduction
2 Literature Review
3 The Setting:
A Continuous-time Process of Autocorrelated Asset Returns
4 Option Pricing When Asset Returns follow an MA(1)-type Process
4.1 The Closed-form Formula of MA(1)-type Call Options
4.2 The Closed-form Formula of MA(1)-type Put Options
5 Numerical Analyses
5.1 Numerical Analyses for MA(1)-type Call Options
5.2 Numerical Analyses for MA(1)-type Put Options
6 Conclusions
A The proof of Lemma 4.1
B The dynamics of stock prices under measure R
Bibliography
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Jokivuolle, E. (1998). Pricing European options on autocorrelated indexes. Journal of Derivatives, 6, 39-52.

Klebaner, F. C. (1998). Introduction to stochastic calculus with applications. London: Imperial College.

Lamberton, D., & Lapeyre, B. (1996). Introduction to stochastic calculus applied to finance. London; New York: Chapman & Hall.

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Roll, R. (1977). An analytic valuation formula for unprotected American call options on stocks with known dividends. Journal of Financial Economics, 5, 251-258.
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