異質信念與自信結構下選擇權的價格與性質分析

Abstract

在近代的財務模型中通常會假設所有的投資者皆了解資產的性質並分享相同的信念。然而在真實世界中，所有投資者的看法皆不同，而且在實證中也發現投資者的異質信念對於資產價格有相當顯著的影響。 在這一篇論文中，我們研究當投資者對於風險性資產具有異質信念與異質自信時對於選擇權的價格之影響。我們在第二章中推導具常態分配信念結構下的選擇權評價公式並且分析投資者的樂觀程度與看法差異程度對於選擇的價格影響。在第三章中，我們放寬了常態分配的假設，並重新推導一個更具一般性的選擇權價格公式。此公式可以引入各種不同形態的信念結構，例如，均勻分配和對數常態分配。經由不同的信念結構我們重新檢驗第二章所得結果是否具一般性。在第四章中，我們推導具有自信結構的選擇價格公式，並且以均勻分配和對數常態分配為特例去分析異質自信對選擇權價格的影響。 我們證明了當市場沒有異質信念和異質自信時，本論文所推導的價格公式將退化成Black-Scholes的選擇權公式。另外我們也發現信念結構與自信結構對於選擇權的價格及價格波動具有相當程度的影響，並且對隱含波動率的微笑曲線(volatility smile)具有相當明顯的解釋力。

In the modern finance literature, standard asset pricing models generally assume that all investors know the structure of the economy or share the same beliefs about the properties of asset dividends. However, agents in the real world differ in their beliefs, and heterogeneous beliefs significantly influence asset pricing (Anderson et al. 2005). In this paper, we study the properties of option prices when agents have heterogeneous beliefs and confidence levels regarding the underlying dividend process of a risky security. In Chapter 2, we derive a call option price formula when the belief structure is approximated by a normal distribution. In Chapter 3, we release the normal distribution assumption and allow this option price formula to be more general, which allows us to choose various distribution functions to model agents’ heterogeneous beliefs. Uniform and lognormal distributions are applied as two special cases to model agents’ heterogeneous belief structures. In Chapter 4, we characterize the option prices and their properties for general distributions of agents’ confidence structure. Again, the uniform and lognormal distributions are used as two special cases to model the structure of agents’ heterogeneous confidences. Our call option price formulas reduce to the Black-Scholes (1973) formula when the belief structure is degenerated into a homogeneous belief structure and the confidence structure is degenerated to a point 0. Otherwise, the call option price, its volatility, and the smile phenomenon of option prices are shown to be, in general, dependent upon the mean and variance of agents’ belief and confidence structures.