存在交易成本下之零水位定價與其普遍性

Zero-level Pricing with Transaction Cost and Universality

王景南(Jying-Nan Wang)

指導教授 ： 古思明

共同指導教授 ： 黃宜侯(Alex YiHou Huang)

元智大學/管理學院/管理研究所/博士(2008年)

摘要

在一般經濟數學的文獻中，市場上的新資產可經由零水位定價法得到唯一的價格。此方法的缺點是它所得到的價格與投資人的效用函數與財富有關。但是在某些情況下，零水位價格是具有普遍性—即此零水位價格與效用函數或財富無關。本文第一部分指出，當投資人的效用函數為HARA (hyperbolic absolute risk aversion)效用函數時，只有一個參數會對零水位價格產生影響。也就是說，如果我們固定這個參數，不論投資人的財富多寡，每一位具有HARA效用函數的投資人都會得到同樣的零水位價格。在第二部分中，我們增加交易成本到Luenberger的模型中。零水位價格在此模型中被證明必然存在。雖然在市場存在交易成本時，零水位定價法和傳統的無套利定價法都只會得到一個價格區間，但是前者得到之區間遠小於後者之區間。我們亦在此存在交易成本的模型中，驗證零水位價格之普遍性。

關鍵字

資產定價 ； 零水位價格 ； 最佳化

並列摘要

In the mathematical economics literature, the zero-level pricing method has been proposed to provide a unique price for a nonmarketable new asset. From the viewpoint of robust pricing theory, its disadvantage is that the method depends on the investor utility function and initial wealth. In some situations, the zero-level price is universal, namely, independent of the utility function and initial wealth. We show that only one parameter of the HARA (hyperbolic absolute risk aversion) utility function affects the zero-level price of a new asset. This implies that, if this parameter is fixed, the zero-level price is identical for all individuals with the HARA utility functions and different levels of initial wealth. And we extend Luenberger’s paper on the zero-level pricing method to the market with transaction cost. We show that the zero-level price exists in this market. Although both the zero-level pricing method and the no-arbitrage pricing approach produce price intervals, the zero-level price interval is much smaller than the no-arbitrage price interval. It is intuitive that if a investor uses the zero-level pricing method to find the price of a nonmarketable new asset, he will get more precise price. The universal properties are also verified in the market with transaction cost.

並列關鍵字

asset pricing ； zero-level price ； hyperbolic absolute risk aversion utility ； maximization

參考文獻

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