不完全市場下之選擇定價

Option Pricing in Imperfect Markets

許溪南(Hsi-Nan Hsu)

《中國財務學刊》 4卷3期 (1997/01) Pp. 13-43

https://doi.org/10.6545/JoFS.1997.4(3).2

摘要

現實的資本市場不是完美的，套利也不可能是完全的。本研究的目的有三：（1）給定B-S模式的正確性，（2）建立不完全市場下的選擇權評價模式，（3）比較不完全市場下的選擇權評價模式與B-S模式的績效。在B-S模式的實證研究上，結果顯示B-S買權模式之隱含波動性呈系統地低於B-S賣權模式之隱含波動性。很難找出正當理由來說明此一系統性的偏差，合理的解釋是B-S模式中，遺漏某些重要影響因素。本研究利用套利不完全的論點，導出選擇權的價格應滿足一個二次偏微分方程，再加上其邊界條件，得出一類似B-S的封閉式選擇權評價模式。兩者的主要差異為前者受到股價預期的影響，而後者則否。不過，當市場趨近完全時，本研究的模式，即為B-S選擇權模式。最後，本研究以隱含波動性作為股價的預期波動性來對兩種模式作實證。在實證方面尚存有許多重要課題待解，值得後續研究的努力。

關鍵字

不完全市場 ； 選擇權評價模式 ； 隱含波動性 ； 隱含成長率 ； 市場不完全度

並列摘要

Capital markets in real world are not perfect and arbitrage mechanism can not be complete. The purposes of this paper are (1) to test the adequacy of the Black-Scholes option pricing model in imperfect markets, (2) to develop an option pricing model in imperfect markets, and (3) to compare the performance between our model and the B-S model. In testing the adequacy of the B-S model, we calculate implied volatilities of options. Results indicate that the implied volatilities of calls are systematicallylower than those of puts. It is difficult to find reasons to explain this systematic bias. Therefore, we conclude that some important factors may be missingfrom the B-S model. In developing an option pricing model in imperfect markets, we base on an argument of incomplete arbitrage mechanism, a second order partial differential equation for options is derived. This partial differential equation can be solved subject to the boundary conditions at the maturity date. The closed form solution is smilar to the B-S model. However an important difference between the two models is that price expectation is an influencing factor in our model but not a factor in the B-S model. However, as markets approach perfect, our model becomes the B-S model. Finally, we use implied volatilities as estimates of market expected volatilities to test the two models. Because there exists some important issues in emperical tests, this area deserves further studies in the future.

並列關鍵字

Imperfect Markets ； Option Pricing Model ； Implied Volatility ； Implied Growth Rate ； Degree of Market Imperfection