四種股價指數期貨定價模式之比較__臺灣人文及社會科學引文索引資料庫

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題名：	四種股價指數期貨定價模式之比較
作者：	王健聰
作者(外文)：	Janchung Wang
校院名稱：	國立成功大學
系所名稱：	企業管理學系
指導教授：	許溪南
學位類別：	博士
出版日期：	2000
主題關鍵詞：	不完美市場；價格預期；套利機能；隱含成長率；股價指數期貨定價模式；模式績效；有限差分法；市場不完全度；Imperfect Markets；Price Expectation；Arbitrage Mechanism；Implied Growth Rate；Pricing Model of Stock Index Futures；Model Performance；Finite Difference Method；Degree of Market Imperfection
原始連結：	連回原系統網址
相關次數：	被引用次數:期刊(1) 博士論文(0) 專書(0) 專書論文(0) 排除自我引用:0 共同引用:0 點閱:36

摘要
現實的資本市場不可能是完美而無摩擦，套利機能運作亦不可能是完全，甚至在某些情況下，套利機能根本無法運作。例如，1987年10月美國股市崩盤期間。因此，依據完美市場假設與標準套利論點所推導出的持有成本模式以及一些放寬完美市場假設之指數期貨定價模式，已有多位學者，例如Cornell & French (1983a&b)、Figlewski (1984)、Modest & Sundaresan (1983)、Eytan & Harpaz (1986)及Bhatt & Cakici (1990)，證實依據這些定價模式所估算出的股價指數期貨的理論價格顯著地偏離實際的期貨的價格。此外，持有成本模式並無法解釋SIMEX摩根台股指數期貨自上市以來持續出現逆價差現象。此似乎暗示著已發展出的這些指數期貨定價模式，仍有可能遺漏某些重要因素。Figlewski (1989)發現在實際的市場如股價指數選擇權，標準的套利活動暴露在相當的風險與交易成本之下，因此，他認為在實際不完美的指數選擇權的市場，的確有空間讓價格預期與風險趨避…等因素，對該選擇權之定價發揮影響力。而股價指數的套利活動亦暴露在相當的風險之下，是否在實際不完美的指數期貨市場，價格預期對於該指數期貨的定價能發揮影響力？基於以上分析，本研究試圖將價格預期因素納入考量，並利用偏微分方程以及套利不完全論點，發展出一套不完美市場下之指數期貨定價模式。此外，對於因指數期貨定價所衍生的相關議題，本研究亦將一併加以探討，本文的研究目的可分述如下：
1.有鑑於建立在完美市場假設下之持有成本模式，是否能合理解釋現實不完美市場下股價指數期貨定價行為受到相當質疑，本研究將提出不完美市場下之指數期貨定價模式，將價格預期的觀念導入定價模式中，並利用套利不完全的論點發展出(1)考慮標的現貨指數(S)為隨機因子情況，導出一因子之不完美市場下之指數期貨定價模式，並經直接求解偏微分方程式得到一封閉式解；(2)考慮標的現貨指數(S)與其報酬的標準差()為隨機因子情況，導出二因子之不完美市場下之指數期貨定價模式，由於該定價模式並無一封閉式解，本文將使用有限差分法，以求得偏微分方程式的近似解。
2.檢視在持有成本模式理論下，股價指數之套利出現的頻率。
3.驗證完美市場假設下持有成本模式是否能解釋並預測在實際不完美市場下之股價指數期貨的價格。
4.檢測實際的不完美市場中，股價指數期貨的價格是否含有對未來現貨指數價格的預期因素在內。
5.本研究將分別提出(1)隱含法；(2)發展一套估計隱含股價成長率的迴歸模式；(3)適應性預期(adaptive expectations)的觀念所建立的迴歸模式等三種方法，以估計隱含股價成長率，並據以推估不完美市場下股價指數期貨之理論價格。
6.本研究將採用完美市場下持有成本模式、Hemler-Longstaff 模式以及本研究所推導出的一因子之不完美市場下股價指數期貨定價模式與二因子之不完美市場下股價指數期貨定價模式等四種模式以推估股價指數期貨理論價格。並比較各種模式所估算理論價格與市場實際價格之差異，以檢定何種模式有較佳預測績效。
7.各種衍生性商品市場的完美程度是不同的，有些成熟市場，如S&P 500 指數期貨市場，則較完美，而新興的市場，如SIMEX摩根台股指數期貨市場與TAIFEX台股指數期貨市場，則相當不完美。因此，本研究將進一步提出市場不完全度的意義與衡量方法。此外，本研究將提出若干市場不完全度與股價指數期貨定價之關係的理論假說與實證，證明市場不完全性對股價指數期貨定價之影響至深且大。
本研究將針對S&P 500指數期貨市場(代表成熟市場)、SIMEX摩根台股指數期貨市場與TAIFEX台股指數期貨市場(代表新興市場)等三個市場進行實證之探討。並以此三種期貨契約之近月到期期貨契約之每五分鐘日內交易資料進行實證分析。
有關本文實證結果可歸納如下：
1.S&P 500指數之逆價差與套利機會出現頻率皆相當的低，反觀SIMEX摩根台股指數與TAIFEX台股指數，逆價差與套利機會出現頻率皆相當的高且是持續出現。
2.建立在完美市場假設下的持有成本模式應用在市場完美程度較高的S&P 500指數期貨市場，有相當高的正確性。不過，如應用在市場不完美程度較高的SIMEX摩根台股指數期貨市場與TAIFEX台股指數期貨市場，其正確性則受到相當大的質疑。
3.本文研究期間S&P 500、SIMEX以及TAIFEX等三種指數期貨的價格的確含有「在期貨到期時的現貨價格資訊」之揭露的功能。因此，利用期貨價格資料將有助於預測期貨到期時的現貨價格。
4.不管是S&P 500指數期貨市場(成熟市場，市場完美程度較高)或是SIMEX摩根台股指數期貨市場和TAIFEX台股指數期貨市場(新興市場，市場不完美程度較高)，也不管是股市處於空頭時期或是多頭時期，運用本文所推導出的一因子之不完美市場下之指數期貨定價模式，且隱含股價成長率以隱含法來估計，所獲得預測績效是最佳的，而且顯著優於持有成本模式、Hemler-Longstaff模式和二因子之不完美市場下之指數期貨定價模式。

以文找文

Abstract
Capital markets in real world are not perfect or frictionless, and arbitrage mechanism can not be complete. Moreover, arbitrage mechanism may not work under certain circumstances. Thus, Several researchers have found that a significant discrepancy between actual futures prices and theoretical values estimated by the cost of carry model and the other pricing models which are relaxed an assumption of perfect markets. For instance, Cornell and French (1983a&b), Figlewski (1984), Modest and Sundaresan (1983) and Eytan and Harpaz (1986) all observed that the actual futures prices were on average below their correspondent values predicted by the cost of carry model. However, Bhatt and Cakici (1990) found that the discrepancy between the actual futures prices and their theoretical values was small but positive, on average. Additionally, the cost of carry model can not explain why the prices of SIMEX MSCI Taiwan stock index futures lower than the prices of its underlying spot index. This suggests that some important factors may be missing from the cost of carry model and the other existing pricing models. Figlewski (1989) simulated the impact of market imperfections and other problems (including uncertain volatility, transaction costs, indivisibility, and rebalancing at discrete intervals) on standard arbitrage trades. He found that, in an actual market such as that for stock index options, the standard arbitrage was exposed to such large risk and transactions costs. Therefore, he concluded that there exists a wide room for price expectation and risk aversion playing a very important role in determining the option prices in real options markets. As for stock index futures, arbitrage is also exposed to such large risk. Is it possible that price expectation also play a very important role in determining the index futures prices in real futures markets? From the above discussion, this study incorporates price expectation, and uses a PDE and an argument of incompleteness of arbitrage mechanism to develop a pricing model of stock index futures in imperfect markets. The purposes of this study can be summarized as follows:
1.This study incorporates price expectation to develop (1) the one-factor pricing model of stock index futures in imperfect markets with stochastic stock index price and (2) the two-factor pricing model of stock index futures in imperfect markets with stochastic stock index price and volatility of return on stock index. However, There are no closed-form solutions to the PDE for the two-factor pricing model in imperfect markets. In this case, we employ finite difference method to find the stock index futures values.
2.The second purpose of this study is to investigate the frequency and persistence of index arbitrage based on the theory of cost of carry model.
3.The third purpose of this study is to test the adequacy of the cost of carry model in imperfect markets.
4.The fourth purpose of this study is to examine whether the index futures contracts contain information of price expectation.
5.The fifth purpose of this study is to propose three methods for estimating implied growth rates of stock in the pricing model of stock index futures in imperfect markets.
6.The sixth purpose of this study is to compare the pricing performance of four alternative pricing models of stock index futures, i.e., cost of carry model, Hemler-Longstaff model, the one-factor pricing model of stock index futures in imperfect markets, and the two-factor pricing model of stock index futures in imperfect markets.
7.The seventh purpose of this study is to propose some hypotheses about the relationship between the degree of market imperfection and the pricing of stock index futures. The impact of market imperfection on the pricing of stock index futures is tremendous, and can not be neglected.
Our empirical evidence is based on three stock index futures contracts, i.e., S&P 500 index futures contracts, SIMEX MSCI Taiwan stock index futures contracts, and TAIFEX Taiwan stock index futures contracts. 5-minute intraday transactions data is used. The empirical results show that :
1.Based on the theory of cost of carry model, arbitrage opportunities are frequent and persistent for the SIMEX MSCI Taiwan stock index futures and the TAIFEX Taiwan stock index futures.
2.The assumption by the cost of carry model that the implied growth rate equals the risk-free rate is not adequate for the SIMEX MSCI Taiwan stock index futures and the TAIFEX Taiwan stock index futures.
3.The stock index futures prices contain information of price expectation that helps to forecast the future spot index prices at maturity for three stock index futures contracts.
4.No matter what futures contracts (matured or immatured) are empirically investigated, the one-factor pricing model of stock index futures in imperfect markets with implied growth rates estimated by direct method of implied growth rates performs much better than the other pricing models.

以文找文

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