台指選擇權價格效率性與市場流動性之關聯分析

Abstract

無套利理論是否發生偏離與市場的摩擦性有關，特別是市場的流動性狀況，因為摩擦性的存在將使得套利行為受到阻礙。然而，當越大的定價誤差（標的物合理價格和真實價格之差）發生時，可能誘發許多套利活動，因而影響流動性。 基於上述觀點，本文欲探討定價誤差與市場流動性兩者之間的動態關係。研究樣本期間為91年01月~94年06月之台指現貨、台指期貨、台指選擇權當日交易明細資料，利用買賣權等價理論(Put-Call Parity)及買賣權期貨等價理論(Put-Call Futures Parity)分別導出現貨和期貨理論價格，並計算出個別之定價誤差(本文簡稱為PCP定價誤差和PCFP定價誤差)，另外同時考量了期貨市場與選擇權市場的流動性，且以買賣價差和有效價差作為衡量指標。 . 結果顯示，PCP定價誤差和PCFP定價誤差皆與期貨和選擇市場流動性有關，唯相對於PCFP定價誤差，PCP定價誤差受影響程度較低，後續研究也證實了流動性並非影響PCP定價誤差的主因。在PCFP定價誤差中也發現，選擇權市場流動性比期貨市場與其有更大的關連性。在Granger因果檢測中，以選擇權報價價差為PCFP定價誤差之原因變數最為顯著;在衝擊反應函數中，PCFP定價誤差受到選擇權有效報價價差改變而有較大的變化幅度。整體看來，市場流動性會促進定價的效率性，證實了財務市場中所說的，流動性確實扮演了驅使價格達到最適水準的重要角色。

Deviate from no-arbitrage theory should be related to frictions of the market, particularly, the market liquidity, because arbitrage will be impeded by frictions. However, the bigger pricing error (the difference between the true price and the theory price of the underlying) occurs, the more arbitrage activities influence liquidity. By these ideas, we want to discuss the joint dynamic structure between the pricing error and the market liquidity. The sample includes comprises the intra_day data from TXO (Taiwan Index Options),TX (Taiwan Index Futures)and Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), from January,2002 to Jun,2005.We use the Put-Call Parity theory and Tucker (1991) Put-Call Futures Parity theory to obtain the fair value of TAIEX and TX , respectively, and calculate the pricing error particularly (we call it PCP and PCFP for short).In addition, we not only consider the liquidity of the futures market but the option market simultaneously bout adopt two index ( quoted spreads and effective spreads) to measure market liquidity. Considering that both PCFP and PCP have relations with market liquidity, in proportion to the PCFP, the influence to PCP is relatively low. Follow-up studies have verified market liquidity is not the main reason of the PCP. In PCFP, there is a significant relation with the option market more than the futures market in the liquidity. In two-way Granger causality ,quoted spreads Granger-cause PCFP pricing error is significant; Impulse response function indicate that shocks to the market liquidity predict pricing error, especially PCFP has the larger range of change by the effective spreads. In a word, it seems equally reasonable to suggest that market liquidity enhances the efficiency of pricing system, and proves the law of one price in financial theory again. Financial market liquidity plays a key role in moving prices to an appropriate level.