流動性與套利效率：台灣指數期貨與選擇權市場的實證研究

Abstract

本篇研究運用期貨-選擇權恆等式來探討在台灣期貨與選擇權市場的套利效率，除了使用成交價格資料，買賣報價資料也一併納入作比較。為了減輕價格非同步的問題，選擇權與期貨價格在一分鐘的區間內進行配對。本篇研究考慮到真實的交易及市場衝擊成本。可行的策略，如持有到到期與提早平倉策略，由事後與考慮交易執行落差的事前模擬試驗來檢視。結果顯示，成交價格資料高估了由買賣報價所引發套利機會的獲利程度；買賣報價卻高估了由成交價格資料所引發的套利機會頻率。事前分析顯示套利機會會在三分鐘內消失。迴歸分析的結果指出買賣報價可對套利者提供有用的套利訊號，利用此報價的獲利性對執行落差與執行風險為負相關。再者，提早平倉策略比持有到到期策略多出了額外的利潤，價格反轉與過度反應的效應使得提早平倉策略更有益。用一般動差法來估計由錯誤定價、買賣價差與市場深度所建構的三方程模型的參數，結果指出，在控制其他因素之下，錯誤定價與買賣價差存在正相關、市場深度卻與買賣價差呈現負相關。除此以外，錯誤定價與市場深度有互補的關係在。

This study adopts put-call-futures parity condition to investigate arbitrage efficiency in Taiwan futures and options markets. Despite using transaction data, bid/ask quotes are also subsumed to make comparison. To alleviate nonsynchronous price problem, options and futures prices are matched within one-minute time intervals. This study allows for realistic trading and market-impact costs. The feasibility of strategies such as hold-to-expiration and early-unwinding is examined with both ex-post and ex-ante simulation tests that take into consideration possible execution time lags for the arbitrage trade. Transaction price data overstate the magnitude of arbitrage opportunities derived from bid/ask quotes. Yet, bid/ask quotes overstate the frequency of arbitrage opportunities that are signaled by transaction price data. Ex-ante analysis shows that potential arbitrage opportunities disappear within three minutes. The regression results suggest that bid/ask quotes provide valuable trading signals to arbitrageurs. Profitability form exploiting the quotes is negatively related to execution delay and execution risk. Furthermore, the early-unwinding strategy adds extra profits over that of the hold-to-expiration strategy. The effects of price reversal and overreaction make early-unwinding strategy more profitable. We estimated the parameters and elasticity of mispricing, bid–ask spread, and market depth in a three-equation structural model, using the generalized method of moments (GMM) procedure. Results indicate that there was a positive relationship between mispricing and spread but an inverse relationship between market depth and bid–ask spread after we controlled for other factors. In addition, mispricing and market depth are complementary relationship.