Liquidity has been generally discussed in many microstructure literatures of financial market because its behaviors affect many kinds of market participants, such as traders, speculators, hedgers, and arbitrageurs, who are interested in obtaining information from liquidity. As a result, many tools of technical analysis are designed to forecast price pattern. Using speculators as an example, Kavajecz and White (2003) claim that technical analysis measures capture changes in the state of the limit order book. Nevertheless, the issues which we want to deliberate mainly focus on the interaction of arbitrageurs’ activities and liquidity.
This thesis adopts the options-futures parity to study the relative pricing efficiency between options and futures markets; through this parity condition we can eliminate model and estimation errors that arise from Black’s (1976) futures-options pricing model. Besides, it’s more convenient to use this condition. For example, both two contracts share the same maturity circles and identical settlement methods. The parity condition is also immune to uncertainty over dividend payouts (Fung & Chan, 1994).
Furthermore, market makers in options usually use futures contracts to hedge their position. (Draper & Fung, 2002) Fleming et al. (1996) found evidence that dealers price the S&P 100 Index options relative to the prevailing S&P 500 futures price.
Thus, it’s appropriate to examine the arbitrage efficiency in the options-futures markets by adopting such parity conditions.
Most empirical researches which examine the parity condition have primarily focused on transaction price data, which give actual trading information on a real-time basis and, unlike bid/ask quotes, are ex post in nature. Philips and Smith (1980) point that the transaction price may obscure the prospective execution prices associated with a particular arbitrage position. In order to investigate influence of different quotes to arbitrage activities, this thesis refers to Fung and Mok (2001) and Fung and Mok (2003) to construct the arbitrage frameworks based on transaction price and bid/ask quotes.
Earlier literatures usually debate the profitability of bid/ask quotes and transaction prices. On the one hand, Bas, Chan, and Cheung (1998) state that due to
two biases1 in evaluating arbitrage profitability based on transaction prices, transaction prices generally overstates the frequency of arbitrage opportunities. On the other hand, Fung and Mok (2001) state bid/ask quotes could overstate the observed frequency and magnitude of arbitrage opportunities because of rapid staling of the quotes and spread costs. Moreover, the index options contracts are quite new in Taiwan. This study analyzes whether the phenomenon discussed above would exist in Taiwan futures and options markets.
The above discussion motivates this research. The first objective of this thesis is to investigate the results of arbitrage efficiency with different quote data. 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. The ex-ante simulation is conducted to track the dynamic efficiency of the options and futures markets. Furthermore, we compare the size and frequency of arbitrage opportunities simulated from bid/ask quotes to parallel tests based on transaction data that are adjusted for bid/ask spread.
Regression analysis is used to examine how various factors such as execution dalay, execution risk, the moneyness of the options used, and the strategy signals affect the change in the potential arbitrage profits derived from transaction prices following a mispricing signal that is inferred from the bid/ask quotes.
Another important issue is how liquidity affects or is affected by mispricing.
Such study is rarely discussed in previous literatures. Roll, Schwartz and Subrahmanyam (2005) find that liquidity and mispricing are contemporaneously correlated. Therefore, Liquidity and mispricing should be simultaneously determined.
As a result, this thesis refers Wang and Yau (2000) to construct three-equation structural model. The empirical model is used to examine the joint determinants of mispricing, spread, and market depth in the futures market. Through discussing this model, this study would like to catch the properties of arbitrage in futures market.
The sample period covers 32 months from January 2002 to August 2004, which
1
There are two biases in evaluating arbitrage profitability based on transaction prices. First, the
frequency of arbitrage opportunities is overstated. Suppose that a futures transaction takes place at the
bid price and, based on the bid price, we conclude that the futures is underpriced. Therefore the
arbitrage strategy is to buy the underpriced futures. However, the price that we could buy at is the ask,
not the bid. If we use the correct price (the ask), there might be no arbitrage opportunity. Second, the
size of arbitrage profits is overstated. Suppose the futures is underpriced, so that the arbitrage strategy
is to purchase futures (at the ask). If only transaction prices are observed, one might mistakenly use a
sale price (at the bid) for a futures purchase, so that the purchase price is understated and the arbitrage
profit is overstated.
is much longer than earlier literatures2. For static ex-post simulation, trade can be executed at the prevailing quotes. The results indicate that bid/ask quotes really overstate the frequency of arbitrage opportunities signaled by transaction data. Yet, bid/ask quotes understate the size of arbitrage profits signaled by transaction prices.
High spread cost may cause the arbitrage threshold to enhance, and the average profits are improved because small profits are filtered out. The same results can be found in the category of nonmember arbitrageurs. However, nonmember arbitrageurs would have higher arbitrage threshold because of incorporating in transaction fees and opportunity costs.
The ex-ante simulation tests
take into consideration possible execution time lags for the arbitrage trade
. The results show thatpotential arbitrage opportunities disappear within three minutes.
The average profits of arbitrageurs which consider into costs are negative after three minutes. This means market making system would dynamically adjust prices to keep market efficient. Furthermore, ex-ante results based on the nearest actual transaction to a detected profitable mispricing signal based on the bid/ask quotes are unfavorable. To take a further study, regression analysis suggests that bid/ask quotes provide valuable trading signals to the arbitrageurs. After controlling for the degree of moneyness and the type of arbitrage strategies, arbitrage profits can be enhanced if the execution delay is shortened and the execution risk reduced.The early-winding strategy could capture the reversals in pricing errors. The results show that early-unwinding strategy adds extra profit to all arbitrageur groups, over and above that of the hold-to-expiration strategy. There is high probability that portfolio could be unwound before maturity. It implies early-unwinding strategy is profitable.
The three-equation model demonstrates that mispricing, bid-ask spread, and market depth are simultaneously determined. The results indicate that there is a positive relationship between mispricing and spread, but an inverse relationship between spread and market depth after we controlled for other factors. Moreover, mispricing and market depth are conditioned by each other. This means that market depth would be enhanced as mispricing enlarges. At the same time, mispricing would be decreased as the growing market depth. Besides, others instrument variables also
2
For example, Fung and Mok (2001) use 20 months data set.
hold important information. As a result, arbitrageurs should monitor these factors when they take advantage of arbitrage opportunities.
The rest of the article proceeds as follows: In the section entitled Literature review, we review the literatures on the arbitrage efficiency and literatures on liquidity and mispricing. In the section entitled Empirical approach, we introduce how to execute strategies and present the specification of the empirical model. We present the data and methodology in the section entitled Data and Methodology. And the results are presented and discussed in the section entitled Empirical Results. We conclude the article with the Conclusions section.