An Analysis of Market Efficiency for Exchange-traded Foreign Exchange Options on an Intraday Basis

This study examines the comparative magnitude of disturbances in intraday data for exchange traded foreign exchange (FX) options. An in-depth time series analysis on the frequency and extent of discrepancies in the disturbances is conducted. The purpose of this study is twofold. First, using intraday data and trading volume, this study attempts to determine whether both put-call parity and lower boundary conditions consistently hold for exchange traded options written on U.S. dollar denominated options on the Euro trading on the Philadelphia Stock Exchange (PHLX). Second, this study attempts to investigate the magnitude of any discrepancies that may exist due to a temporary cessation of either put-call parity or lower boundary conditions. Intraday (tick-by-tick) bid prices, ask prices, and trading volume on U.S. dollar denominated European style call options and put options on the Euro are obtained. Option data is collected through a Structured Query Language (SQL) request from the Bloomberg database. Corresponding tick-by-tick spot rates for the underlying exchange rate are obtained for the same time period. Tick-by-tick 3-month Treasury bill rates are obtained to for use as the relevant risk-free interest rate. The primary data set spans an approximate one month period from 11/1/2011 to 12/6/2011. Call and option pricing data for near-the-money exercise prices are obtained for options expiring in December 2011, January 2012, February 2012, March 2012, June 2012, and September 2012. A total of 7,212 ticks (minutes) are analyzed for the conversion strategy and 7,209 ticks are analyzed for the reversal strategy. The data is structured into an unbalanced panel data set (cross-sectional time series data) using put-call pairs as the cross sectional units and ticks as the time-series unit. To test the efficiency of the foreign exchange options market, lower boundary and put-call parity conditions were tested on tick-by-tick currency option data. Analysis shows that lower boundary conditions hold for the overwhelming majority of options, with less than 0.0001% of violations for the observed options. A more detailed econometric analysis was prepared to test the put-call parity condition for currency options. A fixed effects model specification is used to describe the put-call parity relationship. Based on the analysis, it is possible to obtain arbitrage profits in the short run through the use of either a conversion or reversal strategy even after accounting for transaction costs. Taking the first differences of the variables resulted in a model with stationary variables and statistically significant estimators. The inclusion of dummy variables for moneyness did not add significant explanatory power to the deterministic put-call parity relationship. For both first differences of conversion and reversal strategies, the large t-statistics for the slope coefficients and intercept terms indicate a rejection of the null hypothesis, H0: λ0 = 0 and λ1 = 1 after adjusting for standard error. This implies that once transaction costs are adjusted for, put-call parity does not hold. However, the intercept term is only very slightly negative, and the intercept term is only slightly less than one in both cases. This implies that when put-call parity is violated, arbitrage profit should be relatively small.