Empirical comparison on performance of Ryan and Ritchken bound theories and assessment on pricing bias.

Abstract

The focus of our empirical assessment is on studying two bound theories proposed by Ritchken (1985) and Ryan (1997). The study embarks on two tasks. One task is to answer how much tighter Ryan bounds are. The second is to propose a method to detect the pricing bias problem for a bound theory. The test data set consists of 1910 samples recorded at 9:00am, 11:00am and 2:00pm Central Time at Chicago Board Options Exchange, in total, 20875 S&P 500 index call options. Analysis with our test data set shows that by adding in an additional constraint, Ryan bounds are approximately 22% tighter than Ritchken bounds. The empirical analysis also shows that the proposed method has successfully detected the pricing bias problem for the Ritchken's theory when a lognormal distribution is assumed.