Robert Welch

Relationship between Expected Treasury Bill and Eurodollar Interest Rates: A Fractional Cointegration Analysis

In this paper, we extend Booth and Tses (BT)1995 analysis of fractional cointegration between theexpected Eurodollar and Treasury bill interest ratesimplied by their respective futures contracts. Thedefinition of fractional cointegration suggested byCheung and Lai (1993) and used by BT is refined sothat it requires the cointegrating relationship to bestationary as well as mean-reverting. In addition tothe Geweke and Porter-Hudak method used by BT, a moreefficient Maximum Likelihood (ML) method is used toestimate the cointegrating relationship. The LM (Engle(1982)) test indicates the possible existence of aheteroscedastic cointegrating relationship. Therefore,we use heteroscedastic models (GARCH and ExponentialGARCH) to represent the cointegrating regressioninstead of the simple homoscedastic model used by BT.The empirical evidence cannot reject the nullhypothesis of a stationary fractional cointegrationrelationship between the Eurodollar and Treasury billinterest rates.

A Profitable Call Spreading Strategy on the CBOE

We examine delta-neutral call spreading strategies on the Chicago Board Options Exchange between January 1987 and December 1989 and find substantial profits net of transaction costs. The suggested spread strategies are based on identifying discrepancies between the implied standard deviations of two related calls. In designing the trading rule, we are careful to ensure as much as possible that the indicated trades could have been executed, including requiring that the trading signal be confirmed by several actual prior trades, and that execution be delayed for up to ten minutes. Once established, the positions are kept delta-neutral by adjusting the spreads for every change of at least 10% in the hedge ratio. With lower transaction costs, we find that market makers and arbitrageurs earn up to five times the net profit of public traders. Profits are statistically significant for all traders except the public trader. Profitability is higher before October 1987, which may be the result of the decreased market transactions and volumes after the crash. Our strategy indicates there were three times more trading opportunities (spreads/month) prior to the crash. Vertical spreads (two calls differing only in their strike prices) are the most profitable. We also discover and exploit some interesting behavior of implied standard deviations as a calls maturity approaches.

The relative mispricing of the constant variance American put model

Abstract This paper finds significant mispricing between puts differing only in their exercise price or maturity on the Chicago Board Options Exchange (CBOE) for 1987, 1988 and 1989. Using a matched pair design and implied standard deviations (ISDs) of the constant variance American put model, this relative mispricing exceeds 16.8% for one quarter of the 17,788 pairs differing only in maturity (hereafter referred to as T pairs) and 12.6% for one quarter of the 21,571 pairs differing only in strike price (hereafter referred to as X pairs). For the T pairs the put with the shorter maturity typically has the larger ISD implying that the market over values shorter maturity puts relative to longer maturity puts. This bias in the constant variance model increases as the T pairs move out of the money. Similarly, for X pairs the put with lower strike price typically has the larger ISD implying that the market overvalues the put which is further out of the money (or less in the money). This constant variance model bias increases as X pairs approach maturity. Similar results for various subsamples, such as calender time, dividends and no-dividends, are also presented. Lastly, daily ISD distributions of the sample plotted by days to maturity reveal a significant asymmetry in its dispersion as the time to maturity decreases that is directly related to volume. Even more interesting is an asymmetrical increase in dispersion of ISD distributions as the puts move further into or out of the money that is inversely related to volume.

On the Distribution of CBOE Option Trade Prices Occurring Between Consecutive Stock Trades

This paper examines the volume distribution of option trade prices that occurs when the underlying stock price remains constant. The width of these option trade price bands provides direct evidence on the law of one price and the redundancy of options assumed in many option models. We find that index option bands are narrower than equity option bands. Furthermore, for both equity and index options, puts have narrower bandwidths than calls. In general, option price bandwidth is narrow and can be explained by the minimum price movement allowed by the Chicago Board Options Exchanges (CBOE). This supports the single price law and the redundancy assumption. The existence of bid/ask quotes on the option does not materially affect the above results although it does alter the frequency of multiple option trade prices for a given underlying stock price. We note that over 53% of option trading volume occurs without bid/ask quotes on the CBOE compared to less than 15% a decade ago. Our results suggest that the effective bid/ask spread on options is probably no larger than the minimum price movements allowed by the CBOE. Furthermore, the need for the liquidity services of market makers may be declining if the decline in quoting activity stems from cross trading (i.e. trades not involving market makers).