Maturity and Money-ness Effect on Bid-Ask Spreads of
Equity Index Options

Asitha Kodippili
Fayetteville State University
akodippili@uncfsu.edu

Abstract: An empirical analysis of bid-ask spread (BAS) for S&P 500 options based on a broad sample of real-time market quotes is performed. To empirically establish the maturity and money-ness effect on the BAS of equity options, I performed a preliminary investigation using graphical analysis. Percentage BAS of option contracts depends on time to maturity and money-ness in non-linear manner. Percentage spreads of equity options are found to be negatively related to the contract maturity and positively related to the contract money-ness. I then established the effect of money-ness and maturity on the percentage BAS through ordinary least squares regression analysis. These models can easily be used to calculate profit-loss calculations of option trading strategies.

1. Introduction Unlike the typical bid-ask spread for equities bid-ask spread for options can exceed the value of the option itself for out-of-the-money contracts and generally much higher than the bid-ask spread for equities. As a result, bid-ask spread is especially important in the context of options trading. However, there are a few empirical studies that examine bid-ask spreads for equity options [1, 2, 5] and index options [3, 4]. These studies are mostly based on few liquid contracts. For example; Chan, Chung and Johnson [1] have employed a matching sample, where in each day, the stock is matched with its most active call (put) option. Effectively, for each stock, only one option contract is considered for a day. As opposed to those studies, this empirical study of bid-ask spread is based on a broad sample (10% in-the-money to 10% out-of-the-money) of real-time market quotes for call and put options contracts for S&P 500 index options. The objective of present work is to find out significance of money-ness and maturity as explanatory variables in variation in bid-ask spread, and obtain a suitable model(s) to estimate average bid-ask spread as a function of those variables.

2. Notations and Definitions :

S   Index value    K: Strike Price :  m = K/S Money-ness. T : Time to maturity
Compute the percentage bid-ask spread for each contract by .

3. Empirical Analysis
To empirically establish the money-ness and maturity effects on the bid-ask spread of S&P call option contracts, we first carry out a preliminary investigation of the relation between contract money-ness, maturity and the percentage bid-ask spread using graphical analysis. We then establish the effect of money-ness and maturity on the bid-ask spread through regression analysis. In order to consider most liquid contracts, we drop options contracts that are more than 10% -in or out-of-the money. To see variation related to different money-ness and maturity, we construct a panel by sorting the data into 21 money-ness groups: 0.90,0.91, …, 1.09, 1.10 and six maturity groups: less than 30 days, 30 to 60 days, 60 to 90 days, 90 to 180 days, and 180 to 360 days. The reported spreads are calculated by averaging the spreads over all the listed contracts during the sample period May 2003 to August 2003.

It is evident from the graph that a single model will not give us good estimates for the percentage bid-ask spread for all maturities and money-ness values. Therefore, I obtain three simple models as a function of money-ness for the maturity categories namely between 15 to 45 days, 45 to 90 and above 90 days.

Time to maturity in days	Model for % bid-ask spread
	20.39102 - 42.81842*M + 22.50101*M*M
	4.64452 - 10.09362*M + 5.51207*M*M
	2.29319 - 4.88238*M + 2.62525*M*M

These models can be used to estimate percentage bid-ask spread for S&P 500 call options and hence profit-loss calculations of option trading strategies. The table below show estimate of percentage bid-ask spread for a few money-ness values.

Money-ness
0.95	2.1%	3.0%	2.4%
1.00	7.4%	6.3%	3.6%
1.05	24%	12.3%	6.1%

References
[1] Chan, K.C., Chung. P., and Johnson, H: The intraday behavior of bid-ask spreads for NYSE stocks and CBOE options,
Journal of Financial and Quantitative Analysis 30(3), 329-346 (1995).
[2] Chung, K.H., and Zhao, X.: Intraday variation in the bid-ask spread: Evidence after market reform, Journal of Financial
Research 26, 191-206 (2003).
[3] Fahlenbrach, R., and Sandas, P.: Bid-ask spread and inventory risk: Evidence from the FTSE-100 index options market,
EFA 2003 annual conference paper, No.872 (2003)
[4] George, T., and Longstaff, F.: Bid-ask spreads and trading activity in the S&P 100 index options market, Journal of
Financial and Quantitative Analysis 28, 381-397 (1993).
[5] Mayhew, S.: Competition, market structure, and bid-ask spreads in stock option markets, Journal of Finance, 57, 2, 931-958
(2002).