Methodologies used for option market efficiency test
and the related issues
1.0 Introduction
In the last 20 years, derivatives have become increasingly important in the world of finance, Futures and options are now traded actively on many exchanges throughout the world ( Hull, 20034).There are big changes in financial area. Derivatives become more important for ” “financial engineering” (chance, 1998), specially for us--our industrial and financial students, to understand the basic theory of derivatives is very important.
Moreover, how to price the derivatives is all the way the popular controversial topic for many literatures, (Mcmillian, 1992), specially to devise structuralvelop different option pricing models and use them to test the different markets efficiency are more attractive for many literatures.[1] To get clear figure of option pricing model will become more crucial if we are intending to fulfill our dissertation in this area. More reading and understanding of the option pricing models are very necessary.
Hence, this paperwill reviewseveraltwotypical articles in different sub-areas of option pricingoften referred articles in order to prepare the thesis writing in fall 2004. Like previous three integrated project papers, this assignment will also focus on by focusing on the methodological issues and research design of the selected articles. Besides this, a discussion of the option pricing models will be presented as well..
1.1 Purpose and objectives
We have decided our research area in the option pricing area, andA an appropriate literature review of what others have done on the topic, and how they have been researched, can help us to acquire a deep understandingconstitute the body of knowledge on the topic of your of our own topicresearch (Hart, 1998). So Therefore, tthe main objective of this paper is to get deep understanding theof development of the option pricing theory by reviewing the development of the theoryand the common used methodologies in this area. , Severaltwo most referred articles in the option pricing area will be reviewed and discussed in detail.
A literature review can have numerous different focuses, goals, perspectives, coverage strategies, organization and audiences (Cooper, 1998), with designing our dissertation and choosing the method for our thesis in mind, this assignment will initially focus on previous literature’s methodologies and research design. The discussion of pros and cons of the common used methods within this field will be presented.
In order to knowledge the research topic, we will also general review the development of the topic, also attempt to identify the central issues in this field, to integrate what other have done and said, and finally, to build the bridges between our dissertation preparation to the related topic, and to identify the central issues in this field.
1.2 Problem situation and research questions
In order to fulfill our research objectives, there are several research questions we will explore:
- What are the key methodologies used for market efficiency test?
2. What are the pros and cons of these methodologies?
3.What are the key issues needed to be considered when choosing proper models to test the markets?
1.What others have done in this area? What are the most employed research methods and how they design for the whole research process?
2.How do these two articles test market efficiency and how do they differ from each other during the testing process?
What are the main methodological strengthens and weaknesses of these two reviewed articles?
1.3 Structure
There are five section in these paper. In the introduction part, we present the main objectives, research problems as well as the methods for data collecting, and limitation of the paper. In section 2, A the general literature review in the option pricing market will be explored followed by the summarized table; meanwhile, the common used methodologies and research design in this area will be defined. Thereafter, in section 3, we will review in detail of two often referred articles regarding the put-call parity theory and transaction cost, this will followed by a table instruction and the comparison form will be used to demonstrate our understanding, [w1]1.3 Methodology
13.1 Data collection
As we have decided our research topic-option pricing, this paper will be written in order to get deep understanding and knowledge of this research area. We need to know the theoretical background of the research topic, what others have done, and what the common methodologies are in this area; with these main purposes in mind we have studied several articles in this area and assessed the research methods used.
We began the articles searching by looking for interesting articles in different databases of Gothenburg university library database and E-journal. We used two databases as our main source, JSTOR and Business Source Premier. As we are going to examine the transaction cost effect for the market efficiency testing, we want to read more articles regarding the transaction cost. After reading and assessing different articles, we decided to choose several articles as our mainly review and discussed articles which are typical articles from different sub-research areas.
The difference between this assignment with the previous there papers is that now we have decided our research areas, therefore, one of our main purpose is also to get deep understanding of the topic and what others have done in this area, hence, more articles needed to read to get more knowledge in option pricing, we have selected and read more articles and present them in the Section 2- Literature review of the option pricing model.
1.4.2 Data analysis
As this assignment is a qualitative research, review and analyze will be our main tools to “process” data--articles and books collected. These secondary data are either read up by us to generate idea or used to support our arguments. Specially, we will general review the other literatures in option pricing field with the focusing on the methodology and research design.
1.5 limitations
Due to the time constraint, we can’t review all the interested articles, and also it is not possible to summarize all literatures in the option pricing area. However, we try to collect the comparatively often referred articles and books.
1.6 Structure of this paper
There are four sections in this paper. In the introduction part, we present the main objectives, research problems as well as the methods for data collecting, and limitation of the paper. In section 2, a general literature review in the option pricing market will be explored; meanwhile, the common used methodologies and research design in this area will be defined. Thereafter, in section 3, we will review in detail of several often referred typical articles in different sub-areas, e.g. the put-call parity theory and transaction cost, this will followed by a table instruction and the comparison together with the review to demonstrate our analysis and arguments. Our findings and conclusions after the review will be presented in section 4.
2.0 Literature review of Option pricing Model
This section, we will review literatures’ contributions to the development of the option pricing theory, thereafter, the basic methodologies and research design will be presented. The main purpose for this section is to build up our basic knowledge of the option pricing theory, the research methodology and research design.
2.1 Option pricing theory
Using econometric models[2] to estimate options prices were very popular before Black Scholes’ (1973) paper appeared. However, Black Scholes[3] (1973) published their seminal paper on option-pricing, in this paper, Black and Scholes used data from the over-the-counter options market where options are dividend protected derived the valuation formula for call and put options, then Black-Scholes’ arbitrage-free option pricing methods have dominated finance academics and option industry thereafter.
Although used by option traders, the Black Scholes formula is often reported produce model values that differ in systematic ways from market prices (e.g. Galai, 1977, 1983; MacBeth & Merville, 1980; Rubinstein, 1985; Shastri & Tandon, 1986b; Budurtha & Courtadon, 1987).
These reports have stimulated interest in alternative option-pricing formulas. While several assumptions[4] underlying the Black Scholes analysis have been questioned, subsequent research has focused on the distribution assumptions.
2.1.1 Questioning about BS’s model’s Arbitrage risk free
Merton (1976) indicated that BS Model’s risk free arbitrage formula is not really arbitrage free. A number of researchers have chosen to make no assumptions about the behavior of stock prices and have tested whether arbitrage strategies can be used to make a risk less profit in option markets. Garman (1976) provides a computational procedure for finding any arbitrage possibilities that exist in a given situation. One frequently cited study by Klemkosky and Resnick (1979), tests whether the relationship in Put-call parity[5] equations is ever violated. It concludes that some small arbitrage profits are possible from the relationship. These are due mainly to the overpricing of American calls.
2.1.2 Questioning about dividends (early exercise)
BS Model assumes that Options pay no dividends, which indicates that there is not chance for early exercise. Galai (1977) used data from the Chicago Board Options Exchange (CBOE) where options are not protected against the effects of cash dividends. Galai used the Black Schoels approximation[6] to incorporate the effect of anticipated dividends into the option price. The study shows that in the absence of transaction costs, significant excess returns over the risk-free rate can be obtained by buying undervalued options and the overvalued options. However, it is possible that these excess returns are available only to market makers, and when the transaction costs are considered, the returns vanish.
2.1.3. Transaction cost and Bid offer spread
Tucker, A.l. (1985) and Bodurtha and Courtadon(1987)[7] also investigate in marketing efficiency testing, by applying the put-call parity boundary condition theory, considering the transaction cost, they have the result that the ex ante test shows that the market is efficient after consider the transaction cost because the boundary violation disappeared.
2.1.4 Questioning of Black Scholes constant volatility assumption
Black Scholdes Model assumes the volatility is constant. Chiras and Manaster (1978) carried out a study using COBE data to compare a weighted implied volatility from options on a stock at a point in time with the volatility calculated from historical data. They found that the former provide a much better forecast of the volatility of the stock price during the life of the option. We can conclude that traders use more than just historical data when determining the future volatility. They also tested to see whether it was possible to make average return by buying options with low implied volatility and by selling options with high implied volatility. The strategy shows a 10% per month. Hence their study can be a good interpretation to support BS model and showing that CBOE was inefficient in some aspects.
However, MacBeth and Merville (1979) tested BS Model using a different approach, they looked at different call options on the same stock at the same time and compared the volatilities implied by the option price, and the data they used are AT&T, Avon, Kodak, Exxon, IBM and Xerox. They found that implied volatility tended to be relatively high for in the money options and relatively low for the out of the money options. A relatively high implied volatility is indicative of a higher option price, and relatively low implied volatility is indicative for a low option price, thus, it can be concluded that out of the money call options are overpriced; in the money call options are undervalued.[8] These results were confirmed by Schultz (1990). Another great researcher is Rubinstein (1994), he has the same result with MacBeth and Merville, options with the low strike price has high implied volatility. It is maybe due to that investors fear a repeat of the crash of 1987[9]
2.1.5. Option pricing on assets other than stocks
A number of authors have researched the pricing of options on assets other than stocks, e.g. For the market efficiency and currency options testing, dealing in the currency options has probably been one of the fastest growth areas in foreign exchange market over the last decade, Shastri and Tandon (1986) and Bodurtha and Courtadon (1987) have examined future market efficiency applying BS Model, and Chance (1986) has examined the market efficiency of index options.
2.2 Methodology and research design
From our discussion, we can know that the majority researches in the option pricing field are either to develop or to derive new models[10] from the BS Model, and/or Use option price models to developing trading strategy to test market efficiency (e.g. hedging strategy); the existence of significant profits from such strategies would then be evidence of market inefficiency.
The hedge trading strategy, ex post, and ex ante tests are the most applied methods. During the testing procedure, different statistical model, computer programmings are essential tools for the data process and analysis.
However, according to Hull (2003), a number of problems arise in carrying out empirical research to test the BS Models. The first problem is that any statistical hypothesis about how options are priced has to be a joint hypothesis to the effect that (1) the option pricing formula is correct and (2) market is efficient. If the hypothesis is rejected, it may be the case that (1) is untrue, (2) is untrue or both (1) and (2) are untrue. A second problem is that stock price volatility is an unobservable variable. One approach is to estimate historical volatility and another alternative is to use implied volatility. Recall our discussion, there are researchers have the result towards both of these two volatilities. A third problem is that data on the underlying asset and the option price are synchronous. E.g. if we are pricing stock options, if the option is thinly traded, it is not likely to be acceptable to compare closing option prices with the closing stock price corresponds to a trade at 4:00pm. For the long period, this problem can be corrected by a paired T-test, but for the short time –e.g. one trading day, it is hard to compare. The exes post and ex ante test are necessary in this case.
As a result, we have discussed the theoretical background, for option pricing model (mainly BS Model), the general used research design and methods are roughly presented. Next sections we will review in detail several often referred articles for option pricing. Their methodology will be presented and discussed in detail. The reasons for us to choose these articles, is because we are preparing for our dissertation, as it is helpful for us to analyze more typical articles from different sub-areas in these area.
- Review and discussion of three article’s methodologies
In this section, based on three selected articles in the option pricing area, we will further explore the application of different methodologies, as well as the issues should be considered when applying these methodologies.
3.1Summary of three articles
The first article is J. N. Bourtha and G.R. Courtadon’s Eifficiency Tests of the Foreign Currency Options Market. Written in the mid of 1980’s, when foreign currency just traded in Philadelphia Stock Exchange (PHLX) for a few years, this paper attempted to test the efficiency of the foreign currency options market by comparing the historical option price (2/28/1983-9/14/1984) against eight sets of pricing boundaries derived from BS model. These pricing boundaries are calculated under three different scenarios. The result shows that the market is efficient when price synchronous and transaction cost are considered. The pricing sensitivities towards the issue of price synchronous and the cost of transaction are also revealed.
The second article is A. L. Tucker’s Empirical Tests of the Efficiency of the Currency Option Market. Also written in mid 1980’s, this paper tackles the same research question with the same research subject as the first one, but uses a trade simulation with hedge strategy to test the market. Data was selected from September 1983 to March 1984. The result shows that although the abnormal profit can be generated in theory, but they will be all eliminated by the transaction cost. In addition, the paper also did a simple boundary test of the pricing lower boundary, and the result is double confirmed.
The third article is D. Allen and I. Chau’s A test of various pricing models on options on Australian bank bill futures. Published in 2002, the paper uses a number of often used pricing models to generate a few sets of virtual option price of Australian bank bill futures for the whole year of 1996, and compare each set with the historical price. The discrepancy between both is analysis by OSL regression and graphical analysis. The result shows that the term structure models outperform the other models, and the pricing errors produced by all models are significantly related to a number of obvious factors, such as time to maturity, volatility, moneyness, etc.