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, 2003). There are big changes in financial area. Derivatives become more
important for “financial engineering” (chance, 1998), specially for us--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 structural 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 paper will review several typical articles in different sub-areas of option
pricing in order to prepare the thesis writing in fall 2004. Like previous three integrated
project papers, this assignment will also focus 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, and an appropriate
literature review of what others have done on the topic, and how they have been
1
Black, F & Scholes, M. (1973); Merton,R.C.(1973); Galai, D., (1977); Bodurtha, F.N & Courtadon, G.r.,
(1986), Tucker, A.L. (1985), Tucker, A.L., Peterson D,R., and Scott, E., (1988); Edey, M & Elliott, G,
(1992); etc.
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researched, can constitute the body of knowledge on the topic of your research (Hart,
1998). So the main objective of this paper is to get deep understanding of development of
the option pricing theory and the common used methodologies in this area. Several 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 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.
1.2 Problem situation and research questions
In order to fulfill our research objectives, there are several research questions we will
explore:
1.
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?
1.3 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.
2
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
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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 models2 to estimate options prices were very popular before Black
Scholes’ (1973) paper appeared. However, Black Scholes3 (1973) published their seminal
paper on option-pricing, in this paper, Black and Scholes used data from the over-thecounter 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).
Econometric model assumes that past relation between an option’s price and its determinants is stationary,
the econometrically fitted functional forms to past data can be interpreted as the empirical pricing equations
for the option. (Kassouf, 1965)
3
Black and Scholes (1973) demonstrated that a risk less hedge portfolio can be formed and the fair price of
a call option can be derived from the hedge portfolio.
2
4
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 parity5
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
Basic assumptions for BS model: 1. the stock price follows the Ito’s lemma process (DS =µsdt + бsdz)
with µ and б constant 2. The short selling of securities with full use of proceeds is permitted. 3. There are
no transaction costs or taxes, all securities are perfectly divisible 4. There are no dividends during the life
of the derivatives 5. There is no risk less arbitrage opportunities 6. Securities trading are continuous 7. The
risk free rate of interest, r, is constant and the same for all maturities.
5
The boundary conditional equation derived authors is: So-K<= C-P <= So-K EXP(-Rt), here, So is the
current stock price, K is the exercise price, R is the risk free interest rate, T is the maturity time for options
6
Black,F. (1975) suggests an approximate procedure for talking account of early exercise in call options.
This approximation involves calculating for early exercise value for options with dividends pays off during
the option maturity time: If Dn <=K(1-EXP (-r(T-tn)), it can not be optimal to early exercise options, if Dn
<=K(1-EXP (-r(T-tn)), it is always optimal to exercise early.
4
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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
7
These two articles are the articles we review in detail in the later section
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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
19879
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 models10 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
8
This is also called a volatility smile (Hull, 2003)
Here, we would like to explain a little more: As according to BS Model, the volatility is constant,
however, a higher strike price e.g. calls option has less opportunity to exercise the option, thus, the lower
implied volatility. Hence, the call option price is overvalued, this is more obvious after 1987, as traders
fear to loss more money.
10
E.g. Asay model (1982, modified Black shole’s model) , the extended-Vasicek model (1977) and the
Heath-Jarrow-Merton model, etc.
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7
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.
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3.
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.
3.1
Summary 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
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errors produced by all models are significantly related to a number of obvious factors,
such as time to maturity, volatility, moneyness, etc.
These three articles all tackle the similar research question, but uses different
methodology. As all of the methodologies they used are quite commonly used in this
research area, we believe, by review these three articles, we can get a fairly good picture
about the methodologies could be used in this area.
3.2
Discussion of key Methodologies
3.2.1
Boundary Test
- In review of
J. N. Bourtha and G.R. Courtadon’s Eifficiency Tests of the
Foreign Currency Options Market
The only methodology applied in this article is boundary test. The authors first derive
eight different sets of pricing boundaries, four for call options, and the other four for put
options. Any violation of the boundary will enable the trader gain arbitrage opportunities
either direct from the market or through portfolios of assets which dominate call and put
options. Clearly, if we can see a significant number of boundary violations, the market is
in general can provide arbitrage profit, and therefore is inefficient. This methodology is
very practical, and easy to be carried out. The researchers only need to put the historical
data into each boundary formula, and record every occurrence of boundary violation. The
conclusion can be drawn from presenting the violation in terms of number and percentage.
No additional statistics techniques needed.
However, if the number of violations is not significant, it is not convincible enough that
no arbitrage opportunities are exist in the market. The authors did not demonstrate that
the arbitrage opportunities are not exist when pricing is within the boundary.
Therefore, in our opinion, the boundary test along is not enough to accept a market’s
efficiency. However it is a very practical methodology to reject the market efficiency
hypothesis.
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3.2.2
-
Trading Simulation with Hedge Strategy
in review of A. L. Tucker(1985)’s Empirical Tests of the Efficiency of the
Currency Option Market
In A. L. Tucker’s paper, trading simulation with hedge strategy is the main methodology
to be applied. BS model is selected to generate the efficient option prices. By comparing
the model generated price and the historical price, transaction signals are given to the
simulated trader. When historical price is higher (lower) than the model price, a portfolio
composed of written call (put) options and units of bought (borrowing) foreign bonds per
options is established. The portfolio is liquidated on the following day. The combination
of the foreign bonds and the currency options are in the proportion that the systematic
risk reduced to zero. The profit is aggregated throughout the observation period. This
profit is compared against the profit generated from a passive hedge strategy, which
maintains the over price (under price) options’ initial position over the life of the
currency option.
By definition, an efficient market means there is no arbitrage profit exists in the market.
Therefore, the result is very convincible if the trading generates abnormal high profit. On
the other hand, as the systematic risk of the hedge portfolio is zero, the market efficiency
could be accepted if no abnormal high profit could be generated from the trading
simulation. Therefore, this is a very good approach to test the market efficiency. However,
as the whole test is based on many assumptions, which include the pricing model as well
as the constant and variables to be used in the model, the result is only valid when these
assumptions are validated. This seems to be a general issue for all methodologies applied
in this area. We will further discuss this issue in a later section. On the other hand, if the
abnormal profit is generated from the simulation, and the procedure of the test can be
proved to be viable, the result of market inefficiency can be validated without further
validating the others.
Therefore, similar as the boundary test methodology, this strategy has the high ability of
rejecting market efficiency, but relative weak to confirm the market efficiency. However,
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in terms of the credibility of accepting the market efficiency, this methodology is in
general higher than the boundary test, as the test directly involves the historical price and
the model generated price rather than comparing the historical price with the boundary
derived from the model.
In addition, this methodology involves a lot more calculation then any other
methodologies. This makes it a bit more difficult to be carried out.
3.2.3
Statistical Comparison between historical price and model generated
price
-
In review of D. Allen and I. Chau’s A test of various pricing models on
options on Australian bank bill futures.
The research question of this paper is a bit different from that of the previous twos. It
tries to apply various pricing models to the Australian bank bill future options, and to
both identify the market efficiency and evaluate the applicability of the models for the
underlying option market.
The authors generated option prices for 90-day bank accepted bill futures options
according to four different models. The result from each model is compared with
historical data. Apart from a description statistics, Ordinary Least Square(OLS)
regressions of the pricing errors is carried out.
As the pricing model is supposed to provide “efficient market price”, if there is a
significant statistical discrepancy between the model-generated price and the historical
price, the market could be considered as inefficient. Likewise, if the discrepancy is not
significant, we can say the market is efficient. The main statistical methodology usually
used is regression.
The easy of use is, again, an advantage of this methodology. However, the weakness is
also obvious, as
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a)
The discrepancy of the error may not be normally distributed for all types of
options. Thus the statistical error may not provide a true picture
b)
The validity of the result is very much relying on the validity of the pricing
model no matter in terms of rejecting or confirming the market efficiency.
In this paper, these issues, actually, has been addressed, and multi-regression techniques
has been employed to tackle these issues. We will further discuss this in the next section.
Overall, this is a simple methodology, but the result is not as convincible as the previous
two when rejecting the market efficiency.
3.3 Issues need to be considered when applying the mythologies.
- In review of all three articles
The above three different methodologies have their strengths and limitations. However,
there are many issues to be addressed when applying these models. Misaddressing or
ignoring these issues could result in the outcome totally useless, and carefully
considering these issues when applying the methodologies could dramatically increase
the credibility of the result. Moreover, this could result the research finding more rich in
content.
3.2.1 General Issues with regards to the limitation of the pricing model
Pricing model is of centric in this research area. No matter which methodology to choose,
The test is always starts from a pricing model, which is often derived from BS model.
The BS model is very sustainable with the following assumption:
1)
There are no transactions cost or taxes
2)
All securities are perfectly divisible
3)
There are no dividends during the life of the derivative
4)
Security trading is continuous
5)
The risk-free rate of the interest is constant and the same for all maturities
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Clearly, none of them could be true for any option market. However, on the other hand,
not all of them can dramatically influence the market price, and the level of each item’s
influence differs from market to market.
Therefore, the market feature and limitation has to be reviewed for selecting or deriving a
suitable model. Alternatively, the analysis of the result has to be interpreted with the
consideration of the market feature and limitation.
In addition, as the model need to be feed with historical currency price, interest rate and
volatility. It is also important, those data are reasonable.
In Both Bodurtha and Courtadon (1985)’s article and A. L. Tucker(1985)’s article, two
issues are addressed:
1)
Data Synchronous
Due to the data availability, many of the tests only can be done based on last daily
option and spot price. However, the time of the last currency option transaction
does not synchronize with the time of the last currency transaction. Therefore, in
reality, the option price generated from last daily currency price is not comparable
to the last daily option price.
2)
Transaction Cost
Transaction cost exists in all market, and we can never ignore it.
In the first article, three different scenarios are designed for boundary test
1)
Last Daily Spot and Option Trade Data and No Transaction Cost
2)
Simultaneous Spot and Option Trade Data and No Transaction Cost
3)
Simultaneous Spot and Option Trade Data and Transaction Cost
The second scenario considers the data synchronous problem, while the third scenario
considers both data synchronous and the transaction cost. The result shows that there are
large percentage of boundary violation under scenario one. The violation is reduced
moderately under scenario two, and is almost disappeared under scenario three. This is a
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very good design, which not only takes the consideration of both issues, but also reveals
the price sensitivity towards each issue. Therefore, the result is not only convincible, but
also rich in content.
The second article considered the data synchronous issue, and therefore uses
simultaneous price to guide the hedge strategy. Although the result shows a higher return
from the hedge, the authors believe that the abnormal profit can be totally offset by the
transaction price. It is very good to consider the transaction cost. However, the argument
is very descriptive, and without solid support of data analysis.
In the second article, the choice of volatility is discussed also. Historical Volatility and
the weighted implied standard deviation (WISD) are discussed, and the latter proves to be
a better choice.
Both of the first two articles tackle the currency option, which fortunately does not
require serious consideration of the dividend issue, but the interest rate issues should not
be avoided, as the variation of both domestic interest and foreign currency interest could
deeply affect the profitability of the hedge portfolio, which include foreign currency and
currency options. However, both articles use a constant interest rate. This is due to the
unavailability of the model, which could address interest variation issue, during the
1980’s.
The third article deeply discussed the stochastic behavior of interest rate, and their
applications in different pricing model. The result is analyses with multi-regression of the
pricing errors on a constant, time to maturity, open interest, risk and the degree to which
the options were in or out of the money were performed. This test could find out which
factor dominant the discrepancy between the historical data and the model generated data.
Although the issues may not be considered by all the models, which they applied, the
analysis result still can be analysis against these issues. Therefore, this is also a good
approach to tackle the market limitation.
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In general, all three articles pay significant attention to the market limitation of the
pricing model applied. Therefore, the credibility of their result is relative high and the
result is quite rich in content. The only pities are that the first two articles do not consider
the variation of domestic/foreign interest rate, and the third article does not take in the
consideration of transaction cost.
3.2.2 Data Categorization – another technique to improve the result
The nature of the options is various. In terms of the position on the underlying assets, it
can be divided by call option and put option. In terms of maturity, it can be divided into
30-day, 60-day, 90-day etc… In terms of moneyness, it can be divided into in-the-money,
at-the-money and out-of-the-money. Each category of the option could possibly have
their unique feature, and the result for all options may be dominated by only one or a few
categories of options. Therefore, it is also important to carry out the market efficiency test
against each category so that the result could be more credible and rich in content.
The first article only categorizes the data into Put and Call. Therefore it is very difficult
to answer the question whether most of the boundary violation is due to a maturity issue
or a moneyness issue. However, as the options are on five different currencies, the result
is group by different currencies. This is a plausible approach to find out whether the
result is dominated by any particular currency.
The second article does not categorize the data at all. This reduces the credibility of result.
Although the third article considers the different feature of the options in the regression
model, the statistic result is not categorized by the feature of the options. Therefore, even
the result can indicate how much the maturity, the moneyness of the options should
account for the statistic error, it still can not tell which maturity range or which
moneyness type of the options accounts for more statistic error.
Therefore, in general all three articles do not sufficiently categories the result, in order to
increase the credibility of the result.
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With regards to this issue, V. Bhargava and J. M. Clark’s Pricing US Dollar Index
Futures Options (2003) provides a very good example, which groups the result by
“Put/Call”, maturity and moneyness.
3.3.3
A few more issues to be addressed for trading simulation with hedge strategy
Apart from the general issues about model limitation, there are another two common
issues need to be considered when the methodology of trading simulation with hedge
strategy is employed.
1)
Ex-Ante v. Ex-Post
In theory, when the pricing model signals a mispricing, the trader should take action at
that spot price. This is ex-post hedge. However, as the market moves quickly and the
availability of the option or assets with the spot price is limited, the traders usually may
not be able to trade with the same price as the spot price after the signal triggers.
Moreover, as closing price is widely used for the test, the signal can only guide the
transaction next morning. Therefore, Ex-Ante hedge comes into our picture. The hedge is
established at the next available price when mispricing signal triggers. If we use the
closing price, then the ex-Ante hedge means the hedge will be establish at time t+1 when
the a mispricing detected at time t.
A. L. Tucker’s article uses Ex-Ante Hedge strategy. At time t the hedge ratio is
determined. At time t+1, the hedge position is established, and at time t+2, the hedge is
liquidated. Compare with Ex-post strategy, the ex-ante is more realistic.
2)
Possibility of Hedge Liquidation
As mentioned before, the hedge strategy needs to be completed in three steps at three
consequence time: t, t+1, t+2. If only daily closing price available for test, this will mean
that for the same option, the transaction must be available for three consecutive trading
days. This will require the simulation to exclude the options which can not be available
for three consecutive days. If the excluded samples are of significant number, the validity
of the result is again questionable.
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Fortunately, A. L. Tucker’s article uses intra-daily price. This means that the trader needs
not to wait until next day for establish a hedge, and liquidate it on the subsequent day.
He/she can establish the hedge on the next available price and liquidate it on the other
next available price.
3.4 Summary of Article Review
As a summary, the above articles use different methodologies to tackle the similar
research question- option market efficiency. Although, each methodologies has its own
advantages and limits, the result of the second article, which used the trading simulation
as the key method, seems a bit out perform the other two.
However, they all face the same issue while applying these methodologies. They all have
to carefully select the option pricing model, and design the research, interpret the
research result with the consideration of the limitation of the model. All of them did quite
well in this subject, although the first two are unable to tackle the stochastic of interest
rate, which is an important issue for currency option, and the third one missed transaction
cost. It is very plausible that the first article tackled these issues in a very smart way by
formulating three scenarios, which disclose the pricing sensitivities towards each issue.
The result of all three articles could be better improved by categorize the analysis by the
feature of the options, such as maturity, moneyness, etc.
The second article pays particular attention to the special issues related to the trading
simulation, and the simulation is proved to be viable.
The following table gives an overall picture of our review towards the three articles.
18
Article
J. N. Bodurtha
and G. R.
Courtadon’
article(1985)
Research
Topic
Currency
Option
Efficiency
Advantages
Boundary Test



A. L. Tucker’s
article (1985)
D. Allen and
Lrene Chau’s
article (2002)
Methodology
Main Methodology
Limitations
Issues Addressed
Trading
Simulation
with
Hedge
Strategy
Efficiency
of
the
options on
Bank
Bill
Futures
Comparing
Model
generated data
with
the
historical data
via Regression



Easy to be
carried out
Clear
indication
on market
inefficient
Result
provides
clear
indication
on market
efficiency
Easy to be
carried out
Indicating
whether
under price
or over price
when
the
market
is
inefficient

The validity
is
questionable
when
the
result
indicates
that
the
market
is
efficient
Choice
of
model and
variables
must
be
right




Data
Synchronous
Transaction
Cost
Choice of
Volatility
Transaction
Cost

More
difficult to
carry out

Ex Ante v. Ex
Post

The result
depends on
the choice of
the model.
The validity
is therefore
questionable

Stochastic
behavior of
interest rate
Ability to Accept or Reject
Market Efficiency

Accept:
Medium-Low

Reject:
High

Accept:
Medium

Reject:
High

Accept:
Medium-Low

Reject:
Medium
Secondary
Methodology

N.A.

Boundary
Test

Comparing
Model
generated
data with the
historical
data
via
Description
Statistics
19
4.
Conclusion
As a preparation for our final thesis, in this paper, we try to explore the research topic of
option market efficiency, and the methodologies often applied for the underlying topic.
An extensive literature review brings us a deep understanding of the importance of the
research topic, the development of the research area and the various challenge issues need
to be tackled or already has been tackled by various researchers. Since 1973, when Black
and Scholes proposed the first option pricing model to the world, derivatives have
become increasingly important in the world of finance. Options become a very efficient
tool for the financial engineers to manage the financial risk. In this area, the pricing of
option and the market efficiency is the question of centric, as they are the guidance of any
transaction in the option market. The literatures during the past 30 years developed Black
Scholes’ option pricing model into many variations, which take consideration of a
number of practical issues, such as transaction cost, ask/bid spread, stochastic of volatility
and interest rate, etc.
The literature review further focused on three articles in the research area, and pays
particular attention to the methodologies applied, and the issues need to be considered
along the process of applying these methodologies. The result indicates:
1)
Boundary test, Trading Simulation with hedge strategy and statistical
comparison between historical data and model generated data, being three key
methodologies used in the underlying research area, each has their advantages
and limitations. Trading simulation is the most difficult one in practice, but
gives more convincible result, while the rest two are easier to be carried out. It
would be a good strategy to apply two or three methodologies together to cross
reference the result.
2)
No matter which methodology to choose, we need to face the challenge of
selecting a good option pricing model to address a few practical issues in the
particular market. The issues, which can not completely handled by the pricing
20
model, could be tackled by the research design and the interpretation of analysis
data. These issues includes: transaction cost, data synchronous, ask/bid spread,
dividend, stochastic of interest rate and volatility.
3)
To further improve the credibility of the data, and to make more finding through
the research, it is recommended to category the data by different features of the
options. The main features could be “call/put”, maturity period and moneyness
4)
For the research choosing trading simulation with hedge strategy, there are two
additional practical issues need to be considered. One is to consider whether the
market could duplicate the Ex–Post scenario or only the Ex-Ante scenario could
be duplicated. The other issue is about the liquidity of the options under analysis.
The options, which do not have three continues transaction prices, have to be
excluded for the simulation. The number of exclusions has to be paid attention.
The above result will be a guide for our final thesis, which is about market efficiency of
OMX index.
This paper mainly focused on the methodology of processing and analysis the data, while
leave the area of collecting data. However, given today’s information technology, the
availability of the transaction prices in various key financial markets should not spell any
problem for getting sufficient samples for the analysis.
21
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