cardon, e. - expiration effects in the netherlands, an inquiry applied to four derivative stocks

7/29/2019 Cardon, E. - Expiration Effects in the Netherlands, An Inquiry Applied to Four Derivative Stocks

1/35

Expiration effects in The Netherlands

An inquiry applied to four derivative stocks

http://homepage.uvt.nl/~s900285/BachelorThesis.pdf

word count: 8874 (total, including e.g. appendix)

this thesis contains 35 pages (total, including e.g. appendix)

Tilburg University, The Netherlands

Bachelor Thesis Finance

Tilburg, June 30, 2006

Author: E. Cardon (900285)

Supervisor: Drs. J. Cui

Second reader: Prof. dr. F.C.J.M. de Jong


2/35

2

Plagiarism statement

I understand that I must use research conventions to cite and clearly mark other people's ideas andwords within my paper. I understand that plagiarism is an act of intellectual dishonesty. I understand it

is academically unethical and unacceptable to do any of the following acts:

To submit an essay written in whole or in part by another student as if it were my own. To download an essay from the internet, then quote or paraphrase from it, in whole or in part,

without acknowledging the original source. To restate a clever phrase verbatim from another writer without acknowledging the source. To paraphrase part of another writer's work without acknowledging the source. To reproduce the substance of another writer's argument without acknowledging the source. To take work originally done for one instructor's assignment and re-submit it to another

teacher. To cheat on tests or quizzes through the use of crib sheets, hidden notes, viewing another

student's paper, revealing the answers on my own paper to another student through verbal or

textual communication, sign language, or other means of storing and communicating

information--including electronic devices, recording devices, cellular telephones, headsets,

and portable computers. To copy another student's homework and submit the work as if it were the product of my own

labor.

I understand that the consequences for committing any of the previous acts of academic dishonesty can

include a failing grade for the assignment or quiz, failure in the class as a whole, and even expulsion

from the university. I will not plagiarize or cheat.

Name: E. Cardon

Date: June 30, 2006


3/35

3

Table of contents

1. Introduction................................................................................................................5

2. Expiration effects in international setting ..................................................................8

2.1 Introduction..........................................................................................................82.2 General reasons for abnormal behavior on expiration days.................................8

2.3 Trading volume effects on the underlying asset ..................................................9

2.4 Influence on stocks returns on expiration days..................................................11

2.5 Influence on stocks returns around expiration days...........................................12

2.6 Influence on volatility ........................................................................................13

2.7 Market conditions that might intensify or diminish expiration effects..............15

2.8 Conclusions........................................................................................................16

3. Market information, hypotheses, methodology and data.........................................19

3.1 Introduction........................................................................................................19

3.2 Option expiration characteristics in The Netherlands........................................19

3.3 Data collection ...................................................................................................213.4 Test methods ......................................................................................................22

3.5 Option volume in different expiration months...................................................23

3.6 Abnormal trading volume ..................................................................................25

3.7 Abnormal volatility............................................................................................26

3.8 Abnormal return on expiration day....................................................................27

3.9 Conclusions........................................................................................................28

4. Conclusions..............................................................................................................29

5. Limitations and future research ...............................................................................30

Appendix......................................................................................................................31

References....................................................................................................................34


4/35

4

Abstract

This study examines expiration effects in The Netherlands based on four derivative

stocks for the period 1992-2003. Furthermore, the effects of long term options are

examined, given their expected higher option volume in October. The effects are

examined applying a Wilcoxon matched pair test for the overall test of expiration tests,

while the Mann-Whitney test is applied to test for abnormalities in October, when the

long term options expire. The results show, consistent with previous work, that

although the volume of the underlyings tends to be higher on expiration days, no price

distortions are found. For the long term options, the volume of the underlying is

slightly higher, but not significant. No price distortions were found.


5/35

5

1. Introduction

The influence of options, futures and other derivatives has been extensively discussed

by both the academic world and regulators worldwide, as expiration days might be an

exploitable and pliant source for trading parties. As their use spreads internationally,

for example futures continue to be criticized for causing aberrations in the market

(Stoll and Whaley, 1997). Despite for example concern expressed by the Securities

and Exchange Commission (SEC), until now only mixed evidence has emerged that

derivatives could have an impact on underlying assets; some argue that volatility and

return effects can be found (e.g. Chamberlain et al, 1989), while others find the

opposite (e.g. Vipul, 2005). However, most agree that underlying volume is higher(e.g. Stoll and Whaley, 1987, Pope and Yadav, 1992, Chamberlain et al, 1989 and

Vipul, 2005). Much of the concern seems to be directed to small markets such as the

Oslo Stock Exchange (OSE) (Swidler et al, 1994) and the Spanish stock exchange

(Corredor et al, 2001), which are expected to be influenced more easily, due to the

low trading volumes. Also the so called triple watching hour (which is the last trading

day on the third Friday of the quarterly month when index futures, index options and

equity options expire simultaneously) has gained much attention from regulators.

During these three hours, at the end of the expiration day, most effects are assumed to

occur (e.g. Bollen and Whaley, 1999).

As expiration days are followed attentively by many parties and their importance

evident, given the changes on expiration procedures implemented in for example the

S&P 500 some years ago, the main purpose of this inquiry is to make a contribution to

existing documentation by examining four derivative Dutch stocks. On top of this, the

stocks are also examined on a possible intensifying circumstance on the underlying

stocks. As for example Vipul (2005) finds evidence on more impact of relatively high

derivative stocks, this element is also taken into account as long term options might

be such a factor, given the expected higher option volume on expiration days. A

fundamental factor here is that the increase in volatility is the result of additional cost

of liquidity (Stoll and Whaley, 1997). As the option volume is higher for long term

options over normal (short term) options, this fundamental theorem might be

applicable.


6/35

6

The four stocks (Akzo Nobel, Royal Dutch, Philips and Unilever) were selected as the

long term options were first contingent on them and so a longer data period available,

which make the test results more reliable. The Dutch market is thereby characterized

for its uniqueness as it was the first worldwide with the introduction of such long term

options. Due to there long term view, investors are able to take positions for a longer

period and as such, the importance of the expiration day should increase as more

arbitrageurs are able to influence the market. Despite their success, to my best

knowledge no one has conducted research on the expiration effects of long term

options on for example volatility, returns, volume and expiration days of the

underlying stock. De Roon et al (1998) were one of the first who studied the

efficiency of the market for Dutch long-term call options by testing any deviations

from pricing formulas. They found no serious price inefficiencies in the market.

This inquiry is especially directed to market regulators, investors and traders. If there

is indeed an imperfect market, traders and investors can benefit from this by for

example taking speculative strategies based on any possible abnormalities in the

market. This could be a reason for regulators to revise existing expiration procedures.

At first, an overview of existing literature will be given in chapter two. Chapter three

deals with an overview of the Dutch stock market and subsequently the expiration

effects will be will be tested in it. In appendix 2 an overview of options pricing is

available. These chapters should be able to answer the main research question of this

thesis:

To what extent do expiration effects exist in The Netherlands compared to other

countries?

The major findings of this inquiry indicate that on expiration days no special effects

occur on the four derivative stocks in The Netherlands. Only the volume of the

underlying shares tends to be higher than normal, but volatility and return remain

unaffected. For the high derivatives stocks, no effects are observed as well. Despite a

slightly higher volume, volatility and return than normal expiration days, they remain

insignificant.


7/35

7

Like any other study, this thesis has its limitations, which create opportunities for

future research. Briefly, only four stocks were studied because of the limited time for

the Bachelor thesis, high frequency data was not available and therefore suffers from

precise measurement techniques, different countries should be examined as well and

other factors might influence October expiration days.


8/35

8

2. Expiration effects in international setting

2.1 Introduction

The main purpose of this chapter is to summarize the yielded results of previous

studies in different markets. With respect to the influences corresponding to this

inquiry, different markets are examined and by doing so, for example different

settlement methods and different market structures. These will be considered in this

chapter as well and on their possible relevant implications will be elaborated.

Furthermore, it is interesting to find out the rationale beyond the authors conclusions.

Respectively conclusions with respect to trading volume, returns and volatility on

underlying stocks will be summarized at the end of this chapter.

As there are many studies about expiration effects available, most of them take into

account the effects of options and other derivatives on the underlying asset in terms of

abnormal volume, abnormal volatility, abnormal return and reversals. Abnormal is in

this context what is different from the corresponding benchmark on non-expiration

days. Many authors use a different benchmark for what is normal on an expiration day.

For example, Vipul (2005) uses the average of two preceding Friday trading days and

the two Fridays after the expiration day, while Alkebck and Hagelin (2004) use a

regression model to predict the normal changes in the market. On this will be

elaborated in this chapter as the methods will be discussed. The reversal is defined as

the release of stock returns after the expiration day as they are possibly depressed on

and prior to the expiration day.

2.2 General reasons for abnormal behavior on expiration days

The possible explanations for the concern about abnormal behavior on and around

expiration days may be the result of respectively, the unwinding of arbitrageurs,

speculative strategies by traders and market manipulation (e.g. Stoll and Whaley,

1987 and Jarrow, 1994). Two forms of manipulation may occur: namely action-based

and trade-based manipulation. The former occurs as a result of revealing information


9/35

9

(which can be false information) and the latter occurs by trading in the market with

for example large volumes on an underlying stock (e.g. Allen and Gale, 1992). Trade-

based information is especially important to this inquiry and documented by many

authors. Especially during the last trading hour prior to the expiration, some effects

should be found, but they remain controversial. The argument here is that during the

last trading hour large block transactions occur (Stoll and Whaley, 1997). The option

market can also be a good exploitable market for informed traders as a result of low

transaction costs, lesser capital outlay, a higher leverage and a limited downward

potential (Bhuyan and Chaudhury, 2005). Finally, they provide a fast and inexpensive

means of changing stock market exposures, both domestically and internationally

(Bollen and Whaley, 1999).

2.3 Trading volume effects on the underlying asset

It seems clear that price, volatility and volume can be possibly distorted near

expiration days as a result of the unwinding of arbitrageurs. This claim seems to be

certainly true with respect to large volumes in the index (Stoll and Whaley, 1986,

1987 and 1991). The effects not only seem to occur on the expiration day itself but

also a day or some days prior to the expiration days. These results were for example

yielded in The United Kingdom (Pope and Yadav, 1992).

For testing volume effects, several methods are applied. Lien and Yang (2005)

examine the Australian stock market and use trading volume and relative trading

volume of a stock to measure the trading activity. They define the trading volume of a

given day as the dollar value of all trades that occur during that day. The relative

trading volume is defined as the ratio of the dollar trading volume in the last half-hour

on a given day to the total dollar trading volume on that day. So, relative trading

volume =

ii

ofTradesno

iofSharesnoeicePerShar .Pr

.

1

=

Subsequently, the Mann-Whitney rank test is applied to test for abnormal volume.

They find small effects of individual stock futures and options expiration-days on

trading volume.


10/35

10

This t-test method in connection with the trading volume formula discussed above is

used by Stoll and Whaley (1997), who also examine the Australian Stock Exchange

by examining expiration-day effects of SPI futures. By using high-frequency data,

they find significant results (higher volume) on eight out of fourteen expirations. The

remaining six show higher trading at the close, but the differences remain

insignificant.

The method used by Alkebck and Hagelin (2004) is quite different. They estimated

trading volume as the sum of open-to-close trading for each stock in the index in

Sweden (SEK index). A time trend was used to calculate the predicted volume on an

expiration day. So, volume= tttD +++2

92921 . The dummy is used to correct

for a trend started by the removal of transaction tax, which increased trading volume.

A time-independent trading volume proxy was calculated by dividing the trading

volume for a given observation by its predicted trading volume,

)/( tVolumeVolume . Subsequently, they used the pooled t-test and the Wilcoxon

test to test for any abnormalities. They find evidence for significant higher volumes

on expiration days of index futures and options compared with the respective

benchmark.

Vipul (2005) estimates the benchmark, i.e. what should be normal on an expiration

day in India, by taking the averages of the 14,7,7,14 ++ EEEE trading volume,

where E denotes the expiration day. Subsequently, the nonparametric Wilcoxon

squared rank test is applied to test for potential higher volumes on the expiration. The

author finds indeed evidence for such a higher volume on futures and options

expiration-days.

In the small Spanish market, an increase in the trading volume is found as well

(Corredor et al, 2001). The increase in trading volume is consistent when future

expirations are studied. Karolyi (1996) examined futures contract expirations on the

Nikkei 225 and finds also abnormal trading volumes. In the very large USA market,

the volume exist as well (Stoll and Whaley, 1987).


11/35

11

As most authors agree on the increased volume on expiration days, this increase in

volume of the underlying shares tends to start building up slowly a day prior to

expiration. A possible reason for this is that arbitrageurs unwind their positions prior

to the contract expiration (Bollen and Whaley, 1999), but their effects depend on the

microstructure of the market (Vipul, 2005), the test method and the use of high-

frequency data. Most authors give as a primary reason for higher volumes the

squaring-up by arbitrageurs. This even continues the day after the expiration. The

only reason for this is that the selling activity of investors stimulated by an increase in

the prices after they were depressed for two days. This is shown in for example India

(Vipul, 2005).

2.4 Influence on stocks returns on expiration days

The influence on stock returns is a very important issue as they might be an

exploitable source for trading parties if they exist in the markets on expiration days.

The different findings in several markets in connection with the method used will

therefore be discussed next.

The major difference in the methods is that concerning the use of log transformations.

Log transformations are often made in finance to make the data more normally

distributed (e.g. Chatfield, 1996), as the assumption of normality in financial markets

is often violated (Vipul, 2005).

Lien and Yang (2005) use high frequency data to investigate the option-expiration day

effects by comparing the mean returns of the first hour, the last hour and the whole of

trading hours on the expiration days with the benchmark groups on non-expiration

days in the Australian market. They computed the stock return as

)log()log( 1= ttt ppR . tp denotes the stock price at the end at the end of a five

minute interval. Subsequently, a Mann-Whitney non-parametric test is applied. The

authors find significant effects on returns.

Alkebck and Hagelin (2004) compare the relevant means and medians on the

expiration days to non-expiration-days (comparison group) by respectively applying


12/35

12

the t-test and the W (Wilcoxon)-test as they also use them for other tests such as are

for abnormal volume. They found no serious price distortions in the market.

Vipul (2005) applies again the Wilcoxon test, for the same reasons as indicated in the

previous section. He compares the returns on the expiration day with its respective

benchmark to test for any price distortions. The expiration return is for each period

subtracted from its benchmark. He finds no specific pattern for the expiration-day

returns. He argues that this is the result of a downward pressure on prices prior to the

expiration day which causes the return to remain normal on the expiration days.

In summary, with respect to the influence on returns on expiration days, literature

does not agree. Some authors argue that no significant price return movements on

expiration days can be found (e.g. Vipul, 2005), while others find significant results

(e.g. Ni et al, 2004). One reason for the different findings tends to be the use of high

frequency data, which is likely to make a contribution in detecting abnormalities in

the market. Other reasons for the opacity tend to be the market characteristics and the

test methods used. On the latter will be elaborated later in this chapter.

2.5 Influence on stocks returns around expiration days

As it is empirically still unclear what the effect is of expiration days, one could also

consider stock movements one day prior to an expiration day and one day after. Not

all authors test expiration effects on the expiration day itself. Bollen and Whaley

(2005) and Stoll and Whaley (1997) for example only tested reversals on the

underlying stock. This reversal can be measured in different ways; Lien and Yang

(2005) for example, measure the price reversal as follows:

=

+

+

1

1

t

t

R

RREV if

>

n ) Tis approximately

distributed with mean (Keller and Warrack, 2003)

4

)1()(

+=

nnTE and the standard deviation

24

)12)(1( ++=

nnnT

The standardized test statistic is calculated as

T

TETz

)(=

3.5 Option volume in different expiration months

To test whether option expiration days in October cause more option volume than

January, April and July, which is a necessity to infer that long term option might

cause stronger effects on expiration days, it is necessary to compute the different

option volumes per month and compare them with their respective benchmark. For


24/35

24

this test, a different method is used as by Vipul. Option volumes are much easier to

influence than stock volumes, if for example one trader sells one large block of

options, this could disturb the total picture. Therefore, option volume on expiration

days is taken by the average of the week in which the expiration day takes place. As a

benchmark for non-expiration days, the average of the option volume of the rest of the

month is taken. Table 5 depicts the ratio for each stock each month, where the ratio is

defined as actual option volume / benchmark option volume. The following

hypotheses are advanced:

=0H The distribution of the ratio of the option volume in October is not different

from other months in October.

=aH The distribution of the ratio of the option volume in October is different from

other months.

Table 5: Option volume averages for each month (ratio with benchmark) 1992-2003

Stock January April July October

Akzo 1.70 1.47 1.53 1.65

Philips 1.49 1.62 1.78 1.73

Royal Dutch 1.60 1.69 1.43 1.43

Unilever 1.85 1.77 1.64 2.07

Average 1.66 1.64 1.60 1.72

The average ratio tends to be slightly higher on October expiration days. Table 6

depicts the test results.

Table 6: Statistical results abnormal option volume tests

Jan-Oct April-Oct July-Oct Overall option

volume effect

Mann-Whitney

Rank test

1054.50 1092.50 1039.50

Z -0.204 -0.091 -0.492 -10.910

Significance

(2-tailed)*

0.839 0.928 0.623 0.000*

*significant p-value


25/35

25

3.6 Abnormal trading volume

As there is no evidence that October expiration days cause more option volume than

the other expiration months, then this should also not be noticeable in the trading

volume of their underlying. Table 7 depicts the ratio for each stock each month, where

the ratio is defined as actual trading volume / benchmark option volume. The

following hypotheses are advanced:

=0H The distribution of the ratio of the trading volume of the underlying asset is not

different from other months in October

=aH The distribution of the ratio of the trading volume of the underlying asset in

October is different from other months

Table 7: stock volume averages for each month (ratio with benchmark) 1992-2003


Akzo 2.05 2.19 2.61 2.66

Philips 1.99 1.74 2.10 1.76

Royal Dutch 1.30 1.78 1.45 1.72

Unilever 1.99 1.74 2.10 1.76

Average 1.83 1.86 2.07 1.98

The October average is again slightly higher than the other months, except July. Table

8 depicts the statistical results.

Table 8: Statistical results abnormal stock volume tests


volume effect

(wilcoxon

matched pair

test)

Mann-Whitney

Rank test

850.50 904.500 826.500

Z -0.161 -0.718 -0.773 -10.954

Significance

(2-tailed)

0.872 0.473 0.439 0.000*

*significant p-value


26/35

26

but there is not enough evidence to refute oH . The overall effect turns out to be

significant.

3.7 Abnormal volatility

As mentioned earlier, a positive correlation between trading volume and volatility has

been documented in the financial markets (e.g. Daigler and Wiley, 1999). The

previous section showed that abnormal volume of October expirations was on average

slightly high, but not statistically shown. Abnormal volatility is measured by taking

the procedure from Vipul (2005):

2/)( DayLowDayHigh

DayLowDayHigh

+

Consequently, each number is compared with its benchmark, which is measured by

taking the average of the 14,7,7,14 ++ EEEE days, where E denotes the

expiration day. As the numbers are calculated as a ratio yet, the difference is

calculated with the benchmark. (Volatility-benchmark volatility)

The following hypotheses are advanced:

=0H The distribution of the difference of the volatility of the underlying asset in

October is not different from other months.

=aH The distribution of the difference of the volatility of the underlying asset in

October is different from other expiration months.

Table 9: volatility averages for each month (ratio with benchmark) 1992-2003


Akzo 0.004 0.002 0.016 -0.002Philips 0.003 0.002 0.014 0.001

Royal Dutch 0.004 0.000 0.003 0.004

Unilever -0.004 -0.001 -0.005 -0.003

Average 0.00175 0.00075 0.007 0

Table 9 shows quite unexpected results, the October expiration is on average less

volatile compared with its benchmark in the other months. Table 10 depicts the

statistical results.


27/35

27

Table 10: Statistical abnormal stock volatility tests


volume effect

(wilcoxon

matched pair

test)Mann-Whitney

Rank test

850.50 904.500 826.500

Z -0.087 -0.173 -0.673 -0.221

Significance

(2-tailed)

0.931 0.863 0.501 0.825

There is not enough evidence to refute 0H

3.8 Abnormal return on expiration day

As discussed in chapter 2, some studies conclude that expiration days cause a

downward pressure on stock prices. The following hypotheses are advanced:

=0H The distribution of difference of the return with its benchmark of the

underlying asset in October is not different from other months.

=aH The distribution of the difference of the return with its benchmark of the

underlying asset in October is different from other expiration months.

Table 11: Return averages for each month (ratio with benchmark) 1992-2003


Akzo -0.0005 -0.001 0.0093 -0.005

Philips -0.0081 0.0092 -0.0189 0.0053

Royal Dutch -0.0023 0.0038 0.0031 0.0026

Unilever -0.0029 0.0055 0.0027 0.0113

Average 0.0035 -0.0044 -0.001 0.0036

In several studies a downward pressure was documented on the expiration day itself.

The expectation is therefore that this is also the case for the October series, as their

impact is slightly higher than the other expiration months. As can be seen from table

11, the benchmark return is higher in October, which suggests that returns are slightly

depressed. To test for significance, the Mann-Whitney test was performed.


28/35

28

Table 12: Statistical abnormal stock return tests


volume effect

(wilcoxon

matched pair

test)Mann-Whitney

Rank test

982.000 1022.500 1019.000

Z -1.087 -0.786 -0.643 -0.019

Significance

(2-tailed)

0.277 0.432 0.520 0.985

The tests show again that on October expiration days, there is more pressure on stock

prices, but it is not statistically significant. There is also no evidence that the overall

effect of price pressure exists on the expiration day.

3.9 Conclusions

The major conclusion from this chapter is that an overall volume effect exists on the

four Dutch stocks. However, volatility and return effects remain insignificant. The

option volume of the long term options is also not shown. There tends to be a slightly

higher option and stock volume, although they remain insignificant.


29/35

29

4. Conclusions

The growth in derivatives trading has gained substantial attention from regulators and

trading parties. As their use is spreading internationally, the major concern expressed

tends to be the increased voaltility which might be an indirect result of the higher

volume, as this inference is often made in the financial markets. The concern has

therefore been tested extensively in different markets. Only the abnormal volume

seems to be significant, which tends to be higher on expiration days. The reason for

this tends to be the unwinding of arbitrageurs. The growth in abnormal volume,

however, does not lead to a substantial increase in volatility in most markets. Also

returns tend to remain unaffected. When some authors find significant effects, it isstill difficult to benefit from the abnormalities as transactioncosts outweigh the

benefits and only large parties can profit from them. The test method used depend on

the choice of the researcher, and might influence the existence of an expiration effect.

Most popular are the t-test, the Wilcoxon test and the Mann Whitney test. Only the

first is a parametric test. As the assumption of normal distributions in the financial

markets tends to be violated, for this inquiry the Wilcoxon test and the Mann Whitney

test are applied. The market characterics tend to play a crucial role, for example the

existence of futures has its implications, as they can make the market more complete

and lessen the expiration effects. In The Netherlands, only a higher volume is

observed in the market. The volatility and return remain insignificant. The option

volume of the long term options tends to be slightly higher than normal options,

which gives no reason to infer that their influence exists. This indeed the case as no

abnormal behavior is found for the four Dutch Stocks. The findings are in line with

existing literature, which also only document a higher volume, but mixed findings for

volatility and return.


30/35

30

5. Limitations and future research

Like any other inquiry, this thesis has its limitations, which create opportunities for

future research. Because of the lack of time, it was only possible to study fourindividual stocks. It might be interesting to test if more individual stocks included

change the total picture. Unfortunately, high frequency data was not available; it was

only possible to gather data from DataStream. Lien and Yang (2005) tested some

effects, when high-frequency data was available and observed more significant results.

Stoll and Whaley (1997) also tested with high frequency data the last thirty minutes

around the expiration day. The non-availability of high frequency data is therefore a

major drawback to this inquiry, although they seem to be almost captured by the

Vipuls procedure. As made clear in chapter two, in several markets different

expiration effects occur. It is therefore interesting to test several effects in different

markets. Finally, although is it is likely that long term options might be the major

influencer in the October months, other factors can play a role and should therefore be

a incentive for future research.


31/35

31

Appendix

1. Table of expiration days in The Netherlands 1992-2003

Year/Month January April July October1992 17 17 17 16

1993 15 16 16 15

1994 21 15 15 21

1995 20 21 21 20

1996 18 19 19 18

1997 17 18 18 17

1998 16 17 17 16

1999 15 16 16 15

2000 21 21 21 20

2001 19 20 20 192002 18 19 19 18

2003 17 18 18 17

2. Option pricing

The use of options has become quite popular and has therefore been extensively

studied. Many models for pricing options and other derivatives have been developed

and are still being developed. All models in the option pricing theory agree on four

assumptions. First, traders have symmetric information. Second, markets are complete.

Third, markets are frictionless and fourth, all investors are price takers (Jarrow, 1994).

Quite logical, these assumptions apply to long-term options as well. Until the

beginning of 1970, it was necessary to have knowledge of the expected return of the

underlying asset, which should filled in into different formulas, which limited their

practical use (Stulz, 2003). However, Black and Scholes (1972) were the first with an

easier applicable opting pricing model. It was no longer necessary to have more

knowledge of the expected return of the underlying asset. The model can be applied to

common stock as well as other financial assets.

The price for a European call option is as follows:

)()()(),,,( tTdKNTPdSNtTKSc t =

Where tTtT

KPSd t +

=

5.0)/ln(

and

N(d)=the cumulative standard normal distribution evaluated at d.


32/35

32

Unfortunately, the model by Black and Scholes is only applicable to European options,

since the put-call parity does not hold for American options. The reason is

straightforward: American options can also be exercised prior to the expiration day

and a rather large loss of the underlying violates the put-call parity, which is defined

as:

SXPVCP += )(

In this inquiry the individual options contingent on the five stocks are of the American

type. Many models are available for American options, but none of them seems to

predict option prices precisely. However, if mispricing is large enough, arbitrage

opportunities may occur. Therefore, bounds exist on the call price of an American

option to avoid the possibility of arbitrage opportunities (Stulz, 2003).

KTPStTKSPtTKSCKStTKSP ttt )(),,,(),,,(),,,( ++

Black developed a formula for the pricing of an American call option on a stock that

pays one dividend before maturity:

{ }),',,(),,,,)'((),,,( ttKSctTKDtPScMaxtTKSC tBlack

=

Fortunately, all the models agree on the five important influencing variables that willbe discussed next. The model by Black and Scholes consists of five variables. These

are delta (the exposure of the option price with respect to the stock price), vega

(exposure of the call option with respect to the volatility), rho (the exposure of the

option price with respect to the interest rate), theta (the exposure of the option price

with respect to time maturity) and the impact of a change in the exercise price on the

call option price.

The delta is increasing when the option is more in the money. The vega is positive

correlated to the option price, since more volatility makes it more likely that the

underlying will reach the exercise price. An increase in the interest rate also has an

impact on the value of the option, since it lowers the present value of the exercise

price, which has a positive impact on the value. Theta is trivial, since the longer time

an option has to reach the exercise price, the higher the probability that this will occur.

An increase in the exercise price causes a decrease in the call option price. This is in


33/35

33

contrast to an increase in the exercise price of the put option, which increases the

value of the put.

Quite logical, the largest impact can be found on time to maturity, which increases the

price of long-term options. Options with similar strike price but a longer maturity

have therefore always more value than a short term option. Nevertheless, future

planned dividend payment may violate this statement, as they decrease the share price

by the future planned dividend payments. A difficult estimation, however, is volatility.

It is easier to estimate the volatility of an option expiring in three months than an

option expiring in five years. This is consistent with results from literature, which

indeed indicate that some imperfections were not taken into account in the Black and

Scholes model. With respect to short term options, the models fits quite well, because

it is easier to estimate their volatility, while for long term options, there is still a lot of

uncertainty in the market. Bakshi et al, 2000 studied the distinctiveness of alternative

models based on long term options criteria. It seemed indeed that all the models

assuming stochastic volatility produce stock price option deltas that are drastically

different from those based on the Black and Scholes model. This could mean that it is

quite difficult to value long-term options and this might be a disadvantage of the

introduction of long term options.


34/35

34

References

Allen, F. and D. Gale (1992). Stock price manipulation. Review of financial studies, 5,

503-529

Alkebck, P. and N. Hagelin (2004). Expiration day effects of index futures and

options: evidence from a market with a long settlement period. Applied financial

economics, 14, 385-396

Bakshi, G., C. Cao and Z. Chen (2000). Pricing and hedging long-term options.

Journal of econometrics, 94, 277-318

Bhuyan, R. and M. Chaudbury (2005). Trading on the information content of open

interest. Derivatives use, trading and regulation, Vol. 11, No. 1, 16-36

Bollen, N. and E. Whaley (1999). Do expirations of Hang Seng derivatives affectstock market volatility? Pacific-Basin Finance Journal, 7, 453-470

Bruand, M. and R. Gibson-Asner (1998). The effects of newly listed derivatives in a

thin stock market. Review of derivatives research, 2, 59-86

Chang, R., S. Ghon Rhee and M. Yoshikawa (2000). The effects of conversion from

American- to European-style options on price discovery process of Nikkei 225 index.

Working paper, No. 00-08

Chamberlain, T.W., Cheung, S.C. and C.C.Y. Kwan (1989). Expiration-day effects of

index futures and options: some Canadian evidence. Financial analysts journal, 45,

67-71

Chatfield, C. (1996). The analysis of time series, an introduction. Chapmann & Hall,

fifth edition

Conover, W. (1990). Practical nonparametric tests. John Wiley & Sons Inc, third

edition

Corredor, P., P. Lechn and R. Santamaria (2001). Option-expiration effects in small

markets: the Spanish Stock Exchange. Journal of future markets. Vol. 21, No. 10, pp.905-928

Daigler, R. and M. Wiley (1999). The impact of trader type on the futures volatility-

volume relation. The journal of finance, Vol. 24, No.6

Gammill, J. and T. Marsh (1988). Trading activity and price behavior in the stock and

stock index futures markets in October 1987. The journal of economic perspectives,

Vol. 2, No. 3. pp. 25-44

Hancock, G., (1993). Whatever happened to the Triple Watching hour? Financial

Analysts journal, 49,3


35/35

Jarrow, A. (1994). Derivative security markets, market manipulation, and option

pricing theory. The journal of financial and quantitative analysis, Vol 29, No. 2., pp

241-261

Karolyi, G. (1996). Stock market volatility around expiration days in Japan. Journal

of derivatives, 4, 23-43

Keller, G. and B. Warrack (2003) Statistics for management and economics. Thomson,

sixth edition

Lien, D. and L. Yang (2005). Availability and settlement of individual stock futures

and options expiration-day effects: evidence from high-frequency data. The quarterly

review of economics and finance, 45, 730-747

Ni, S., N. Pearson and A. Poteshman (2002). Stock price clustering on option

expiration days. Journal of financial economics.

Pope, P. and P. Yadav (1992). The impact of expiration on underlying stocks: The UK

evidence. Journal of business finance and accounting, 19, 329-344

Roon, de F., C. Veld and J. Wei (1998). A study on the efficiency of the market for

Dutch long-term call options. The European journal of finance, 4, 93-111

Stoll, H. and R. Whaley (1986). Expiration day effects of index options and futures.

Monograph series in finance and economics, Monograph 1986-3

Stoll, H. and R. Whaley (1987). Program trading and expiration day effects.

Financial analysts journal, 43, 16-28

Stoll, H. and R. Whaley (1991).Expiration-day effects: what has changed? Financial

analysts journal, 47, 58-72

Stoll, H. and R. Whaley (1997). Expiration day effects of the all ordinaries share

price index futures: emipircal evidence and alternative settlement procedures.

Australian journal of management, Vol. 22, No. 2

Stulz, R. (2003). Risk management and derivatives. Thomson South-Western, first

edition.

Swidler, S., L. Schwartz and R. Kristiansen (1994). Option expiration day effects in

small markets: evidence from the Oslo Stock Exchange. Journal of financial

engineering, Vol. 3, No. 2

Vipul (2005). Futures and options expiration effects: The Indian evidence. The

journal of Futures markets. Vol. 25, No. 11, 1045-1065

cardon, e. - expiration effects in the netherlands, an inquiry applied to four derivative stocks

Documents