Valuation of European gold option in Vietnam Luận văn thạc sĩ

MINISTRY OF EDUCATION AND TRAINING
UNIVERSITY OF ECONOMICS HO CHI MINH CITY

Huynh Ngoc Trang

VALUATION OF EUROPEAN SJC GOLD OPTION
IN VIETNAM

ECONOMICS MASTER THESIS

In Banking
Ology code: 60.31.12

Supervisor
Dr. Pham Huu Hong Thai

Ho Chi Minh city, 2010


ACKNOWLEDGEMENT

This research project would not have been possible without the support of many
people. Firstly I wish to express my deep sincere gratitude to my supervisor, Dr.
Pham Huu Hong Thai for his invaluable advices and helps. Without him, this thesis
could not have been completed. Special thanks to all instructors without whose
knowledge and assistance this study would not have been successful.
I would like to express my deepest gratitude and honor to my dear parents for
not only the love they devote to me but also for the time I took from them which
should have been my devotion to them in their aged time.
My thanks would also go to all of my classmates, Ms Vu Thi Thu Van and Mr
Tran Quoc Trong for all of their friendship and encouragement. I also wish to thank

my friends in Eximbank for their great support.
Finally, my greatest thanks would go to my husband, Mr Le Minh Nhat who is
the greatest inspiration and encouragement for me to overcome all difficulties
through the duration of my study.


1

ABSTRACT

The main idea of this thesis is to find the most suitable approach to the valuation
of SJC gold. We use the modified Black-Scholes model to price European SJC gold
brand option in Vietnam, our focus is to compare the difference between option
price derived by modified Black-Scholes model and option price in TOKYO
COMMODITY EXCHANGE (TOCOM) in the period from 1/7/2010 to 15/8/2010.
The results show that the option price derived by modified Black-Scholes model is
different from the option price in TOCOM. Since the two option price is different,
we carry out the ex post and ex ante test to investigate the efficiency of Vietnam
gold option market when applying the option price in TOCOM into Vietnam. The
evidences from these tests provide the rejection of our hypothesis of market
efficiency due to the existing of abnormal profit.

Key words: SJC gold, option pricing, modified Black-Scholes model, Vietnam
gold market.


2

TABLE OF CONTENT

Acknowledgement
Abstract

1

Table of content

2

Abbreviation

4

List of tables

5

Chapter 1: Introduction

6

Chapter 2: Review of modified Black- Scholes option pricing models

10

and some empirical evidences
2.1 Option and boundary conditions

10

2.1.1 Upper bound

10

2.1.2 Lower bound

11

2.2 Review of modified Black- Scholes model

11

2.3 Some empirical evidences

14

2.4 Testing the market efficiency of K.Shastri and K.Tandon

17

2.5 Volatility

18

Chapter 3: Research methodology

21

3.1 Data

21

3.1.1 SJC gold brand price

21

3.1.2 Gold price and option price listed in TOCOM

22

3.2 Modified Black Scholes Model

24

3.2.1 Spot rate and exercise price

25


3

3.2.2 Interest rate of VND and Interest rate SJC gold brand

25

3.2.3 Time to expiration

25

3.2.4 Volatility

26

3.3

27

The ex post and ex ante hedging test

Chapter 4: Empirical results and discussion

30

4.3 A comparison of SJC gold option price and

30

the option price quoted in TOCOM
4.3 The result of the Ex post tests

31

4.3 The result of the Ex Ante Tests

33

Chapter 5: Conclusion

36

List of references

38

Appendix

42

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4

ABBREVIATION
ACB: Asia Commercial Bank
COMEX: NewYork Commodities Exchange
Eximbank: Vietnam Export Import Commercial Joint-Stock Bank
PNJ: Phu Nhuan Jewelry Joint Stock Company
SBJ: Sacombank Jewelry Limited Company
SBV: State Bank of Vietnam
SJC: Saigon Jewelry Holding Company
TOCOM: Tokyo Commodity Exchange, Inc.
VND: Vietnam Dong


5

LIST OF TABLES

Table 4.1: A comparison of the difference between the call option price of SJC gold

derived by Black- Scholes model and call option price of TOCOM
Table 4.2: A comparison of the difference between the put option price of SJC gold
derived by Black- Scholes model and put option price of TOCOM
Table 4.3: Excess return from ex post hedging strategy for calls
Table 4.4: Excess return from ex post hedging strategy for puts
Table 4.5: Excess return from ex ante hedging strategy for calls
Table 4.6: Excess return from ex ante hedging strategy for puts


6

Chapter 1: INTRODUCTION

In Vietnam, the gold markets have developed for more than 7 years, gold is used
as a hedge against inflation, payment for real estate and traded as a currency for
speculation. Among many gold brand in the market, such as: ACB gold brand, SBJ
gold brand, PNJ Gold brand, SJC gold brand, the most popular gold brand traded in
the market is SJC gold brand (manufactured by Sai Gon Jewelry holding company).
Vietnamese investors trade gold in three ways: spot, forward and option. The
turn over of spot transaction is largest, about 95% of total, forward 4%, option 1%.
From 5/2007, a breakthrough of gold market in Vietnam: the opening of first
gold floor named Saigon gold exchange run by Asia Commercial Bank, and
followed by lots of other gold centers. Members of the Gold exchange center are
legal entities which have gold trading license and gold traders in Vietnam. The
Bank is acting as a trading intermediary among the counter-partners, which ensures
the settlement capacity and liquidity. Margin deposit ratio, transaction fee, and
interest rate are regulated by the Bank.
At the end of 2009, Vietnam has around 20 gold trading floors where investors
could deposit a small fund and then trade 14 times the value of their initial
investment. Investors can timely grasp their investment opportunities and earn

expected profits.
On 30 December 2009, the Government Office issued Notice No. 369/TB-VPCP
to convey the Prime Minister’s request to all banks to close their gold trading
centres and settle all the obligations with customers by 31 March 2010. The
decision was an attempt to stabilize the country’s foreign exchange market.
On 6 January 2010, SBV issued Circular No.01/2010/TT-NHNN to request all
credit institutions in Vietnam to stop their overseas gold margin trading activities,
and close overseas margin gold trading accounts by 31 March 2010.


7

Since January 2010, after the issuance of the two circular of the State bank of
Vietnam, the domestic gold market become very quiet with investment demand
down sharply.
*Statement of problems:
Investing in gold attract many people with a high return prospect. However, in
the current situation of many uncertainty in the economy, politics in the world (and
in Vietnam in particular), the investment in gold may encounter high risk.
Therefore, it is necessary to use a hedge against risk, option is one of the popular
method in hedging risk.
However, in Vietnam, investors and hedgers do not usually trade option as a
hedge against risk or as an investment in both stock market and currency/gold
market. At present, only some bank offer option in gold and currency.
To calculate the option premium offered for their customer, banks base on the
option price of the gold option listed in the TOCOM or COMEX or the premium
offered by their counterparts in overseas. At the time of the investigation, trading
gold in the overseas account has been terminated by the State Bank of Vietnam,
moreover it is necessary that the banks base on a model to calculate the option
premium base on the characteristic of the domestic gold markets so that the option

premium could be acceptable for both the banks and their customer.
In the early 1970's, Myron Scholes, Robert Merton, and Fisher Black made an
important breakthrough in the pricing of complex financial instruments by
developing what has become known as the Black-Scholes model. In 1997, the
importance of their model was recognized world wide when Myron Scholes and
Robert Merton received the Nobel Prize for Economics. The Black-Scholes model
displayed the importance that mathematics plays in the field of finance. It also led to
the growth and success of the new field of mathematical finance or financial
engineering. In this thesis, we use the modified Black-Scholes models for foreign


8

currency options to calculate the option price of SJC gold in the European style and
compare this option price with the option price quoted in the TOCOM.
* Objectives and Rationale of the study:
This study is motivated to investigate whether the modified Black-Scholes
model should be used in valuation of the SJC gold option price in Vietnam
by examining the difference between the option calculated by modified BlackScholes model and the gold option price listed in the TOCOM and investigating the
efficiency of the gold option market.
*Research Significance:
The study suggests a compatible method for commercials banks in Vietnam in
valuating the European gold option price. The gold option market in Vietnam could
be developed when the option price is acceptable for both investors and
commercials banks.
* Research questions:
Is option price of SJC gold brand calculated by modified BlackScholes model equal to the option price of the gold traded in TOCOM?
Is it effective when apply the option price quoted by TOCOM in
Vietnam gold option market?
Our hypothesis:

The first hypothesis is that option price of SJC gold brand derived by
the modified Black-Scholes model is equal to the option price of the gold
traded in TOCOM
The second hypothesis is that the application of TOCOM option price
for Vietnam gold option market is still effective. The effectiveness of the
market is that traders could earn no abnormal profit.


9

We apply the modified Black – Scholes model to price SJC gold option in the
period of 1/7/2010 to 15/8/2010 for the options matured on August, October and
December. The comparison between the SJC option price derived from modified
Black – Scholes model and the option price quoted in TOCOM show that these two
option price is different. Duplicating Kishore Tandon and Kuldeep Shatri, we carry
out empirical tests include ex post and ex ante test to test the efficiency of the
market when applying the option price quoted in TOCOM into Vietnam market.
The tests result that the market is not efficient because that the traders can earn
abnormal profit.
Organization of the thesis: Chapter 1 is an introduction, Chapter 2 is a review on
modified Black – Scholes model and on K.Shastri and K.Tandon test of market
efficiency. Chapter 3 gives the research methodology including Data collection,
modified Black – Scholes model and the ex post, ex ante test. Chapter 4 is empirical
results and discussion. The last chapter concludes the thesis.


10

Chapter 2: REVIEW OF MODIFIED BLACK- SCHOLES OPTION
PRICING MODELS AND SOME EMPIRICAL EVIDENCES

2.1.

Option and boundary conditions:

2.1.1. Upper bound:
For a call option, regardless of the fact that it is an American or a European call
option, the option will give the holder the right to purchase 1 share of a stock/a unit
of foreign currency for a certain price. However, regardless of how high the price
rises for an option; its price can never exceed that of the stock/foreign currency
price. Since it is the stock or share price which the option basis its own price on.
The right can never be worth the underlying asset it is written on. Therefore the
upper bound for call option prices is the underlying stock price.
This means that the value of any American or European call option must be less
than or equal to that of the current stock price. If the above boundaries were not as
they appear, then any arbitrageur would be able to easily make a riskless profit
simply by purchasing the stock and then immediately selling the call option.
The upper bound for the purposes of both American and European put options is
a little different. As for a put option, regardless of the fact that it is an American or a
European call option, the option will give the holder the right to sell 1 share of a
stock for a certain price (the strike price). However, regardless of how much the
stock price falls, the price of the option can never exceed that of the strike price (as
this is the price at which you will be able to sell the underlying stock for). Since it is
the stock or share price which the option basis its own price on. The right can never
be worth the strike price at which you will be selling the underlying stock or share.
Therefore the upper bound for put option prices is the options strike price. This
means that the value of any American or European put option must be less than or
equal to that of the options strike price.

11

Also, it must be noted that for European options at maturity can not be worth
more than the strike price. This is because of the fact that the option cannot be
worth more than the present value of the strike price today.
This means that the value of any American or European put option must be less
than or equal to that of the options strike price multiplied by the natural e, to the
power of negative risk-free interest rate multiplied by the options time to expiry.
2.1.2. Lower bound
The lower bound for any non-dividend paying call option is:

This means that the lower bound is equal to the current stock price minus the
options strike price multiplied by the natural e, to the power of negative risk-free
interest rate multiplied by the options time to expiry.
The lower bound for the put is the reverse of that of the call. It would be the
difference between the discounted value of the strike price at the risk free rate
against the stock price. If this rule is violated the investors can gain profit by
borrowing money and buying a put and the stock. This would lead to a positive cash
flow on maturity
2.2.

Review of modified Black- Scholes model

In valuation of the options price, Fisher Black and Myron Scholes (1972) were
the first authors to deal with pricing for European style options, the Black-Scholes
option pricing model provides the foundation for the modern theory of options
valuation. In deriving the formula for the value of an option in terms of the price of
the stock, they assumed “ideal conditions” in the market for the stock and for the
option:
-

The stock follows a Geometric Brownian Motion.

-

There are no penalties for short sales


12

-

Transaction costs and taxes are zero

-

The market operates continuously

-

The risk-free interest rate is constant

-

The stock pays no dividend

The Black – Scholes option pricing formula:
c

SN

ln( S / X ) [r

(
T

2

/ 2)]T

e

rT

XN

ln( S / X ) [r

(

2

/ 2)]T

(1.1)

T

Where S is the spot price, X is the exercise price,

2

is the instantaneous

variance of the stock’s return, r is the risk free interest rate and N is the cumulative
standard normal distribution function, T is the expiration date of the option.
Many theoretical studies and empirical tests have provided support for the Black
Scholes option pricing formula in pricing stock with no dividend and have some
modification in pricing currency option.
As Black – Scholes assumes no dividend are paid on the stock during the life of
the option, their model cannot be applied to value option on a foreign currency
(Nahum Biger and John Hull, 1983). When Merton (1973) and Smith (1976) use the
Black-Scholes formula in valuation of the currency options, they found that the
Black-Scholes formula can not be applied directly to pricing the currency option if
the risk free interest rate can be earned on the foreign currency holding. This model
is extended by Merton (1973) and Smith (1976) for continuous dividends. Since the
interest gained on holding a foreign security is equivalent to a continuously paid
dividend on a stock share, the Merton and Smith version of the Black-Scholes can
be applied to foreign security. To value currency option, stock price are substituted
for exchange rates. Merton (1973) and Smith (1976) consider that the dividend
yield, , is constant, they introduced a formula which called modified Black-Schole
formula to calculate the European currency option price:


13

c

e

T

SN

ln( S / X ) [r

(

2

/ 2)]T

T

rT

e

XN

ln( S / X ) [r

(

2

/ 2)]T

(1.2)

T

However, often a dividend payment will be scheduled during the life of an
option, but the amount of the payment has not yet been announced. This is an
additional source of uncertainty the Merton model can not reflect.
In 1983, using Black- Scholes methodology, Nahum Biger and John Hull
assumed that if the risk-free interest rate can be earned on the foreign currency
holding, r*, is constant, the dividend yield from an investment in the foreign
currency is constant and equal to r*, under the assumption that:
-

The price of one unit of foreign currency follows a Geometric Brownian
Motion.

-

The foreign exchange market operates continuously with no transaction cost
or taxes.

-

The risk-free interest rate in both the foreign country and the home country
are constant during the life of option.

Nahum Biger and John Hull (1983) provided a valuation formula for a European
call option on the foreign currency as follow:
c

e

r *T

SN

ln(S / X ) [r r *

(

2

/ 2)]T

T

e

rT

XN

ln(S / X ) [r r * (

2

/ 2)]T

(1.3)

T

The variables are redefined as follows:
S: spot price of one unit of the foreign currency.
2

: instantaneous variance of the return on the foreign currency holding.

X, T: exercise price and date of a European call option to purchase one unit of the
foreign currency.
R: risk free rate of interest in the home country.


14

In the valuation formulas of option, the forward rate plays a central role (Nahum
Biger and John Hull, 1983). Define F as the forward rate on the foreign currency for
a contract with delivery date T, the above formula reduces to:
c

e

rT

FN

ln( F / X ) (

2

/ 2)T

e

T

rT

XN

ln( F / X ) (

2

/ 2)T

(1.4)

T

Given the premium of a European call option (call C), the premium for a
European put option (called P) on the same currency and same exercise price (X)
can be derived from put-call parity:
p

c (X

p

e

rT

XN

F )e

(1.5)

rT

ln( X / F ) (

2

/ 2)T

T

e

rT

FN

ln( X / F ) (

2

/ 2)T

(1.6)

T

The Black-Scholes model, as the initial assumption, can be used to valuing the
European style option price. The Black-Schole European option model exhibit
systematic mispricing biases when used to value American call and put option
(Kuldeep Shastri and Kishore Tandon, 1986), this systematic mispricing is related
to three different factors: the time to maturity of the option, the degree the option is
in or out of the money, and the volatility of the underlying security. The probability
of early exercise depends on these three factors.
Same as the Black-Scholes model, the model developed by Biger and Hull
(1983) is referred to as the European model because it does not account for exercise
before the expiration day. American options do allow for early exercise while
European option does not. This extra flexibility of American currency option may
justify a higher premium on American currency option than on European currency
option with the same characteristics.
2.3.

Some empirical evidences

When Black and Scholes published their option pricing model in 1973 their study
were pioneering. Many studies have been published since then some of which


15

are developments

of

the

Black

and

Scholes

model

and

some

new

competing models. Many previous studies of the Black and Scholes model show
conflicting results andwe will present such results from a couple of authors.
The results from the authors who will be presented are: Macbeth and Merville,
Merton, Hull and White and finally Byström. In 1979 the two researchers Macbeth
and Merville tested the Black and Scholes empirically on call options. They
found that the Black and Scholes model tends to overprice out of the
money options and underprice in the money options with a remaining duration
of less than ninety days.
Stan Beckers (1982) use a riskless hedging strategy the Black-Scholes call option
pricing model was used to test market efficiency and to check for consistent
discrepancies between model and market prices. Again, no evidence of market
inefficiency could be found. However, there are indications that the Black-Scholes
model is not appropriate to price out-of-the-money gold options.
Furthermore, they came to the conclusion that the more in the money an

option is the more the model underprices and vice versa for out of the money
options. Macbeth and Merville relate to the results of Black and Merton in this study
and points out the fact that Black on the other hand came to the conclusion that deep
out of money options are underpriced

by

the

model

while

deep in the

money options are overpriced by the model.
This is not the only conflicting empirical result made by researchers. The results
of Merton’s study conflict with the result of the previous mentioned author Macbeth,
Merville and Black. Merton suggest the Black and Scholes theoretical option
prices are lower than market option prices for both deep in the money and deep out
the money options.
Later in 1987, Hull and White made an empirical study of the Black and Scholes
model using random (stochastic) volatility instead of assuming constant volatility.
This is a wide spread adaptation of the model today, but was new when Hull and


16

White made their study. Their result showed that the theoretical prices of options in
the money are underpriced and options out of the money are overpriced. These

results show that the overpricing increase with the remaining time of duration and
also points out the more out of the money the higher the overpricing.
A study was made on OMX index call options in 2000 by a Swedish researcher,
H. Bystrom. He showed that regardless of whether using a constant or a stochastic
volatility the Black and Scholes model more accurately prices options at the money
and in the money than options out of the money.
Marc Chesney and Louis Scott (1989) use the modified Black-Scholes model
and a random variance pricing model to study prices of European currency options
traded in Geneva. They use the modified Black-Scholes model and a random
variance model to price calls and puts on the dollar/Swiss franc exchange rate and
compare the prices to bid-ask quotes for options traded in Switzerland. Data
consists of prices on the foreign currency options traded by Credit Suisse First
Boston Futures Trading in Geneva. They find that the two models produce different
theoretical prices and that the Black- Scholes models prices are closer to the bid-ask
quote observed in the market.
C (S , t )

St e

r f (T t )

N (d1 )

Xe

rd (T t )

N (d 2 )

(1.7)

Where:
d1

d2

ln(S t / X ) (rd

T

1/ 2

T

d1

rf

2

)(T

t)

t

t

(1.8)

(1.9)

Where N(x) is the distribution function for standard normal random variable. T
represents maturity and X is the strike price.


17

After calculating the call options, they use put-call parity theorem to obtain the
price for European puts:
P(S , t ) C (S , t ) e

rd (T t )

X

e

r f (T t )

St

(1.10)

They find that the actual prices on calls and puts conform closely to the BlackScholes model if they allow the variance rate to be revised everyday. In case of the
random variance model, there is some mispricing but the mispricing is not large
enough for small investor who transact at the bid-ask spread to earn abnormal
profits.
Corrado C.J. and Su T. (1998) found that the Black-Scholes model price
accurately the at- the- money options but it often misprices deep in- the -money and

deep out- of- the money options. This due to the model assumption that security log
prices follow a constant variance diffusion process.
2.4.

Testing the market efficiency of Kuldeep Shastri and Kishore Tandon:

Kuldeep Shastri and Kishore Tandon (1986) test the efficiency of the market for
foreign currency options using the option pricing model developed by Biger and
Hull. The test are based on data for four currency options: the British Pound, the
German Mark, the Japanese Yen and the Swiss Franc.
Kuldeep Shastri and Kishore Tandon examine the ability of hedging strategies to
produce excess profits when an option’s market price deviates from its model price.
The test are in ex post and ex ante form. The expost tests assume that the trading
strategy can be executed immediately at the market prices that indicate deviations
from the model, while in the ex ante tests, the strategy is executed at the price
quoted the next day. The results of these tests indicate that the ex post hedging
strategy yields abnormal profits, but these excess returns disappear if the execution
of the strategy is delay by one day.
The results suggest that during the period investigation, if the market participant
can duplicate the ex post strategy, the foreign currency market on the Philadenphia


18

stock exchange inefficient. However if they can only duplicate the ex ante strategy,
the market would be efficient.
Our thesis use the way Kishore Tandon and Kuldeep (1986) test the efficiency
of the market. We apply the data of Vietnam market such as: SJC gold price,
volatility, interest rate to calculate the option price and apply the gold option price
quoted in TOCOM in Vietnam market to test the efficiency of Vietnam market. If

the market is efficient, trader could not earn abnormal profit when duplicate ex post
or ex ante strategy.
2.5.

Volatility

One parameter that can not be directly observed is the volatility of the currency
price. Volatility is an essential element determining the level of option prices, it is a
measure of uncertainty about the returns provided by the stock or currency. If
volatility is high, the premium on the option will be relatively high, and vice versa.
The higher the volatility, the more likely it is that the underlying price will be
above the exercise price before the maturity date and hence the option will then
have a higher premium. If the volatility of the underlying instrument is expected to
be low then there is less chance that the option will be profitable and will have a
lower expected option value.
The volatility ( ) can be estimated by using the implied standard deviation
(ISD) from observed option prices or by using historical estimates of

from

changes in the foreign exchange rate (Marc Chesney and Louis Scott, 1989).
The historical volatility is estimated by historical standard deviation (Kuldeep
Shastri and Kishore Tandon, 1985). To estimate the volatility of a stock price
empirically, the stock price is usually observed at fixed intervals of time (e.g., every
day, week, or month).
Define:
n+1

: number of observations

19

Si

: Stock (currency) price at end of ith interval, with i= 0,1,…,n
: number of intervals per annum

And let
ui

Si
Si 1

ln

(1.11)

The usual estimate, s, of the standard deviation of the ui is given by

1

s

n
i 1

n 1

2

(1.12)

ui u

or

s

1

n

n 1

i

u2
1 i

1
n(n 1)

n
i 1 ui

2

(1.13)

Where u is the mean of ui
The volatility estimated per annum is:
s

(1.14)

For example: if daily data is used the interval is one trading day and we use
= 252, if the interval is a week = 52 and = 12 for monthly data.
Since the volatility of an asset changes over time the measurement of historical
volatility is merely an estimate of the future volatility of the asset. It is therefore
hard to decide on how many historical days to base the calculations.
Hull (2003) discusses this issue in his book “Options futures and other derivative
s” and he suggests that a good rule of thumb is to set the number of observations to
the same amount of days that the volatility is to be applied to. In other
words when setting the price of an option with 120 days left to expiration on


20

should base the historical volatility measurement on 120 days alike.
The implied volatility is often used in practice. These are the volatilities implied
by option prices observed in the market.
However the price of deep in-the-money and deep out-of-the-money options are
relatively insensitive to volatility. Therefore, implied volatilities calculated from
these options tend to be unreliable (John C. Hull, 2000).


21

Chapter 3: RESEARCH METHODOLOGY

3.1.

Data

3.1.1. SJC gold brand price:
This study uses data from SJC gold price quoted by Vietnam Eximbank.
The Vietnam Export Import commercial joint stock bank (Eximbank) was
established on May 24, 1989, being one of the first joint-stock commercial banks of
Vietnam. Trading gold since 2004, Eximbank is one of the first bank which trade
gold in Vietnam.
Providing 4 methods of gold trading: spot, forward, swap, options. Eximbank,
along with ACB, SJC and Sacombank, had the largest gold turnover and profit in
Vietnam during 2006-2009.
Due to the world gold price fluctuation, supply and demand of gold in the
domestic market, the gold price quoted by Vietnam Eximbank changed accordingly
in order to keep the price competitively. The SJC gold price could represent for the
SJC gold price of the domestic market.
The gold price quoted at Eximbank used to trade for all branch. So, the price
quoted have a spread between the buying and selling rate. To estimate the volatility
accurately, we use the mid point price of buying and selling price. The mid point of
SJC gold price from 1/1/2010 to 30/6/2010 is used to calculate the historical
volatility.
The total number of daily observations is 6846 gold price quoted during the time
observed, then we to collect the gold price at 11AM, 14PM and daily closing price
at 17PM (Vietnam time).


22

3.1.2. Gold price and option price listed in TOCOM
The gold price and gold option price listed in TOCOM collected during
01/07/2010 to 15/08/2010.
Gold options are listed in TOCOM since May 17, 2004 with 2 types of Trade:
Call Options on Gold Futures and Put Options on Gold Futures.
Contract Unit: 1 kg / contract
Minimum Price Fluctuation: JPY 1 per gram
Trading Hours : Day Session 9:00 a.m. to 3:30 p.m., (JST)
Night Session 5:00 p.m. to 11:00 p.m. (JST)
Trading Method: Computerized Individual Auction
Contract Months: All even months within 6 months (On the day when a New
Contract Month is generated, there will be 3 even months starting from the next
even month after the month which the said day belongs to)
Last Trading Day : Day session on the last business day of the month preceding
to the underlying futures delivery month.
First Trading Day of New Contract Month: Day session on a business day
following the First Trading Day of a New Contract Month of the underlying.
Strike Price Interval: JPY 50 per gram
Listing of Strike Prices: At the commencement of trading, 5 strikes shall be
listed. New strikes will be added to maintain 5 strike prices above and below the
strike price nearest to the previous day's settlement price of the underlying asset for
the current contract month, until the fifth business day prior to the last trading day.
Exercise Period : The options buyers may exercise their options at any time from
the First Trading Day of a New Contract Month to the Last Trading Day. (American
type)


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Limitation on Exercise : No limitation. The Exchange may require statement of

reason when options are exercised out-of-the Money beyond a certain level.
Circuit Breaker Trigger Level: The CB trigger level is to be set everyday at the
start of a clearing period (i.e.the start of a night session at 17:00) and is based on the
settlement price of the previous clearing periond (or the settlement price of the
preceding contract month, in case of a new contract month)
Base Amount of Initial Clearing Margins (sellers only; per contract) 50% of the
underlying.
Extraordinary Clearing Margin: When the Exchange deems it necessary for
market management purposes, Extraordinary Clearing Margins shall be imposed.
Customer Position Limit : 5,000 contracts (long/short call, long/short put each)
Settlement Price: Theoretical price in principle
Assignment of Exercise : Assignment of option contracts starts after 15:45
p.m(JST).
Method of Assignment: TOCOM randomly assigns exercised option contracts to
short positions (at the unit of sub account). Within a broker member, allocation will
be made from the oldest outstanding positions with regard to their customer
positions (affiliate Members and Member Customer's positions)
We use the gold option price quoted in the TOCOM to compare with the option
price derived from the modified Black-Scholed model. Although the option in
TOCOM is American style. In the literature on equity options, it is well known that
the use of European model to price American calls represents a major measurement
problem only if the dividends on the underlying security are not small. In the case
of foreign currency call, the use of a European model would represent a major
measurement problem only if the foreign interest rate is large in comparison to the
domestic interest rate. Kuldeep Shastri and Kishore Tandon show that the early
exercise of call on foreign currency will not cause the mispricing of the modified