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
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 references 38
Appendix 42

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



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

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 Black-
Scholes 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 Black-
Scholes 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

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

- 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:
⎭
⎬
⎫
⎩
⎨
⎧
−+
−
⎭
⎬
⎫
⎩
⎨
⎧
++
=
−
T
TrXS
XNe
T

yield, δ, is constant, they introduced a formula which called modified Black-Schole
formula to calculate the European currency option price: 13
⎭
⎬
⎫
⎩
⎨
⎧
−−+
−
⎭
⎬
⎫
⎩
⎨
⎧
+−+
=
−−
T
TrXS
XNe
T
TrXS
SNec
rTT
σ

⎩
⎨
⎧
−−+
−
⎭
⎬
⎫
⎩
⎨
⎧
+−+
=
−−
T
TrrXS
XNe
T
TrrXS
SNec
rTTr
σ
σ
σ
σ
)]2/([)/ln()]2/([)/ln(
2*2*
*

(1.3)

−−
T
TXF
XNe
T
TXF
FNec
rTrT
σ
σ
σ
σ
)2/()/ln()2/()/ln(
22

(1.4)
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:
(1.5)
rT
eFXcp
−
−+= )(
⎭
⎬
⎫
⎩
⎨
⎧

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

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.
)()(),(
2
)(
1
)(
dNXedNeStSC
tTr
tTr
t
d
f
−−
−−
−=
(1.7)
Where:
tT
tTrrXS
d
fdt
−
−+−+
=
σ
σ
))(2/1()/ln(
2

Scholes 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,

And let

1
ln
i
i
i
S
u
S
−
⎛⎞
=
⎜⎟
⎝⎠

(1.11)
The usual estimate, s, of the standard deviation of the u
i
is given by ()
2
1
1
1
n
i
i

=
−−
∑∑

(1.13)
Where
u is the mean of
i
u
The volatility estimated per annum is:

s
σ
τ
=
(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

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

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