This thesis aims to identify the most effective method for valuing SJC gold using the modified Black-Scholes model to price European SJC gold brand options in Vietnam We compare the option prices obtained from the modified Black-Scholes model with those from the Tokyo Commodity Exchange (TOCOM) during the period from July 1, 2010, to August 15, 2010 The findings reveal a significant disparity between the two option prices Consequently, we conduct both ex post and ex ante tests to assess the efficiency of the Vietnam gold option market by applying the TOCOM option prices The results of these tests lead to the rejection of our hypothesis regarding market efficiency, indicating the presence of abnormal profits.
Key words: SJC gold, option pricing, modified Black-Scholes model, Vietnam gold market.
Chapter 2: Review of modified Black- Scholes option pricing models 10 and some empirical evidences
2.2 Review of modified Black- Scholes model 11
2.4 Testing the market efficiency of K.Shastri and K.Tandon 17
3.1.2 Gold price and option price listed in TOCOM 22
3.2.1 Spot rate and exercise price 25
3.2.2 Interest rate of VND and Interest rate SJC gold brand 25
3.3 The ex post and ex ante hedging test 27
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
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
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
Introduction 6
In Vietnam, the gold market has evolved over the past seven years, serving as a hedge against inflation, a payment method for real estate, and a speculative currency Among various gold brands available, including ACB, SBJ, and PNJ, the SJC gold brand, produced by Sai Gon Jewelry Holding Company, stands out as the most popular choice among traders.
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%.
In May 2007, Vietnam witnessed a significant advancement in its gold market with the launch of the Saigon Gold Exchange, operated by Asia Commercial Bank, which paved the way for numerous other gold trading centers This exchange comprises licensed legal entities and gold traders in Vietnam, with the bank serving as a trading intermediary to facilitate settlements and enhance liquidity Additionally, the bank regulates the margin deposit ratio, transaction fees, and interest rates, ensuring a structured trading environment.
By the end of 2009, Vietnam boasted approximately 20 gold trading floors, allowing investors to deposit a modest amount and trade up to 14 times their initial investment This setup enabled investors to quickly seize opportunities and achieve their desired profits.
On December 30, 2009, the Government Office released Notice No 369/TB-VPCP, directing all banks to shut down their gold trading centers and resolve customer obligations by March 31, 2010 This decision aimed to stabilize the foreign exchange market in the country.
On January 6, 2010, the State Bank of Vietnam (SBV) issued Circular No 01/2010/TT-NHNN, mandating that all credit institutions in Vietnam cease overseas gold margin trading activities and close their overseas margin gold trading accounts by March 31, 2010.
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.
Investing in gold appeals to many due to its potential for high returns However, given the current economic and political uncertainties globally, and specifically in Vietnam, gold investment carries significant risks To mitigate these risks, employing hedging strategies, such as options, is essential for investors.
In Vietnam, the practice of trading options as a means of hedging against risk or as an investment strategy in the stock, currency, and gold markets is not commonly adopted by investors and hedgers Currently, only a limited number of banks provide options for gold and currency trading.
To determine the option premium for their customers, banks rely on the gold option prices listed on exchanges like TOCOM or COMEX, as well as premiums from international counterparts However, following the State Bank of Vietnam's termination of overseas gold trading, banks must utilize a model that reflects the unique characteristics of the domestic gold market This approach ensures that the option premium is reasonable and acceptable for both the banks and their clients.
In the early 1970s, Myron Scholes, Robert Merton, and Fisher Black revolutionized financial instrument pricing with the Black-Scholes model, which later earned Scholes and Merton the Nobel Prize in Economics in 1997 This model highlighted the critical role of mathematics in finance and spurred the development of mathematical finance or financial engineering This thesis utilizes modified Black-Scholes models for foreign currency options to determine the European-style option price of SJC gold and compares it with the option price available in TOCOM.
* Objectives and Rationale of the study:
This study aims to evaluate the applicability of the modified Black-Scholes model for valuing SJC gold options in Vietnam By comparing the option prices derived from the modified model with those listed on the TOCOM, the research seeks to uncover discrepancies and assess the overall efficiency of the gold options market.
A recent study proposes an effective approach for commercial banks in Vietnam to evaluate European gold option prices By establishing a pricing model that meets the expectations of both investors and commercial banks, the development of the gold option market in Vietnam could be significantly enhanced.
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?
The initial hypothesis posits that the option price of the SJC gold brand, calculated using the modified Black-Scholes model, is equivalent to the option price of gold traded on the Tokyo Commodity Exchange (TOCOM).
The second hypothesis posits that the use of TOCOM option prices remains effective in the Vietnam gold option market, suggesting that traders are unable to achieve abnormal profits.
We utilized the modified Black-Scholes model to price SJC gold options from July 1, 2010, to August 15, 2010, focusing on options expiring in August, October, and December Our analysis revealed discrepancies between the SJC option prices derived from the modified Black-Scholes model and those quoted on TOCOM Following the methodology of Kishore Tandon and Kuldeep Shatri, we conducted empirical tests, including ex post and ex ante assessments, to evaluate market efficiency when integrating TOCOM option prices into the Vietnamese market The results indicate that the market is inefficient, as traders are able to achieve abnormal profits.
The thesis is structured into five chapters: Chapter 1 serves as the introduction, while Chapter 2 reviews the modified Black-Scholes model and the K Shastri and K Tandon test of market efficiency Chapter 3 outlines the research methodology, detailing data collection, the modified Black-Scholes model, and both ex post and ex ante tests Chapter 4 presents the empirical results and discussion, culminating in Chapter 5, which concludes the thesis.
Review of modified Black- Scholes option pricing models 10
Option and boundary conditions 10
A call option, whether American or European, grants the holder the right to purchase one share of stock or a unit of foreign currency at a specified price However, the price of the call option cannot exceed the price of the underlying asset, as it is directly tied to it Consequently, the maximum value of a call option is capped at the price of the stock or currency it is based on, meaning the option's worth can never surpass that of the underlying asset.
The value of any American or European call option cannot exceed the current stock price; otherwise, arbitrageurs could exploit this discrepancy for riskless profit by buying the stock and selling the call option simultaneously.
The upper bound for American and European put options differs slightly, but both grant the holder the right to sell one share of stock at a predetermined strike price Regardless of how much the stock price declines, the value of the put option cannot exceed the strike price, as this is the maximum amount at which the underlying stock can be sold Consequently, the option's value is intrinsically linked to the stock price, ensuring that it cannot be worth more than the strike price at which the stock will be sold.
The upper limit for put option prices is defined by the strike price, indicating that the value of both American and European put options cannot exceed the strike price.
European options at maturity cannot exceed their strike price, as their value is limited to the present value of the strike price.
The value of any American or European put option is capped at the product of the option's strike price and the natural exponential function e raised to the power of the negative risk-free interest rate multiplied by the time until the option expires.
The lower bound for any non-dividend paying call option is:
The lower bound of an option is determined by subtracting the strike price from the current stock price and then multiplying that result by the natural exponential function raised to the power of the negative risk-free interest rate, adjusted for the time remaining until the option's expiry.
The lower bound for a put option is determined by the difference between the present value of the strike price, discounted at the risk-free rate, and the current stock price If this lower bound is breached, investors can exploit the opportunity by borrowing funds to purchase both the put option and the underlying stock, resulting in a positive cash flow at maturity.
Review of modified Black- Scholes model 11
Fisher Black and Myron Scholes pioneered the pricing of European style options with their groundbreaking 1972 model, establishing the Black-Scholes option pricing framework as a cornerstone of modern options valuation theory Their formula for determining an option's value is based on the stock's price and relies on the assumption of "ideal conditions" in both the stock and options markets.
- The stock follows a Geometric Brownian Motion.
- There are no penalties for short sales
- Transaction costs and taxes are zero
- The risk-free interest rate is constant
- The stock pays no dividend
The Black – Scholes option pricing formula:
The spot price (S) represents the current market value of the asset, while the exercise price (X) is the predetermined price at which the option can be exercised The instantaneous variance of the stock’s return is denoted as (σ²), and the risk-free interest rate is represented by (r) Additionally, (N) refers to the cumulative standard normal distribution function, and (T) indicates the expiration date of the option.
Numerous theoretical studies and empirical tests have validated the Black-Scholes option pricing formula for valuing non-dividend stock options, while also highlighting necessary modifications for pricing currency options.
The Black-Scholes model, which assumes no dividends are paid on stocks during the life of an option, cannot be directly applied to value foreign currency options (Nahum Biger and John Hull, 1983) Merton (1973) and Smith (1976) discovered that when using the Black-Scholes formula for currency options, it fails if the risk-free interest rate can be earned on foreign currency holdings They extended the model to accommodate continuous dividends, recognizing that interest earned on foreign securities is akin to continuously paid dividends on stocks By substituting stock prices with exchange rates, Merton and Smith developed a modified Black-Scholes formula to accurately calculate the price of European currency options, assuming a constant dividend yield (δ).
Dividend payments may be scheduled during the lifespan of an option, yet the specific amount is often not disclosed in advance This creates an added layer of uncertainty that the Merton model fails to account for.
In 1983, Nahum Biger and John Hull applied the Black-Scholes methodology to analyze foreign currency investments, positing that if the risk-free interest rate (r*) remains constant, then the dividend yield from holding foreign currency also remains constant and is equivalent to r*.
- 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:
The variables are redefined as follows:
S: spot price of one unit of the foreign currency. σ 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.
The forward rate is crucial in option valuation formulas, as highlighted by Nahum Biger and John Hull in 1983 When defining F as the forward rate for a foreign currency contract with a delivery date T, the formula simplifies accordingly.
The premium of a European put option (P) can be calculated using the put-call parity formula, which states that P equals the premium of a European call option (C) plus the present value of the exercise price (X) minus the forward price (F), discounted at the risk-free interest rate (r) over the time to expiration (T).
The Black-Scholes model is primarily designed for valuing European style options, but it shows systematic mispricing biases when applied to American call and put options, as noted by Kuldeep Shastri and Kishore Tandon in 1986 This mispricing is influenced by three key factors: the option's time to maturity, its moneyness (whether it is in or out of the money), and the volatility of the underlying asset Consequently, the likelihood of early exercise is contingent upon these three elements.
Same as the Black-Scholes model, the model developed by Biger and Hull
European options, established in 1983, are characterized by their restriction against early exercise before the expiration date, unlike American options, which permit this flexibility This additional feature of American currency options often leads to higher premiums compared to European currency options that share similar attributes.
Some empirical evidences 14
In 1973, Black and Scholes introduced their groundbreaking option pricing model, which has since inspired numerous studies, including both enhancements to their original framework and the emergence of alternative models However, research examining the Black and Scholes model has yielded mixed findings, and we will highlight conflicting results from several authors to illustrate these discrepancies.
In 1979, researchers Macbeth and Merville conducted an empirical test of the Black-Scholes model on call options, revealing that the model tends to overprice out-of-the-money options while underpricing in-the-money options with a remaining duration of less than ninety days.
Stan Beckers (1982) employed a riskless hedging strategy using the Black-Scholes call option pricing model to assess market efficiency and identify any persistent discrepancies between model and market prices The findings revealed no evidence of market inefficiency; however, they suggested that the Black-Scholes model may not be suitable for pricing out-of-the-money gold options.
The study reveals that options that are deep in the money are often overpriced by the model, while those that are deep out of the money tend to be underpriced Macbeth and Merville align their findings with Black and Merton, emphasizing that the model consistently underprices in-the-money options and overprices out-of-the-money options.
Research findings reveal a notable conflict in empirical results, particularly between Merton's study and the earlier work of Macbeth, Merville, and Black Merton indicates that the theoretical option prices derived from the Black-Scholes model are lower than the actual market prices for both deep in-the-money and deep out-of-the-money options.
In 1987, Hull and White conducted an empirical study on the Black-Scholes model by incorporating random (stochastic) volatility, moving away from the traditional assumption of constant volatility This innovative approach has since become a widely accepted adaptation of the model in contemporary financial analysis.
A study conducted by White revealed that in-the-money options are generally underpriced, while out-of-the-money options are overpriced The findings indicate that the degree of overpricing increases with the remaining time until expiration, highlighting that the further out of the money an option is, the greater 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) investigate European currency option prices in Geneva using a modified Black-Scholes model alongside a random variance pricing model Their study focuses on pricing calls and puts for the dollar/Swiss franc exchange rate, comparing theoretical prices to actual bid-ask quotes from options traded by Credit Suisse First Boston Futures Trading The findings reveal that the two models yield differing theoretical prices, with the modified Black-Scholes model aligning more closely with observed market bid-ask quotes.
Where N(x) is the distribution function for standard normal random variable T represents maturity and X is the strike price.
After calculating the call options, they use put-call parity theorem to obtain the price for European puts:
The study reveals that actual prices for calls and puts align closely with the Black-Scholes model when the variance rate is updated daily Although the random variance model shows some mispricing, it is not significant enough for small investors trading at the bid-ask spread to achieve abnormal profits.
Corrado C.J and Su T (1998) discovered that while the Black-Scholes model effectively prices at-the-money options, it frequently misprices deep in-the-money and deep out-of-the-money options This discrepancy arises from the model's assumption that security log prices adhere to a constant variance diffusion process.
2.4 Testing the market efficiency of Kuldeep Shastri and Kishore Tandon:
Kuldeep Shastri and Kishore Tandon (1986) evaluated the efficiency of the foreign currency options market by applying the option pricing model established by Biger and Hull Their analysis focused on data from four key currency options: the British Pound, German Mark, Japanese Yen, and Swiss Franc.
Kuldeep Shastri and Kishore Tandon investigate the effectiveness of hedging strategies in generating excess profits when there is a discrepancy between an option's market price and its model price Their analysis includes both ex post and ex ante tests; the former assumes immediate execution at market prices reflecting model deviations, while the latter executes the strategy at the following day's quoted price Findings reveal that the ex post hedging strategy achieves abnormal profits, but these excess returns vanish if the strategy's execution is postponed by one day.
The findings indicate that the foreign currency market on the Philadelphia Stock Exchange is inefficient if market participants can replicate the ex post strategy during the investigation period Conversely, if they can only replicate the ex ante strategy, the market demonstrates efficiency.
This thesis examines market efficiency by utilizing the methodology of Kishore Tandon and Kuldeep (1986) We analyze data from the Vietnamese market, including SJC gold prices, volatility, and interest rates, to calculate option prices Additionally, we apply gold option prices quoted in TOCOM to assess the efficiency of the Vietnamese market Our findings suggest that if the market is efficient, traders will be unable to achieve abnormal profits through either ex post or ex ante strategies.
Volatility 18
Volatility, an unseen yet crucial parameter, significantly influences currency price and option pricing It serves as a measure of uncertainty regarding potential returns from stocks or currencies When volatility is elevated, option premiums tend to increase, while lower volatility results in reduced premiums.
Higher volatility increases the likelihood that the underlying asset's price will exceed the exercise price before expiration, resulting in a higher option premium Conversely, if the underlying instrument is expected to experience low volatility, the chances of the option being profitable diminish, leading to a lower expected option value.
Volatility (σ) can be assessed through the implied standard deviation (ISD) derived from observed option prices or by analyzing historical estimates of σ based on fluctuations in the foreign exchange rate, as noted by Marc Chesney and Louis Scott in 1989.
Historical volatility is calculated using the historical standard deviation, as noted by Kuldeep Shastri and Kishore Tandon in 1985 To empirically assess a stock's volatility, its price is typically monitored at regular intervals, such as daily, weekly, or monthly.
Si : Stock (currency) price at end of ith interval, with i= 0,1,…,n τ : number of intervals per annum
⎝ S i1 ⎠ The usual estimate, s, of the standard deviation of the ui is given by s (1.12) or s (1.13)
Where u is the mean of u i
The volatility estimated per annum is:
For example: if daily data is used the interval is one trading day and we use τ
= 252, if the interval is a week τ = 52 and τ = 12 for monthly data.
The volatility of an asset fluctuates over time, making historical volatility an estimate rather than a definitive measure of future volatility Consequently, determining the appropriate number of historical days for these calculations can be challenging.
In his book "Options, Futures, and Other Derivatives," Hull (2003) emphasizes the importance of aligning the number of observations with the time frame of volatility application Specifically, when pricing an option with 120 days until expiration, it is advisable to base the historical volatility measurement on the same 120-day period.
The implied volatility is often used in practice These are the volatilities implied by option prices observed in the market.
Deep in-the-money and deep out-of-the-money options exhibit relative insensitivity to volatility, leading to unreliable implied volatilities derived from these options (John C Hull, 2000).
Research methodology 21
Modified Black Scholes Model 24
Interest in option pricing has grown significantly, leading to the development of various competing models through scientific research Among the most recognized are the Black-Scholes model and the Binomial Option Pricing Model, both of which are widely utilized in financial markets for their effectiveness in pricing options.
In this study, we use modified Black – Scholes model developed by John Hull to value call and put options on SJC gold brand:
3.2.1 Spot rate and exercise price
The option is currently at-the-money, and we have calculated the prices for both call and put options that expired in August, October, and December 2010 The calculations utilized the spot rates recorded at 11 AM, 2 PM, and 5 PM from July 1, 2010, to August 15, 2010.
3.2.2 Interest rate of VND and Interest rate SJC gold brand
The interest rate of VND collected to value the option is the risk free interest rate of the SBV : 8%
We use interest rate of gold is : 1% (which is the mid point of deposit and loan interest rate of Eximbank at the time of investigation)
In TOCOM, gold call and put options are traded in even months, specifically for the next six months To evaluate the differences in option pricing using the modified Black-Scholes model, we analyzed call and put options from July 1, 2010, to August 15, 2010, focusing on the same values as those for gold options traded in TOCOM for August, October, and December, with the last trading day for these options occurring on the 30th of each even month The pricing formula utilized is: c = e^(-rT)SN(d) - e^(-rT)XN.
We analyze daily gold spot prices from January 1, 2010, to June 30, 2010, to estimate volatility While the ideal measure would be the average volatility of forward rates, which accounts for interest rate volatility over the maturity of contracts, we focus on spot price volatility This approach is justified because the differences between spot and forward rate volatility are minimal during periods of stable foreign/domestic interest rate differentials In our study period, the differential between gold and the Vietnamese Dong (VND) remains relatively stable, making spot rate volatility a reliable measure for our analysis.
The Black-Scholes-Merton model assumes constant variance; however, while variance may remain stable over short time intervals, it can vary significantly over longer periods This paper posits that currency variance is constant within a single day but changes daily, making the Black-Scholes model applicable for short intervals, such as one day, while acknowledging that variance fluctuates from one day to the next.
In Vietnam, the development of derivatives in gold, foreign exchange, and stocks remains limited, with gold options not being traded regularly As a result, the application of implied volatility calculations is impractical This study focuses on estimating volatility using historical SJC gold prices.
To be able to make all the necessary calculations we used MS Excel as a tool for analyzing the data.
When calculating historical volatility one must solve for the optimal number of days or observations, n, to base the volatility calculation on Hull
According to 2003, a useful guideline for calculating historical volatility is to set 'n' equal to the number of days until option expiration For example, when valuing an option with 90 days remaining, historical volatility should be computed based on the previous 90 days However, we impose a minimum constraint, ensuring that historical volatility is never calculated using fewer than 90 days of data Thus, historical volatility is determined based on the days left until expiration, but if this number is less than 90, we default to using a 90-day period.
We analyze the daily closing SJC gold prices from January 1, 2010, to June 30, 2010, to estimate volatility, as more extensive data typically enhances accuracy However, it's important to note that volatility can fluctuate over time, and older data may not effectively predict future trends, as highlighted by John C Hull In the Vietnamese gold market, investors typically speculate over a maximum interval of one year, with most trading activities occurring within a 1 to 6-month timeframe.
The ex post and ex ante hedging test 27
According to Shastri,K and K.Tandon (1986), to test market efficiency, one must investigate whether excess (abnormal) profit opportunities exist in the market.
When opportunities for profit persist over time, it indicates market inefficiency during the examined period Conversely, if no profitable opportunities emerge, it suggests that the market operates efficiently concerning the trading rule applied An efficient market, by definition, implies the absence of arbitrage profits.
This section focuses on the hedging strategy as the primary methodology for testing market efficiency To generate efficient option prices, we utilize the modified Black-Scholes model developed by John Hull, as discussed in Chapter 2.
This article examines two types of hedging strategies: the ex post strategy and the ex ante strategy The ex post strategy allows for transactions at market prices that reflect deviations from model prices, while the ex ante strategy interprets these deviations as signals to initiate a transaction at the subsequent price point.
According to K Shastri and K Tandon (1986), the initial test merely identifies current deviations from equilibrium, whereas the subsequent test serves as a definitive assessment of market efficiency.
The simulated trader receives transaction signals by comparing the model-generated option price with the market option price When the market price exceeds the model price, the trader establishes a portfolio consisting of written call options and purchased foreign bonds Conversely, if the market price is lower than the model price, the trader creates a portfolio of written put options and borrowed foreign bonds.
The domestic currency value at time t of this portfolio is
It can be shown that a long position in a domestic bond is equivalent to a long position in (-α/β) foreign bonds and a (1/β) written (short) position in a call option.
When an option is overpriced, a strategy involving (1/β) written calls and (-α/β) purchased foreign bonds can outperform a long position in domestic bonds Conversely, if an option is underpriced, a portfolio consisting of (1/β) bought calls and borrowing equivalent to (-α/β) foreign bonds can deliver better returns than a short position in domestic bonds.
The trading strategy is described as follow:
Step 1: At time t, the equation (2.1) is used to calculate the model price of the call option, C model market model
Step 2: if the call is overpriced (Ct >Ct ), we form a portfolio composed of (1/β) written calls and (-α/β) bought foreign bonds The cost of this portfolio is 1
⎝ ⎠ ⎝ ⎠ The portfolio is liquidated at the next trade The excess return on this portfolio is: t
If the call is underpriced, then the portfolio is formed oppositely.
The trading strategy for put is similar to those used aboved The strategy is as follows:
Step 1: At time t, the equation (2.2) is used to calculate the model price of the put option, P model market model
Step 2: if the put is overpriced (Pt >Pt ), we form a portfolio composed of (-1/β) written puts and borrowing equivalent to (-α/β) foreign bonds The cost of this portfolio is 1
The portfolio is liquidated at the next trade to yield excess returns:
If the put is underpriced, we follow the opposite strategy.
Positive profit (excess return >0) would indicate market inefficiency.
1 For the ex ante test, the cost of the portfolio is given by:
Where α and β are calculated based on values at time t.
2 For the ex ante test, the excess return is given by substituting t+2 for t+1, and t+1 for t.
3 Equation (3.5) and (3.7) are for the ex post version of the strategy The corresponding equations for the ex ante strategy are obtained by substituting t+2 for t+1, and t+1 for t in equation (3.5) and (3.7).
Empirical results and discussion 30
The result of the Ex post tests 31 The result of the Ex Ante Tests 33
Since 2010, Vietnam has prohibited trading gold on overseas accounts, restricting the ability to hedge options on TOCOM This limitation affects banks' capacity to manage risks associated with writing options, making the use of foreign gold option prices incompatible Our study aims to determine the suitability of the modified Black-Scholes model for valuing European SJC gold option prices in Vietnam.
The study analyzes two sets of data: the first comprises SJC gold prices and interest rates for VND and gold collected from the Vietnamese market between January 1, 2010, and August 15, 2010 The second set includes gold prices and gold option prices sourced from TOCOM, covering the period from July 1, 2010, to August 15, 2010, specifically for options maturing in August, October, and December.
We utilize the modified Black-Scholes model, as developed by Hull and White, to evaluate the option price of the SJC gold brand Our findings reveal a discrepancy between this calculated option price and the gold option prices listed on TOCOM.
To evaluate the efficiency of the Vietnam gold market, we replicate the methodology of K Shastri and K Tandon (1986) by conducting both ex post and ex ante tests Utilizing gold option prices from TOCOM, we implement hedging strategies in the Vietnam gold market The findings reveal that traders can achieve abnormal profits by executing hedging strategies at prevailing market prices.
The application of gold option prices from TOCOM to the Vietnamese gold market is incompatible due to the presence of abnormal trader profits It is recommended that banks utilize a modified Black-Scholes model to assess at-the-money options for the SJC gold brand, employing a European style and implementing risk hedging strategies.
Conclusion 36
Since 2010, Vietnam has prohibited trading gold on overseas accounts, which has restricted banks' ability to hedge risks associated with writing options Consequently, the use of gold option prices quoted by foreign counterparts or on exchanges like TOCOM and COMEX is no longer feasible This article aims to explore the applicability of the modified Black-Scholes model for valuing European SJC gold options in Vietnam.
The study utilizes two sets of data to analyze the gold market The first dataset comprises information gathered from the Vietnamese market between January 1, 2010, and August 15, 2010, which includes the SJC gold price, VND interest rates, and gold prices The second dataset is sourced from TOCOM, covering gold prices and gold option prices from July 1, 2010, to August 15, 2010, specifically for options maturing in August, October, and December.
We utilize the modified Black-Scholes model, as developed by Hull and White, to evaluate the option price of the SJC gold brand Our findings reveal a discrepancy between this calculated price and the gold option prices quoted on the Tokyo Commodity Exchange (TOCOM).
To evaluate the effectiveness of the Vietnam gold market, we replicate the methodology of K Shastri and K Tandon (1986) by conducting both ex post and ex ante tests Utilizing the gold option prices from TOCOM, we implement hedging strategies within the Vietnam gold market The findings reveal that traders can achieve abnormal profits by executing a hedging strategy at the prevailing market prices.
The application of gold option prices from TOCOM is incompatible with the Vietnamese gold market due to abnormal trader profits It is recommended that banks employ a modified Black-Scholes model to value at-the-money options for the SJC gold brand, utilizing a European style Additionally, banks should implement delta hedging, as outlined by Black-Scholes, especially given the prohibition on overseas gold trading.
This study offers valuable insights into the calculation of gold options for commercial banks in Vietnam, revealing a significant disparity between the gold option prices quoted on TOCOM and those derived from the modified Black-Scholes model The application of TOCOM's gold option prices in the Vietnamese market may create arbitrage opportunities between the two pricing methods By introducing a novel approach to gold option valuation, this research aims to enhance the development of the gold option market in Vietnam.
The study presents several limitations that future research should address Firstly, it focuses solely on at-the-money options, suggesting a need for exploration of in-the-money and out-of-the-money options using a larger sample size Secondly, the analysis relies on historical volatility for option pricing, indicating that future studies should utilize implied volatility for more accurate calculations Lastly, while the research examines the application of the Black-Scholes model for valuing SJC gold options, it does not discuss hedging strategies Future articles will introduce the use of delta for hedging option positions.
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PRICE OF GOLD CALL OPTION TRADED IN TOCOM
Date Strike price OPTION PRICE
At 11AM At 14PM At 17PM
Souces: http://www.tocom.or.jp/souba/gold_op_call/index.html
PRICE OF GOLD PUT OPTION TRADED IN TOCOM
Date Strike price OPTION PRICE
At 11AM At 14PM At 17PM
Souces: http://www.tocom.or.jp/souba/gold_op_put/index.html? chart=on
PRICE OF GOLD CALL OPTION TRADED IN TOCOM
Date Strike price OPTION PRICE
At 11AM At 14PM At 17PM
Souces: http://www.tocom.or.jp/souba/gold_op_call/index.html
PRICE OF GOLD PUT OPTION TRADED IN TOCOM
Date Strike price OPTION PRICE
At 11AM At 14PM At 17PM
Souces: http://www.tocom.or.jp/souba/gold_op_put/index.html? chart=on
PRICE OF GOLD CALL OPTION TRADED IN TOCOM
Date Strike price OPTION PRICE
At 11AM At 14PM At 17PM
Souces: http://www.tocom.or.jp/souba/gold_op_call/index.html
PRICE OF GOLD PUT OPTION TRADED IN TOCOM
Date Strike price OPTION PRICE
At 11AM At 14PM At 17PM
Souces: http://www.tocom.or.jp/souba/gold_op_put/index.html? chart=on
Appendix 7: Comparison of call option price of SJC gold brand derived by modified Black-Scholes model and the call option price of gold traded in TOCOM
Number of Days SJC Spot price
CALL option price of SJC (5)
Call option price of TOCOM gold (8)
Call of TOCOM gold option price/
Deferrence between SJC and TOCOM option price (10)=(6)-(9)
- The SJC option price (5) is calculated by modified Black-Scholes model
- The unit of SJC gold and option price is VND/tael
- The unit of gold and option price quoted in TOCOM is JPY/gram
Number of Days SJC Spot price
CALL option price of SJC (5)
Call option price of TOCOM gold (8)
Call of TOCOM gold option price/
Deferrence between SJC and TOCOM option price (10)=(6)-(9)
Date(1) Maturity date (2) Number of
CALL option price of SJC (5)
Call option price of TOCOM gold (8)
Call of TOCOM gold option price/ Strike (9)=(8)/(5)
Deferrence between SJC and TOCOM option price (10)=(6)-(9)
Appendix 8: Comparison of put option price of SJC gold brand derived by modified Black-Scholes model and the put option price of gold traded in TOCOM
PUT option price of SJC (5)
Put option price of TOCOM gold (8)
Put of TOCOM gold option price/ Strike (9)=(8)/(7)
Deferrence between SJC and TOCOM option price (10)=(6)-(9)
- The SJC option price (5) is calculated by modified Black-Scholes model
- The unit of SJC gold and option price is VND/tael
- The unit of gold and option price quoted in TOCOM is JPY/gram
Date(1) Maturity date (2) number of days
PUT option price of SJC (6)
Put option price of TOCOM gold (8)
Put of TOCOM gold option price/ Strike (9)=(8)/(5)
Deferrence between SJC and TOCOM option price (10)=(7)-(9)
Date(1) Maturity date (2) number of days SJC Spot price
PUT option price of SJC (6)
Put option price of TOCOM gold (8)
Put of TOCOM gold option price/ Strike (9)=(8)/(5)
Deferrence between SJC and TOCOM option price (10)=(7)-(9)
Appendix 9: Results of Ex Post test for maturity month of August, Ocober and December for call option:
We use the ex post strategy in Chapter 3 to test the efficiency of the market We compare the SJC gold option price derived by the
The Black-Scholes model is utilized to evaluate call options, with the option price quoted on Tocom at 11 AM A portfolio is constructed by taking a long position in (1/β) call options and a short position in (-α/β) SJC gold at the same time By liquidating this portfolio at 2 PM, any excess return above zero indicates that the trader has achieved abnormal profit.
Deal date Maturity date number of days (t)
TOCOM call 11AM in VND α β V portfolio SJC gold price 14PM
TOCOM call 14PM in VND excess return VND/day (1 tael)
Deal date maturity date number of days (t)
TOCOM call 11AM in VND α β V portfolio SJC gold price 14PM
TOCOM call 14PM in VND excess return VND/day (1 tael)
Deal date maturity date number of days (t)
TOCOM call 11AM in VND α β V portfolio SJC gold price 14PM
TOCOM call 14PM in VND excess return VND/day (1 tael)
Appendix 10: Results of Ex Post test for maturity month of August, Ocober and December for put option:
We use the ex post strategy in Chapter 3 to test the efficiency of the market We compare the SJC gold option price derived by the
The Black-Scholes model is utilized to analyze the option price quoted on Tocom at 11 AM When the put price calculated using the modified Black-Scholes model is lower than the Tocom option price, a portfolio is established by writing a put option (-1/β) and borrowing an equivalent amount of SJC gold (-α/β) at 11 AM, which is liquidated at 2 PM Conversely, if the Tocom option price exceeds the calculated price, an opposite strategy is employed An excess return greater than zero indicates that the trader has achieved abnormal profit.
Deal date maturity date number of days (t)
SJC gold price 11AM Strike price (X) PUT model
TOCOM put 11AM in VND α β V portfolio
TOCOM put 14PM in VND excess return VND/day (1 tael)
Deal date maturity date number of days (t)
TOCOM call 11AM in VND α β V portfolio
TOCOM call 14PM in VND excess return VND/day (1 tael)
Deal date maturity date number of days (t)
SJC gold price 11AM Strike price
TOCOM call 11AM in VND α β V portfolio SJC gold price 14PM TOCOM call
14PM in VND excess return
Appendix 11: Results of Ex ante test for maturity month of August, Ocober and December for call option:
We use the ex ante strategy in Chapter 3 to test the efficiency of the market We compare the SJC gold option price derived by the
The Black-Scholes model, specifically the call option model, is utilized to analyze the option price quoted on Tocom at 11 AM Subsequently, a portfolio is constructed that includes a long position in (1/β) call options and a short position in (-α/β) SJC gold at 2 PM, which is then liquidated at 5 PM An excess return greater than zero indicates that the trader has achieved an abnormal profit.
Deal date maturity date number of days (t)
SJC gold price 11AM Strike price
TOCOM call 11AM in VND α β SJC gold price 14PM
TOCOM call 14PM in VND
TOCOM call 17PM in VND excess return VND/day
Deal date maturity date number of days (t)
SJC gold price 11AM Strike price
TOCOM call 11AM in VND α β SJC gold price 14PM
TOCOM call 14PM in VND
V portfolio SJC gold price 17PM
TOCOM call 17PM in VND excess return VND/day
Deal date maturity date number of days (t)
SJC gold price 11AM Strike price
TOCOM call 11AM in VND α β SJC gold price 14PM
TOCOM call 14PM in VND
V portfolio SJC gold price 17PM
TOCOM call 17PM in VND excess return VND/day
Appendix 12: Results of Ex ante test for maturity month of August, Ocober and December for put option:
We use the ex ante strategy in Chapter 3 to test the efficiency of the market We compare the SJC gold option price derived by the
The Black-Scholes model is utilized to analyze option prices quoted on Tocom at 11 AM When the put price calculated using the modified Black-Scholes model is lower than the Tocom option price, a portfolio is created by writing a put option and borrowing an equivalent amount of SJC gold This position is liquidated at 5 PM Conversely, if the Tocom option price exceeds the calculated price, the opposite strategy is implemented An excess return greater than zero indicates that the trader has achieved abnormal profit.
Deal date maturity date number of days (t)
TOCOM put 11AM in VND α β SJC gold price 14PM
TOCOM put 14PM in VND
TOCOM put 17PM in VND excess return VND/day
Deal date maturity date number of days (t)
SJC gold price 11AM Strike price
TOCOM put 11AM in VND α β SJC gold price 14PM
TOCOM put 14PM in VND
V portfolio SJC gold price 17PM
TOCOM put 17PM in VND excess return VND/day
Deal date maturity date number of days (t)
TOCOM put 11AM in VND α β SJC gold price 14PM
TOCOM put 14PM in VND
V portfolio SJC gold price 17PM
TOCOM put 17PM in VND excess return VND/day