Applying black scholes model in option pricing for VN30

Applying Black – Scholes Model in option pricing for VN-30 | 2015 Bachelor of Finance and Banking Thesis Nguyen Thi Huyen Trang SB60524 “Applying Black – Scholes in option pricing for VN 30” PhanModel Quoc Buu SB60515 Group members Hoang Tuan Anh Supervisor SB60383 Ms Bui Thi Thao Ly, MBA Ho Chi Minh City May 2015 Applying Black – Scholes Model in option pricing for VN-30 | 2015 Table of Contents Applying Black – Scholes Model in option pricing for VN-30 | 2015 ACKNOWLEDGEMENT We would like to express our special thanks of gratitude and deep obligation to Ms Bui Thi Thao Ly, who has helped, supported and guided us to complete our thesis with the topic “Applying Black Scholes Models in option pricing for VN30” We also thankful to our Teachers in Corporate Finance department –FPT University, who have given us a lot of valuable lessons through years studying here It is the essential foundation knowledge for us to study the project and precious baggage in the future In addition, we are highly indebted to previous colleagues, who have done research, conference document and journal before Hence, we have a better view about our topic We own sincere thanks to my parents and friends for their moral support and giving us inspiration to achieve this task We have taken a lot of efforts in this project However, due to the lack of study experience, limitation of knowledge and very new topic, we might not able to recognize all mistakes ourselves We are looking forward to receiving helpful comments and suggestions to implement our thesis in the best way Thanks to all again who support us Wish you all have good health and successful in life and career Applying Black – Scholes Model in option pricing for VN-30 | 2015 ABSTRACT This study addresses the questions of can and how to apply Black-Scholes model in option pricing for VN30 index The aim of celebrated Black-Scholes model is to evaluate the European options by a simple calculation steps and efficient numerical for options optimally Their formula and its variants have remained remarkably the industry standard in equity and currency markets for the last 30 years It is an undeniable fact that the Black-Scholes model is so popular approach which used by a lot of investors in the world in order to hedge risk Sharing the same purpose, this paper aims to research the topic “Applying Black – Scholes Model in option pricing for VN-30” by testing the assumption of Black – Scholes model and calculating the option value of the contract Through this study, the author can evaluate the effectiveness and the realistic of the Black-Scholes model when apply this model for the Vietnam’s stock market Besides authors also consider variables input of Black-Scholes European call and put options such as market price, strike price, volatility, time to maturity, dividend, and risk-free interest rate Next, the research has tested Argument Dickey-Fuller test and BSM by using daily price of Vn30 Index from February 6, 2012 to June 19, 2015 By using E-view software to analyze data for the purpose of describes statistical data and predict future price As the results, VN30 index satisfy all the required three primary conditions such as: VN-30 Index have lognormal distribution, compound continuous return of VN-30 index are normally distributed, the volatility of continuously compounded returns is known and constant Moreover, we calculate the Greeks to analyze the sensitive of the value of option to a small change in a given VN-30 stock price in order to help the investor reduce risk and protect their portfolio In conclusion, the result of this research shows that there is a positive outlook for traders on option pricing for VN30 index by BSM Furthermore, the final numerical proves that applying BS model in option pricing for VN30 is totally possible Applying Black – Scholes Model in option pricing for VN-30 | 2015 LIST OF ABBREVITIONS ADF Argument Dickey-Fuller BSM Black-Scholes Model CME Chicago Mercantile Exchange ETF Exchange Traded Fund FTA Free trade agreement HOSE Ho Chi Minh Stock Exchange TPP Trans-Pacific Partnership VFM VietFund Management Applying Black – Scholes Model in option pricing for VN-30 | 2015 LIST OF NOTATIONS Applying Black – Scholes Model in option pricing for VN-30 | 2015 LIST OF FIGURES Figure 1: Chart of the changing in the VN-Index Price…………………………………………12 Figure 2: Long/Short call option…………………………… …………………………………18 Figure 3: Long/Short put option…………………………… ………………………………….19 Figure 4: Research Onion…………………………… ……………………………………… 32 Figure 5: Deductive Approaches …………………………… …………………………………33 Figure 6: Argument Dickey – Fuller Hypothesis Test of Ln [St] ……………………………….41 Figure 7: Argument Dickey – Fuller Hypothesis Test of Ln {St/St-1}……………………… 42 Figure 8: Histogram and stats of return of VN-30 Index……………………………………… 44 Figure 9: Call Delta of different TIME TO EXPIRATION with Stock price ………………….48 Figure 10: Put Delta of different TIME TO EXPIRATION with Stock price ………………….49 Figure 11: Call- Put Gamma of different TIME TO EXPIRATION with Stock price …………50 Figure 12: Call –Put Vega of different TIME TO EXPIRATION with Stock ………………… 51 Figure 13: Call Rho of different TIME TO EXPIRATION with Stock ………………… …… 52 Figure 14: Put Rho of different TIME TO EXPIRATION with Stock………………………… 53 Figure 15: Call Theta of different TIME TO EXPIRATION with Stock …………………… 54 Figure 16: Put Theta of different TIME TO EXPIRATION with Stock……………………… 55 LIST OF TABLES Table 1: Input data – Output data and Value of Option of Black-Scholes Model……………….45 Table 2: The changes of input data effect to value of option (Black-Scholes Model)……… 47 Applying Black – Scholes Model in option pricing for VN-30 | 2015 Table 3: Greeks …… ………………………………………………………………………… 47 Applying Black – Scholes Model in option pricing for VN-30 | 2015 CHAPTER 1.1 INTRODUCTION AND THESIS OUTLINE Introduction Theoretical and practical prove those important instruments to prevent and reduce risks in the investment of stock are derivative securities and including options Vietnam stock market had operated over 12 years with many ups and downs Therefore, it makes investors a lot of huge losses in previous time So far, options has not yet formally trade to prove it is own key functions Option is a financial activity and it should be valued Option pricing is very important, because just a small fluctuation of prices could affect the profitability of the contract Searching Valuation Models applications is necessary to give reasonable premiums The purpose is about reconciling both of writer and buyer Although there are many piece of research for option pricing in the world, option pricing is new sector in Vietnam This is why authors introduce option pricing models and show their applications Black-Scholes model is one of most popular that brings high effect Famous formula for option pricing was both of Fischer Black and Myron Scholes announced in 1973 In 1997 he was awarded the Nobel Memorial Prize in Economic Sciences for a method to determine the value of derivatives VN30 index had constructed by Ho Chi Minh City Stock Exchange, a free-float adjusted market cap-weighted index of 30 stocks that have the highest market capitalization and liquidity listed on HOSE VN30 index accounted for 80% market capitalization and 60% of total market transactions The functions of VN30 index are measure market's total value and its evolution ETF is a security that stimulates an index or a basket of stocks like an index fund VFMVN30 ETF is the first ETF Funds in Vietnam which is established by VFM The purpose of VFMVN30 ETF is to track the performance of the VN30 index after deducting all of expenses of the Fund and ETF trades like a stock on an exchange When the basket of securities of the VN30 Index changes, the VFMVN30 ETF will make adjustments the Fund's portfolio to suit with VN30' portfolio Applying Black – Scholes Model in option pricing for VN-30 | 2015 1.1.1 Research Background It is an undeniable fact that stock market assumes a pivotal role in economy advancement of many countries worldwide In Vietnam, stock market has been going up very fast It makes up a big part in capital mobilization for country economy developing However, goods on stock market are too monotonously, there is no other product except stock and bond In developed stock market countries, besides trading stock and bond, there are a lot of exciting activities of derivatives products such as securities bond, stock index option and future contract According to Cappon (1998), derivatives are one of the effective tools in order to manage a risk, the economies is perfect when it is in the direction of capital market It means derivative market managed efficiently risk and financial market securities controlled saving intermediately 1.1.2 Overview of Viet Nam Stock Market 1.1.2.1 History Vietnam's stock market officially operated in 2000 with the operation of two stock exchanges in Ho Chi Minh City in July 20th and Hanoi in August 8th 2005 After 15 years, Vietnam’s stock market has developed and significant contributed to the Vietnam’s economy However, with the establishment of the Vietnam only 15 years compared to the stock market of developed countries, it only was secondary market and still young Besides, information on companies operating in the market was not yet complete , inexperienced investors , business processes of market was not yet stable, the legal framework was incomplete The special milestone of Vietnam stock market was the period from 2007-2009 In the beginning of 2007, VN index stood at 751.77 points but after only months, it reached the peak of 1,170.67 points This was the greatest time of Vietnamese stock market after years of developing In the following years, Vietnamese stock market went through the most difficult time The economy was affected by the financial crisis and the market fell down to 11 the bottom at 286.85 points In the end of 2008, it close at 315.61, which means it dropped nearly 70% from the peak 10 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.420 5/5/2014 614.36 -0.0285 6.405 4/2/2015 576.13 0.0116 6.3563 5/6/2014 605.2 -0.0150 6.412 4/3/2015 577.66 0.0027 6.3590 5/7/2014 609.51 0.0071 6.354 4/6/2015 572.71 -0.0086 6.3504 5/8/2014 575.31 -0.0577 6.376 4/7/2015 577.69 0.0087 6.3590 5/9/2014 587.91 0.0217 6.333 4/8/2015 575.94 -0.0030 6.3560 5/12/2014 563.3 -0.0428 6.328 4/9/2015 4/10/201 578.35 0.0042 6.3602 5/13/2014 560.11 -0.0057 6.366 4/13/201 583.34 0.0086 6.3688 5/14/2014 581.83 0.0380 6.355 4/14/201 589.77 0.0110 6.3797 5/15/2014 575.53 -0.0109 6.366 4/15/201 587.24 -0.0043 6.3754 5/16/2014 581.93 0.0111 6.379 4/16/201 590.78 0.0060 6.3814 5/19/2014 589.31 0.0126 6.380 4/17/201 595.09 0.0073 6.3887 5/20/2014 590.27 0.0016 6.391 4/20/201 599.12 0.0067 6.3955 5/21/2014 596.82 0.0110 6.384 4/21/201 595.82 -0.0055 6.3899 5/22/2014 592.75 -0.0068 6.387 4/22/201 593.67 -0.0036 6.3863 5/23/2014 594.35 0.0027 6.390 4/23/201 594 0.0006 6.3869 5/26/2014 596.24 0.0032 6.406 4/24/201 592.71 -0.0022 6.3847 5/27/2014 5/28/2014 605.87 614.88 0.0160 0.0148 6.421 4/27/201 596.1 593.15 0.0057 -0.0050 6.3904 6.3854 77 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.427 5/29/2014 618.59 0.0060 6.426 5/4/2015 576.52 -0.0284 6.3570 5/30/2014 618 -0.0010 6.415 5/5/2015 585.45 0.0154 6.3724 6/2/2014 610.99 -0.0114 6.417 5/6/2015 579.39 -0.0104 6.3620 6/3/2014 612.49 0.0025 6.403 5/7/2015 582.4 0.0052 6.3672 6/4/2014 603.83 -0.0142 6.399 5/8/2015 5/11/201 582.91 0.0009 6.3680 6/5/2014 601.6 -0.0037 6.411 5/12/201 579.41 -0.0060 6.3620 6/6/2014 608.48 0.0114 6.415 5/13/201 571 -0.0146 6.3474 6/9/2014 610.92 0.0040 6.411 5/14/201 569.28 -0.0030 6.3444 6/10/2014 608.59 -0.0038 6.422 5/15/201 569.89 0.0011 6.3454 6/11/2014 615.52 0.0113 6.423 5/18/201 561.87 -0.0142 6.3313 6/12/2014 616.11 0.0010 6.426 5/19/201 552.9 -0.0161 6.3152 6/13/2014 617.73 0.0026 6.427 5/20/201 556.44 0.0064 6.3216 6/16/2014 618.62 0.0014 6.430 5/21/201 572.34 0.0282 6.3497 6/17/2014 620.61 0.0032 6.427 5/22/201 578.64 0.0109 6.3607 6/18/2014 618.61 -0.0032 6.419 5/25/201 586.58 0.0136 6.3743 6/19/2014 613.82 -0.0078 6.408 5/26/201 588.36 0.0030 6.3773 6/20/2014 6/23/2014 607.23 609.99 -0.0108 0.0045 6.413 5/27/201 591.13 589.82 0.0047 -0.0022 6.3820 6.3798 78 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.417 5/28/201 6/24/2014 612.54 0.0042 6.426 5/29/201 594.27 0.0075 6.3873 6/25/2014 618.1 0.0090 6.429 589.32 -0.0084 6.3790 6/26/2014 619.91 0.0029 6.424 6/1/2015 593.61 0.0073 6.3862 6/27/2014 616.85 -0.0049 6.421 6/2/2015 588.63 -0.0084 6.3778 6/30/2014 615.06 -0.0029 6.426 6/3/2015 585.6 -0.0052 6.3726 7/1/2014 617.96 0.0047 6.430 6/4/2015 587.48 0.0032 6.3758 7/2/2014 620.2 0.0036 6.441 6/5/2015 592.22 0.0080 6.3839 7/3/2014 627.17 0.0112 6.447 6/8/2015 594.51 0.0039 6.3877 7/4/2014 631.02 0.0061 6.456 6/9/2015 6/10/201 593.36 -0.0019 6.3858 7/7/2014 636.75 0.0090 6.455 6/11/201 595.06 0.0029 6.3887 7/8/2014 636.21 -0.0008 6.456 6/12/201 601.4 0.0106 6.3993 7/9/2014 636.64 0.0007 6.443 6/15/201 604.29 0.0048 6.4041 7/10/2014 628.78 -0.0124 6.441 6/16/201 604.53 0.0004 6.4045 7/11/2014 627.1 -0.0027 6.449 6/17/201 600.92 -0.0060 6.3985 7/14/2014 632.54 0.0086 6.455 6/18/201 598.25 -0.0045 6.3940 7/15/2014 636.09 0.0056 6.457 6/19/201 600.45 0.0037 6.3977 7/16/2014 7/17/2014 637.13 636.3 0.0016 -0.0013 6.455 603.26 0.0047 6.4023 79 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.470 7/18/2014 645.52 0.0144 6.469 7/21/2014 645.33 -0.0003 6.464 7/22/2014 641.95 -0.0053 6.462 7/23/2014 640.84 -0.0017 6.471 7/24/2014 646.64 0.0090 6.464 7/25/2014 641.96 -0.0073 6.446 7/28/2014 630.3 -0.0183 6.451 7/29/2014 633.58 0.0052 6.444 7/30/2014 629.07 -0.0071 6.456 7/31/2014 637.04 0.0126 6.453 8/1/2014 635.01 -0.0032 6.459 8/4/2014 638.98 0.0062 6.467 8/5/2014 643.56 0.0071 6.467 8/6/2014 644 0.0007 6.468 8/7/2014 644.19 0.0003 6.464 8/8/2014 641.93 -0.0035 6.458 8/11/2014 8/12/2014 638.22 639.96 -0.0058 0.0027 6.461 80 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.469 8/13/2014 645.17 0.0081 6.476 8/14/2014 649.85 0.0072 6.469 8/15/2014 645.13 -0.0073 6.472 8/18/2014 647 0.0029 6.470 8/19/2014 645.46 -0.0024 6.469 8/20/2014 645.44 0.0000 6.476 8/21/2014 649.94 0.0069 6.484 8/22/2014 654.96 0.0077 6.494 8/25/2014 661.76 0.0103 6.504 8/26/2014 668.25 0.0098 6.504 8/27/2014 667.9 -0.0005 6.505 8/28/2014 668.96 0.0016 6.517 8/29/2014 676.82 0.0117 6.520 9/3/2014 678.9 0.0031 6.520 9/4/2014 678.59 -0.0005 6.518 9/5/2014 677.62 -0.0014 6.520 9/8/2014 9/9/2014 678.83 664.65 0.0018 -0.0211 6.499 81 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.501 9/10/2014 666.42 0.0027 6.499 9/11/2014 665.09 -0.0020 6.506 9/12/2014 669.78 0.0070 6.504 9/15/2014 668.42 -0.0020 6.502 9/16/2014 666.66 -0.0026 6.500 9/17/2014 665.66 -0.0015 6.491 9/18/2014 659.63 -0.0091 6.483 9/19/2014 654.54 -0.0077 6.481 9/22/2014 653.19 -0.0021 6.489 9/23/2014 658.31 0.0078 6.484 9/24/2014 655.14 -0.0048 6.482 9/25/2014 653.39 -0.0027 6.476 9/26/2014 649.63 -0.0058 6.466 9/29/2014 642.98 -0.0103 6.468 9/30/2014 644.25 0.0020 6.484 10/1/2014 655.06 0.0166 6.491 10/2/2014 10/3/2014 659.64 659.25 0.0070 -0.0006 6.491 82 Applying Black – Scholes Model in option pricing for VN-30 | 2015 6.495 10/6/2014 662.43 0.0048 6.491 10/7/2014 659.16 -0.0049 6.490 10/8/2014 658.98 -0.0003 6.487 10/9/2014 10/10/201 657.11 -0.0028 6.479 10/13/201 651.72 -0.0082 6.478 10/14/201 651.07 -0.0010 6.463 10/15/201 641.13 -0.0154 6.464 10/16/201 641.63 0.0008 6.435 10/17/201 623.76 -0.0282 6.437 10/20/201 624.77 0.0016 6.442 10/21/201 628.09 0.0053 6.451 10/22/201 633.81 0.0091 6.458 10/23/201 637.85 0.0064 6.447 10/24/201 630.84 -0.0111 6.445 10/27/201 629.52 -0.0021 6.421 10/28/201 615.15 -0.0231 6.428 10/29/201 618.99 628.1 0.0062 0.0146 6.442 83 Applying Black – Scholes Model in option pricing for VN-30 | 2015 10/30/201 6.441 10/31/201 627.21 -0.0014 6.459 638.78 0.0183 6.468 11/3/2014 644.64 0.0091 6.461 11/4/2014 639.91 -0.0074 6.457 11/5/2014 637.68 -0.0035 6.457 11/6/2014 637.56 -0.0002 6.465 11/7/2014 11/10/201 642.77 0.0081 6.466 11/11/201 642.9 0.0002 6.464 11/12/201 642.02 -0.0014 6.464 11/13/201 641.89 -0.0002 6.459 11/14/201 638.87 -0.0047 6.458 11/17/201 637.9 -0.0015 6.457 11/18/201 637.21 -0.0011 6.442 11/19/201 627.84 -0.0148 6.435 11/20/201 623.66 -0.0067 6.443 11/21/201 628.8 0.0082 6.435 11/24/201 623.74 616.39 -0.0081 -0.0119 6.423 84 Applying Black – Scholes Model in option pricing for VN-30 | 2015 11/25/201 6.434 11/26/201 623.23 0.0110 6.424 11/27/201 616.48 -0.0109 6.422 11/28/201 615.57 -0.0015 6.415 611.15 -0.0072 6.420 12/1/2014 614.44 0.0054 6.419 12/2/2014 613.57 -0.0014 6.428 12/3/2014 619.29 0.0093 6.436 12/4/2014 624.31 0.0081 6.437 12/5/2014 624.67 0.0006 6.429 12/8/2014 619.87 -0.0077 6.403 12/9/2014 12/10/201 603.85 -0.0262 6.414 12/11/201 610.81 0.0115 6.404 12/12/201 604.8 -0.0099 6.412 12/15/201 609.33 0.0075 6.403 12/16/201 603.92 -0.0089 6.383 12/17/201 591.78 -0.0203 6.345 12/18/201 569.71 578.88 -0.0380 0.0160 6.361 85 Applying Black – Scholes Model in option pricing for VN-30 | 2015 12/19/201 6.346 12/22/201 570.61 -0.0144 6.376 12/23/201 587.56 0.0293 6.379 12/24/201 589.61 0.0035 6.382 12/25/201 591.19 0.0027 6.371 12/26/201 585.19 -0.0102 6.367 12/29/201 582.45 -0.0047 6.368 12/30/201 583.36 0.0016 6.382 12/31/201 591.18 0.0133 6.399 601.66 0.0176 Appendix B: Histogram and stats of return of Vn30- Index price (from 06/02/2012 to 19/6/2015) 86