MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF ECONOMICS HO CHI MINH CITY NGUYEN TRI MINH PERFORMANCE OF STOCHASTIC OPTION PRICING MODELS AND CONSTRUCTION OF VOLATILITY SMILES FOR OPTION PRICING IN AN EMERGING DERIVATIVES MARKET PhD THESIS Ho Chi Minh City – 2023 MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF ECONOMICS HO CHI MINH CITY PERFORMANCE OF STOCHASTIC OPTION PRICING MODELS AND CONSTRUCTION OF VOLATILITY SMILES FOR OPTION PRICING IN AN EMERGING DERIVATIVES MARKET Major: Finance and banking Code: 9340201 PhD THESIS Supervisor: Prof. Tran Ngoc Tho Ho Chi Minh City – 2023 OPENING DECLARATION I hereby declare that the PhD thesis “Performance of Stochastic Option Pricing Models and Construction of Volatility Smiles for Option Pricing in an Emerging Derivatives Market” is my independent research, conducted under supervision of Prof. Tran Ngoc Tho. The research was carried out with integrity and based on reliable data sources.
The referenced works are properly cited within the thesis. PhD student Nguyen Tri Minh Table of Contents ABSTRACT. Research objectives and contributions. Summary of methodology and results.
THEORETICAL FRAMEWORK AND LITERATURE REVIEW. What is an option. Option price/premium. The classic Black-Scholes option pricing model.
Risk-neutral pricing. Stochastic volatility and stochastic option pricing models. Heston model’s process. The implied volatility surface.
Implied volatility and volatility smile. Deriving an expression of implied volatility. Basic facts about machine learning. Literature review and research contributions.
Stochastic option pricing models. Methods of determining implied volatility surface. Option pricing in illiquid markets. Application of machine learning in option pricing.
METHODOLOGY AND DATA. Performance of stochastic option pricing models. Stochastic volatility models. The Heston model for European options.
Heston and Heston++ models’ characteristic functions. Bates model’s characteristic function. Heston-Hull-White’s characteristic function. Risk-neutral moments.
Construction of implied volatility smiles for illiquid options. RESULTS AND DISCUSSIONS. Performance of stochastic option pricing models. In-sample pricing performance.
Out-of-sample pricing performance. Implied volatility surface characteristics. Risk-neutral return distribution characteristics. Construction of implied volatility smiles.
Result figures for Correlation method. Result figures for K-nearest neighbor method (KNN). Result figures for weighted K-nearest neighbor method (WKNN) .132 LIST OF THESIS-RELATED PUBLICATIONS .135 LIST OF ABBREVIATIONS AR: autoregressive GDP: gross domestic product IV: implied volatility KNN: K-nearest neighbor LIBOR: London interbank offered rate RMSE: root-mean-square error RNK: risk-neutral kurtosis RNS: risk-neutral skewness RNV: risk-neutral variance TED: Treasury-Eurodollar WKNN: weighted K-nearest neighbor LIST OF TABLES Table 3.1: Starting values and parameter bounds .2: Descriptive statistics per calibration .1: Median calibrated model parameters .2: AR(1) coefficients of the model parameters .3: Model performance and implied volatility surface characteristics ($RMSE) .4: Model performance and implied volatility surface characteristics (%RMSE) .5: Model performance and risk-neutral return distribution characteristics ($RMSE) .6: Model performance and risk-neutral return distribution characteristics (%RMSE) .7: Model performance and industry characteristics ($RMSE) .8: Model performance and industry characteristics (%RMSE) .9: Early exercise premium and bid-ask spread .10: Early exercise premium and bid-ask spread relative to the market option prices .11: Backtesting results for the correlation method .12: Backtesting results for the KNN method .13: Backtesting results for the Weighted KNN method .131 LIST OF FIGURES Figure 3.1: Number of call options .2: Number of put options .3: Average call moneyness .4: Average put moneyness .6: Average implied volatility .8: Average trading volume .9: Average open interest .1: Median root mean square error .2: Median 1-day ahead change in the root mean square error .3: Median hedging error .4: IV smile for low realized skewness and low realized kurtosis.5: IV smile for low realized skewness and high realized kurtosis .6: IV smile for high realized skewness and low realized kurtosis .7: IV smile for high realized skewness and high realized kurtosis .8: IV smile for low realized skewness and low realized kurtosis.9: IV smile for low realized skewness and high realized kurtosis .10: IV smile for high realized skewness and low realized kurtosis .11: IV smile for high realized skewness and high realized kurtosis .12: IV smile for low realized skewness and low realized kurtosis.13: IV smile for low realized skewness and high realized kurtosis .14: IV smile for high realized skewness and low realized kurtosis .15: IV smile for high realized skewness and high realized kurtosis .127 1 ABSTRACT This thesis has two objectives. The first objective is carrying out a comparison of performance between four stochastic option pricing models (Heston, Heston++, Bates and Heston-Hull-White), based on pricing a cross-section of stock options across various industries.
The second is proposing a method of constructing implied volatility (IV) smiles for stock options in a new or illiquid option market (Vietnam in this case), using data from an existing market to do so (the US in this case). For the first objective, the results show that the Heston model performs the best in in- sample pricing, as well as capturing the characteristics of the market, while Heston ++ performs the best in out-of-sample pricing and hedging. For the second objective, the three proposed methods for constructing IV smiles, namely correlation, K-nearest neighbor (KNN) and weighted KNN, perform reasonably well, with weighted KNN considered the best among them. Research background Vietnam is striving to be a prominent economic center, at least for the region of Southeast Asia, in terms of both trading and finance.
Therefore, global integration is very important for the Vietnamese economy as a whole. This is the general direction of the country as a whole since 1986, when the reformation policies led to the opening of Vietnamese economy. Furthermore, in 1995, normalization of diplomatic relations with the US has left the country with no more antagonistic relationship with the rest of the world, paving the way for Vietnam to take the necessary steps for joining the global community and establishing cooperative relationships with every country around the world. Regarding trading, the country has been doing well, with joining the World Trade Organization being a major stepping stone.
For many years, Vietnam has been diligent in developing trading relationships around the world, both bilateral and multilateral, as shown by various free trade agreements at various levels being signed. This makes Vietnam become one of the most open economies in the world, with trade equaling 186% of gross domestic product, the tenth highest value of the world and second highest in Southeast Asia (behind Singapore which has 338%, the third highest globally) according to the World Bank. In general, Vietnam has undergone a drastic transformation in terms of trading in the past decades, as evident by the fact that the trade to GDP value of the country was only 43% back in 1995. On a global scale, Vietnam has made themselves a trustworthy trading partner to every other nation, with mutual benefits forming the core of Vietnam’s trading relationships, and become an attractive destination for multinational corporations to open their businesses in, thanks to the country’s stable political climate and accommodating policies.
However, global integration of the economy is not decided by trade alone. The transformation of the Vietnamese financial market to become globally integrated is 3 also very important. The reason is that such a financial market can help Vietnamese firms reach out to a vast pool of potential investors around the world, freeing them from the bounds of the local capital market. Unfortunately, regarding that aspect of global integration, Vietnam is still rather lacking and still needs catching up, compared to her neighbors.
In particular, the size of the Vietnamese financial market is still small compared to other Southeast Asian countries. According to Vu (2022), at the end of 2020, the total assets of Vietnamese financial institutions is approximately 219% of the country’s GDP, while the average value of the top five ASEAN countries is 320%; market capitalization of the Vietnamese stock market is about 84% of GDP, only higher than Indonesia (the rest of Southeast Asia have values ranging from 93% to 243%). The values of stocks traded in Vietnam compared to GDP is also modest compared to the other ASEAN countries. According to the World Bank, in 2020, the value of stocks traded to GDP of Vietnam is only 16.4%, which is higher than the Philippines (9%) and Indonesia (12.4%), but significantly lower than those of Malaysia (73.
Those are the signs that the Vietnamese financial market is still lagging behind the major players in the region, and has not fully tapped its potential to flourish and compete on equal ground with those countries. In other words, there are still a lot of measures to be taken in order to further develop, and modernize, the Vietnamese financial market. Even though Vietnam has a very prominent advantage of being politically stable, meaning that foreign investors are welcome and able conduct their activities without security concerns, that factor alone is not sufficient for a developed financial market. The potential global investors are going to require more than that in order to participate in the Vietnamese financial market and stay there for the long term.
Hence, similar to how the Vietnamese industries seek to attract new customers globally and retain them, the Vietnamese financial market need to do the same to international investors. In other words, the Vietnamese financial market has to make itself attractive in many ways, to show that global investors can see the country as not only a safe destination, 4 but also a flexible and profitable one which can help fulfil their diverse investment needs. Therefore, developing the Vietnamese financial market further remains a key role in improving the country’s standing in both regional and global stages. There have been a number of proposals to transform the country into a prominent financial center, where investors from around the world are welcome to inject capital to the Vietnamese financial market.
The establishment of such a financial center can be a major stepping stone for Vietnamese firms introduce themselves to the global financial market, attract financing from overseas and make themselves more competitive worldwide. However, such proposals are still on paper and subject to debate, hence there has not been much progress on that matter. However, this highlights the fact that modernizing the Vietnamese financial market and establishing a global financial center is not a simple matter, and such goals require efforts from all the relevant authorities. There are many things to be done in order to achieve this goal: keeping the business environment stable and friendly to foreign investors, investing in advanced technology, educating a capable workforce, giving out attractive tax policies for potential international investors, refining policies regarding the flow of capital in and out of the country, removing regulatory barriers that hinder investment activities.
Last but not least, the Vietnamese financial market has to provide a wide variety of products, or financial assets and tools, in order to draw in investors. The reason is that various investors has various preferences. More products being offered means that there are more choices available to them to fulfil their investment objectives, as well as carry out various risk management strategies that suit their preferences. Furthermore, modernizing the financial market does not simply involve investing in state-of-the-art technology (even that measure by itself is very beneficial in its own right, as it helps in improving the speed of transaction, increasing security of financial transactions, encouraging investors from around the world to participate in the market 5 activities, etc.
Modernization also means that the market has to be able to many alternative tools and products to satisfy the needs of as many potential investors as possible, enabling various investment and risk management strategies, from simple to complex. In other words, the market has to show investors that there are many possibilities for them to explore, and there are many things that they can do within that market.