Cheung, Kwan Hung Edwin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Levy Process --- p.4 / Chapter 2.1 --- Levy-Khintchine representation --- p.5 / Chapter 2.2 --- Variance Gamma process --- p.6 / Chapter 3 --- Minimum-Variance Static Hedge with Index futures --- p.8 / Chapter 3.1 --- Capital Asset Pricing Model with static hedge --- p.10 / Chapter 3.2 --- Continuous CAPM under Levy process --- p.11 / Chapter 4 --- Option pricing under Levy process --- p.15 / Chapter 4.1 --- Option pricing under the fast Fourier transform --- p.16 / Chapter 4.2 --- The modified fast Fourier transform on call option price --- p.19 / Chapter 5 --- Empirical Results --- p.23 / Chapter 5.1 --- Proposed model for empirical studies --- p.25 / Chapter 5.2 --- Calibration Procedure and Estimates of Betas --- p.26 / Chapter 5.3 --- Hedging performance of Betas --- p.32 / Chapter 6 --- Conclusion --- p.37 / Bibliography --- p.39

本研究鑑於八十六年一月上市的摩根台股指數期貨，市場價格與理論價格發生頗大幅度的乖離，故以日成交量資料綜觀此市場實際狀況後，擷取最近月和部份次近月的五分鐘資料進行實證研究。 考量借貸利率差異和我國證券市場融券保證金制度，將產生不同的期貨理論價格，加上交易成本建構出無套利機會區間，再考慮風險溢酬後設定無套利執行區間。利用二次規劃模型以累計追蹤誤差最小化為目標式，求得最適指數模擬投資組合，依此進行指數套利交易。 研究結果摘要如下： 一、樣本期間二十一個期貨合約的市場價格，並不符合持有成本模型下的理論價格，有十八個期貨合約價格顯著偏低。 二、總樣本僅有48.9%落在具效率的無套利機會區間中，20.2%低於無套利執行區間下限，可進行融券放空股票買入期指的反向套利；有0.7%高於無套利執行區間上限，可進行買入股票賣出期指的正向套利。 三、反向套利執行機會持續期間平均1.1小時，最長高達20.8小時；正向套利平均持續期間為22.7分鐘。套利部位平均存續期間為15.1日。 四、平均套利利潤為2.26%，反向套利最大利潤高達11.55%，正向為4.42%。第一類交易者模擬套利交易一年的報酬率為25.43 五、以第二類交易者成本進行模擬組合套利交易七回合，累計一年的報酬率為22.39%。模擬期間平均累計追蹤誤差0.23%、匯率誤差值－0.07%，期貨保證金追繳機率為6%。 第一章 緒論 ……………………………………………… 1 第一節 研究背景與動機 …………………………… 1 第二節 研究目的 …………………………………… 3 第三節 研究範圍與架構 …………………………… 4 第二章 文獻探討 ………………………………………… 7 第一節 無套利條件 …………………………………… 7 第二節 持有成本模型下的價格偏誤 ……………… 17 第三節 市場組合的建構 …………………………… 20 第三章 研究方法與資料整理 …………………………… 24 第一節 樣本期間與資料來源 ……………………… 24 第二節 指數期貨合約定價模式 …………………… 27 第三節 相對價格偏誤的衡量 ……………………… 31 第四節 建構無套利區間 …………………………… 32 第五節 建立模擬組合 ……………………………… 35 第四章 實證結果與分析 ………………………………… 41 第一節 期貨的價格偏誤 …………………………… 41 第二節 期貨的無套利區間 ………………………… 45 第三節 模擬套利交易 ………….…………………… 61 第五章 結論與建議 …………………………………… 100 第一節 結論 …………………………………………… 100 第二節 研究限制與未來研究建議 ……………… 102 參考文獻 ………………………………………………… 103 / This paper is induced by the serious mispricing of MSCI Taiwan index futures,listed in January 1997. The empirical evidence is based on five minutes intraday data of nearby and far nearest futures contracts. There are different theoretical futures prices as the risk-free borrow-ing and lending rate are different and concerning our securities market short selling rules.We build the no-arbitrage opportunity bounds and the no-arbitrage trading bounds after added trasaction costs and risk premium. We get the optimal mimic portfolio to pull the trigger by using the quadratic programming which minimizing the accumulative tracking errors.The important results are as follows： 1. The 21 futures contracts market prices of my sample period can not be described by the cost of carry model.The average size of mispricing is significantly different from zero.There are 18 futures contracts actual prices significantly underpricing. 2. There are only 48.9% intraday observations efficiently priced within the no-arbitrage boundaries.It existed 20.2% observations under the no-arbitrage trading lower bounds to trigger short arbitrages and 0.7% observations over the higher bounds to trigger long arbitrages. 3. The average time of underpricing subsequent violations is 1.1hours and at the longest is 20.8 hours. The average time of overpricing subsequent violations is 22.7 mimutes.The average holding period of arbitrages position is 15.1 days. 4. The average arbitrage profits are 2.26%.The maximum profit of short arbitrages has reached 11.55% and long arbitrages reached 4.42%. We earn 25.43% returns from simulating arbitrage trading for one year depending upon the category 1 traders. 5. Depending upon the category 2 traders,we simulate arbitrage trading by mimic portfolio and futures contracts for 7 rounds.The average of accumulative tracking errors is 0.23%,exchange rate errors is -0.07%, futures margin call probability is 6%.The total returns are 22.39% for one year.

In this thesis, we propose a model which applies the genetic programming (GP) to train the profitable and stable trading strategy in the training period, and then the strategy is applied to trade stocks in the testing period. The variables for GP in our models include 6 basic information and 25 technical indicators. We perform our models on Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) from 2000/9/14 to 2010/5/21, approximately ten years. We conduct five experiments. In these experiments, we find that the trading strategies generated by GP with two arithmetic trees have more stable returns. In addition, if we obtain the trading strategies in three historical periods which are the most similar to the current training period, we earn higher return in the testing periods. In each experiment, 24 cases are considered, with training periods of 90, 180, 270, 365, 455, 545, 635 and 730 days, and testing periods of 90, 180 and 365 days, respectively. The testing period is rolling updated until the end of the experiment period. The best cumulative return 165.30\% occurs when 730-day training period pairs with 365-day testing period, which is much higher than the return of the buy-and-hold strategy 1.19\%.

This thesis investigates the pricing relationship between the FTSE 100 Stock Index and the FTSE 100 Stock Index futures market. We develop and apply a framework in which it is possible to evaluate whether or not markets can be said to function effectively and efficiently. The framework is applied to both the daily and intra-daily pricing relationship between the aforementioned markets. In order to analyse the pricing relationship within days, we develop a new method to remove the effects of nonsynchronous trading from the FTSE 100 Index. We find that on a daily basis the markets generally function effectively, although this does not carryover to the intra-daily pricing relationship. This is especially true during the October 1987 stock market crash, where it is argued that a possible cause of the breakdown lies with the stock market. If this is the case, then any regulation should be aimed at the stock market, not the stock index futures market.

This research investigated the feasibility and capability of neural network-based approaches for predicting the direction of the Australian Stock market index (the target market). It includes several aspects: univariate feature selection from the historical time series of the target market, inter-market analysis for finding the most relevant influential markets, investigations of the effect of time cycles on the target market and the discovery of the optimal neural network architectures. Previous research on US stock markets and other international markets have shown that the neural network approach is one of most powerful techniques for predicting stock market behaviour. Neural networks are capable of capturing the non-linear stochastic and chaotic patterns in the stock market time series data. This study discovered that the relative return series of the Open, High, Low and Close prices of the target market, show 6-day cycles during the studied period of about 14 years. Multi-layer feedforward neural networks trained with a backpropagation algorithm were used for the experiments. Two major testing methods: testing with randomly selected test data and forward testing, were examined and compared. The best neural network developed in this study has achieved 87%, 81% 83% and 81% accuracy respectively in predicting the next-day direction of the relative return of the Open, High, Low and Close prices of the target market. The architecture of this network consists of 33 input features, one hidden layer with 3 neurons and 4 output neurons. The best input features set includes the relative returns from 1 to 6 days in the past of the Open, High, Low and Close prices of the target market, the day of the week, and the previous day’s relative return of the Close prices of the US S&P 500 Index, US Dow Jones Industrial Average Index, US Gold/Silver Index, and the US Oil Index. / Master of Information Technology by Research

This research investigated the feasibility and capability of neural network-based approaches for predicting the direction of the Australian Stock market index (the target market). It includes several aspects: univariate feature selection from the historical time series of the target market, inter-market analysis for finding the most relevant influential markets, investigations of the effect of time cycles on the target market and the discovery of the optimal neural network architectures. Previous research on US stock markets and other international markets have shown that the neural network approach is one of most powerful techniques for predicting stock market behaviour. Neural networks are capable of capturing the non-linear stochastic and chaotic patterns in the stock market time series data. This study discovered that the relative return series of the Open, High, Low and Close prices of the target market, show 6-day cycles during the studied period of about 14 years. Multi-layer feedforward neural networks trained with a backpropagation algorithm were used for the experiments. Two major testing methods: testing with randomly selected test data and forward testing, were examined and compared. The best neural network developed in this study has achieved 87%, 81% 83% and 81% accuracy respectively in predicting the next-day direction of the relative return of the Open, High, Low and Close prices of the target market. The architecture of this network consists of 33 input features, one hidden layer with 3 neurons and 4 output neurons. The best input features set includes the relative returns from 1 to 6 days in the past of the Open, High, Low and Close prices of the target market, the day of the week, and the previous day’s relative return of the Close prices of the US S&P 500 Index, US Dow Jones Industrial Average Index, US Gold/Silver Index, and the US Oil Index. / Doctor of Philosophy

This research investigated the feasibility and capability of neural network-based approaches for predicting the direction of the Australian Stock market index (the target market). It includes several aspects: univariate feature selection from the historical time series of the target market, inter-market analysis for finding the most relevant influential markets, investigations of the effect of time cycles on the target market and the discovery of the optimal neural network architectures. Previous research on US stock markets and other international markets have shown that the neural network approach is one of most powerful techniques for predicting stock market behaviour. Neural networks are capable of capturing the non-linear stochastic and chaotic patterns in the stock market time series data. This study discovered that the relative return series of the Open, High, Low and Close prices of the target market, show 6-day cycles during the studied period of about 14 years. Multi-layer feedforward neural networks trained with a backpropagation algorithm were used for the experiments. Two major testing methods: testing with randomly selected test data and forward testing, were examined and compared. The best neural network developed in this study has achieved 87%, 81% 83% and 81% accuracy respectively in predicting the next-day direction of the relative return of the Open, High, Low and Close prices of the target market. The architecture of this network consists of 33 input features, one hidden layer with 3 neurons and 4 output neurons. The best input features set includes the relative returns from 1 to 6 days in the past of the Open, High, Low and Close prices of the target market, the day of the week, and the previous day’s relative return of the Close prices of the US S&P 500 Index, US Dow Jones Industrial Average Index, US Gold/Silver Index, and the US Oil Index. / Master of Information Technology by Research

This research investigated the feasibility and capability of neural network-based approaches for predicting the direction of the Australian Stock market index (the target market). It includes several aspects: univariate feature selection from the historical time series of the target market, inter-market analysis for finding the most relevant influential markets, investigations of the effect of time cycles on the target market and the discovery of the optimal neural network architectures. Previous research on US stock markets and other international markets have shown that the neural network approach is one of most powerful techniques for predicting stock market behaviour. Neural networks are capable of capturing the non-linear stochastic and chaotic patterns in the stock market time series data. This study discovered that the relative return series of the Open, High, Low and Close prices of the target market, show 6-day cycles during the studied period of about 14 years. Multi-layer feedforward neural networks trained with a backpropagation algorithm were used for the experiments. Two major testing methods: testing with randomly selected test data and forward testing, were examined and compared. The best neural network developed in this study has achieved 87%, 81% 83% and 81% accuracy respectively in predicting the next-day direction of the relative return of the Open, High, Low and Close prices of the target market. The architecture of this network consists of 33 input features, one hidden layer with 3 neurons and 4 output neurons. The best input features set includes the relative returns from 1 to 6 days in the past of the Open, High, Low and Close prices of the target market, the day of the week, and the previous day’s relative return of the Close prices of the US S&P 500 Index, US Dow Jones Industrial Average Index, US Gold/Silver Index, and the US Oil Index. / Doctor of Philosophy

In this thesis we search for optimal hedging strategy in stock index futures markets by providing a comprehensive comparison of variety types of models in the related literature. We concentrate on the strategy that minimizes portfolio risk, i.e., minimum variance hedge ratio (MVHR) estimated from a range of time series models with different assumptions of market volatility. There are linear regression models assuming time-invariant volatility; GARCH-type models capturing time-varying volatility, Markov regime switching (MRS) regression models assuming state-varying volatility, and MRS-GARCH models capturing both time-varying and state-varying volatility. We use both Maximum Likelihood Estimation (MLE) and Bayesian Gibbs-Sampling approach to estimate the models with four commonly used index futures contracts: S&P 500, FTSE 100, Nikkei 225 and Hang Seng index futures. We apply risk reduction and utility maximization criterions to evaluate hedging performance of MVHRs estimated from these models. The in-sample results show that the optimal hedging strategy for the S&P 500 and the Hang Seng index futures contracts is the MVHR estimated using the MRS-OLS model, while the optimal hedging strategy for the Nikkei 225 and the FTSE 100 futures contracts is the MVHR estimated using the Asymmetric-Diagonal-BEKK-GARCH and the Asymmetric-DCC-GARCH model, respectively. As in the out-of sample investigation, the time-varying models such as the BEKK-GARCH models especially the Scalar-BEKK model outperform those state-varying MRS models in majority of futures contracts in both one-step- and multiple-step-ahead forecast cases. Overall the evidence suggests that there is no single model that can consistently produce the best strategy across different index futures contracts. Moreover, using more sophisticated models such as MRS-GARCH models provide some benefits compared with their corresponding single-state GARCH models in the in-sample case but not in the out-of-sample case. While comparing with other types of models MRS-GARCH models do not necessarily improve hedging efficiency. Furthermore, there is evidence that using Bayesian Gibbs-sampling approach to estimate the MRS models provides investors more efficient hedging strategy compared with the MLE method.

Thesis (Ph. D.)--University of North Texas, Dec., 2007. / Title from title page display. Includes bibliographical references.