Volatility Surface, Term Structure and Meta-learning-based Price Forecasting for Option Strategies Design

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1 CITY UNIVERSITY OF HONG KONG 香港城市大學 Volatility Surface, Term Structure and Meta-learning-based Price Forecasting for Option Strategies Design 基於波動率曲面, 期限結構及元學習的價格預測與期權策略研究 Submitted to Department of Management Sciences 管理科學系 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 哲學博士學位 by Zhou Shifei 周仕飛 July 2013 二零一三年七月

究 Submitted to Department of Management Sciences 管理科學系 in Partial Fulfillment of the

2 I Abstract The forecasting of underlying asset price is important for investors to make financial decisions. A successful prediction can save investors from risk of losing money. This thesis focuses on the forecasting of underlying asset price and develops an option-based trading system. A literature review is conducted on volatility and its related topics. These topics include volatility forecasting, implied volatility smile, implied volatility term structure, implied volatility surface, local implied volatility and stochastic volatility. The major forecasting models and methodologies of volatility prediction are introduced and classified. This classification also gives a direct blueprint for the composition of this thesis. Based on the investigation, this thesis proposes three research topics and makes contributions as follows. First, a model-free term structure-based stochastic model with adaptive correlation is proposed for price forecasting. Based on observations, the constant assumption of correlation of stochastic volatility model is found to be unsuitable for analyzing Hong Kong options market. The least squares method is used to evaluate this correlation. Besides, the term structure implied volatility is obtained by integrating option price and strike price from current time to expiry date. This model-free term structure is used as the long-run mean level of stochastic model to make use of information contained in term structure. Empirical test shows our model outperforms CEV model and Regression model in terms of one-day-ahead prediction performance and 78-day distribution of underlying asset price. Second, a novel local volatility model with mean-reversion process is proposed. This mean-reversion term is functioned as long run mean level of local volatility surface. The larger local volatility departs from its mean level, the greater rate local volatility will be reverted with. Then, a B-spline with moving average knot control scheme is applied to interpolate local volatility matrix. The bi-cubic B-spline is used

These topics include volatility forecasting, implied volatility smile, implied volatility term structure, implied volatility surface, local implied volatility and stochastic volatility.

3 II to recover local volatility surface from this local volatility matrix. Finally, Monte Carlo simulation is adopted to predict underlying asset price. Empirical tests show our mean-reversion local volatility model has a good prediction performance than traditional local volatility models. Third, an improved EMD meta-learning rate-based model for gold price forecasting is proposed. Firstly, we adopt the EMD method to divide the time series data into different subsets. Secondly, a back-propagation neural network model (BPNN) is used to function as the prediction model in our system. We update the online learning rate of BPNN instantly as well as the weight matrix. Finally, forecasting results from different BPNNs are summed as a final price forecasting result. The experiment results show that our system has a good forecasting performance. Based on the above three theoretical innovation to current financial models, the forecasting results of three different models are integrated by an average method as a final forecasting price value. This value is used to decide the movement trend of underlying asset price. According to the trend, six different movement patterns are classified. The corresponding option trading strategies are also designed. Then, the optimal option trading strategy is selected by three criteria. There are Expected Return, Value at Risk, and Conditional Value at Risk. To sum up, this thesis proposes three different models to forecast price and designs option trading strategies based on three criteria. The future works contain two aspects. First, the system will be improved for high frequency trading. The improvement includes calculation optimization and model optimization. Second, the system will be applied to other options and futures markets.

Third, an improved EMD meta-learning rate-based model for gold price forecasting is proposed. Firstly, we adopt the EMD method to divide the time series data into different subsets.

4 V Table of Contents Abstract... I Acknowledgements...III Table of Contents...V List of Tables... VII List of Figures...IX Chapter 1 Introduction Background and Motivations Research Problems and Objectives System Framework and Research Contributions Summary...13 Chapter 2 Literature Review Volatility Forecasting Realized Volatility Forecasting Implied Volatility Forecasts Volatility Forecasting on other Markets Implied Volatility Volatility Smile Volatility Term Structure Volatility Surface Local Volatility Local Volatility Models Local Volatility Surface Recovering Local Volatility Stochastic Volatility Two Factors Stochastic Volatility Forecasting of Stochastic Volatility...54 Chapter 3 A Novel Term Structure-Based Stochastic Model with Adaptive Correlation for Trend Analysis Introduction Related Works Volatility Model Motivation Adaptive Correlation Model Heston Model Adaptive Correlation Coefficient Model-free Term Structure Price Distribution of Underlying Asset Empirical Tests Summary...82

..21 2.1.3 Volatility Forecasting on other Markets...22 2.2 Implied Volatility...23 2.2.1 Volatility Smile...23 2.2.2 Volatility Term Structure...28 2.2.3 Volatility Surface...31 2.3 Local Volatility.

5 VI Chapter 4 A Novel Mean Reversion-based Local Volatility Model Introduction Motivations Mean reversion-based local volatility model Local Volatility Surface Least Squares Method Bi-cubic B-Spline Function Empirical Tests Summary...99 Chapter 5 A Dynamic Meta-Learning Rate-Based Model for Gold Market Forecasting Introduction Motivation Contributions Related Works Empirical Mode Decomposition Online Learning Algorithm Improved Empirical Mode Decomposition Model (IEMD) IEMD Model Structure Back-propagation Neural Network Prediction Model Rating Improved Online Learning Algorithm Online Weight Update Online Learning Rate Update Experiments Evaluation Criteria Experimental Results Summary Chapter 6 Option Trading Strategies Design System Framework Option Strategies Uni-Option Strategies Bi-Option Strategies Tri-Option Strategies Quad-Option Strategies Selection Criterion Expected Return Value at Risk Conditional Value at Risk Summary Chapter 7 Conclusions and Future Works Conclusions Future Works References...149

1 Introduction...101 5.1.1 Motivation...101 5.1.2 Contributions...103 5.2 Related Works...104 5.2.1 Empirical Mode Decomposition...104 5.2.2 Online Learning Algorithm...105 5.

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