蘇永成臺灣大學：財務金融學研究所張凱淋Chang, Kai-linKai-linChang2007-11-282018-07-092007-11-282018-07-092005http://ntur.lib.ntu.edu.tw//handle/246246/60740本研究檢驗在封閉解GARCH選擇權模型中的假設下，報酬與變異數序列的關係。論文中設定多方假設檢定來探求兩數列間的因果關係與檢定Heston & Nandi (2000)GARCH選擇權模型中的假設在實證上之結果。各國間指數的實證結果顯示報酬與變異數並未存在同期的完全正相關的特性，亦即同期關係。實證顯示存在單一方向關係，即報酬領先變異數，或者回饋關係，兩數列受到過去資訊交互影響。不同的GARCH模型有相同的結果。此結論可解釋為何HN模型在某些選擇權交易的應用上，如避險行為上，有較差的表現。This paper examines the dynamic relations between return and volatility series under the assumption of closed form GARCH model. A multiple hypotheses testing method is employed to identify causal relations between the two series and to test the empirical implication of the assumption of Heston and Nandi (2000) on GARCH option pricing model. The international empirical results show that returns and volatility series do not perfectly correlated instantaneously, that is contemporaneous relation. There exists unidirectional, return lead volatility, or feedback relation; two series are cross-correlated by past information. Different GARCH models also have the same result. It is found that return leads volatility. This result help explain why HN model has inferior performance in some option application, such as hedging.Content 1. Introduction 1 2. Literature Review 3 2.1 GARCH Option Pricing Model 3 2.2 The Relation between Return and Volatility series 6 2.3 GARCH Continuous Limit Process 6 2.4 Empirical Studies on Heston and Nandi model 7 3. Data Description and Related test 9 4. Methodology 11 4.1 GARCH models 11 4.1.1.Mean equation 11 4.1.2.Variance equation 11 4.2 Causality testing procedure 13 4.2.1 Definition of Granger’s Causal Relation 13 4.2.2 A VAR test on dynamic relations between variables 14 4.2.3 A multiple hypotheses testing procedure 16 4.3 Testing procedure 17 5. Empirical results 20 5.1 Daily result 20 5.1.1 GARCH parameters 20 5.1.2 Causality relations 21 5.2 Weekly result 22 5.2.1 GARCH parameters 22 5.2.2 Causality relations 23 6. Conclusion 25 References 27 Figure 1: Causality Backward Testing procedure 30 Figure 2: Causality Forward Testing Procedure 31 Table 1 Unit root test result 32 Table 2 VAR order selection 35 Table 3 Hypotheses on the dynamic relations of a bivariate system 39 Table 4 Estimation of GARCH in Mean Models for Daily Returns Data 40 Table 5 Causality results of likelihood ratio tests in daily level series 46 Table 6 Causality results of likelihood ratio tests on daily level series of error and differenced series of volatility 50 Table 7 Estimation of GARCH in Mean Models for Weekly Returns Data 54 Table 8 Causality results of likelihood ratio tests on weekly level series 60 Table 9 Causality results of likelihood ratio tests on weekly level series of error and differenced series of volatility 64en-USGARCH報酬與變異數因果關係GARCH選擇權模型GARCH option pricingCausalityreturn and volatilitythesis