非线性金融波动率模型及其实证研究
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摘要
金融市场具有高收益与高风险并存的特性。现代金融理论通常以波动率度量金融资产的风险,波动率在金融衍生品定价、投资组合、风险管理、对冲投资策略中扮演重要的角色。因此,波动率的估计和预测一直是经济学家研究的热点。在一定条件下,传统金融波动率模型对资产收益波动率的预测是较为成功的。为了进一步提高传统金融波动率模型的预测精度,本文将灰色预测理论、支持向量机理论及模糊推理技术与传统金融波动率模型相结合,主要完成了以下工作:
1、将最小二乘支持向量机应用于CARRX模型,建立基于最小二乘支持向量机的非线性CARRX模型(LSSVR-CARRX),通过对沪深300指数的实证研究,发现LSSVR-CARRX模型的样本外预测能力优于CARRX模型。LSSVR-CARRX模型能够在长期预测中很好地刻画极差波动率的变动趋势,而CARRX模型对中短期极差波动率的预测准确度较高。
2、以GM-GARCH类模型为基础,分别将SVRGM模型、RGM预测模型与GARCH模型、EGARCH模型相结合,以减少误差项的随机性和非线性因素。实证结果表明,SVRGM-GARCH模型及RGM-EGARCH模型均比GM-GARCH类模型有更好的波动率预测能力,适合于短期波动率预测。
3、以极差替代收益的标准差来度量波动率,运用灰色支持向量机预测模型(GSVR)预测深市基金波动率,并将v支持向量机作为基准方法。实证结果表明,在中短期预测中,GSVR模型的基金波动率预测效果好于v-SVR模型,而在长期预测中,v-SVR模型则有更好的预测表现。
4、将TSK模糊模型应用于GARCH类模型,建立基于TSK的非线性GARCH模型(TSK-GARCH)及TSK非线性组合预测模型,采用ANFIS方法确定TSK模糊模型的结构、调整模型的参数。实证研究表明,基于TSK的波动率模型比基准模型供了更好的波动率预测值。
本研究将灰色预测理论、支持向量机理论及模糊推理技术应用于传统金融波动率模型中,建立非线性金融波动率模型。对中国金融市场的实证研究表明,这些理论能够有效地提高传统金融波动率模型的样本外预测性能。这一研究对金融波动率的建模及预测具有重要的理论和实际应用价值。
High return and high risk appear simultaneously in financial markets. The risk in financial assets is usually measured by volatility in the modern finance theory. Volatility plays an important role in securities valuation, portfolio optimization, risk management, and hedge investment strategies. Therefore, it is popular for economists to estimate and forecast volatility. Under certain conditions, the traditional financial volatility models have been successfully used for forecasting volatility of assets return. To improve the forecasting accuracy of these models, in this study, grey forecasting theory, support vector machine theory and fuzzy inference technology are combined with the traditional financial volatility models, respectively. The main content of this dissertation is as follows:
First, least squares support vector machine is applied to CARRX model and LSSVR based nonlinear CARRX model is established (LSSVR-CARRX). The empirical research on Hushen 300 index shows that LSSVR-CARRX model performs better than CARRX model in out-of-sample volatility forecasting. LSSVR-CARRX model captures the varying trend of range volatility better in long-term forecasting, and CARRX model has relatively accurate range volatility forecasts in short- and middle-term forecasting.
Second, based on GM-GARCH type model, this study integrates SVRGM with GARCH model and Residual GM(1,1) model with EGARCH model, respectively, to reduce the stochastic and nonlinearity of the error term sequence. Empirical results indicate that SVRGM-GARCH model and RGM-EGARCH model outperform their benchmark models in forecasting volatility of Shenzhen stock index returns, respectively and are applicable to short-term volatility forecasting.
Third, volatility is measured using range instead of return’s standard deviation. Then grey support vector regression (GSVR) is applied to forecasting the volatility of Shenzhen fund market and v-SVR is the benchmark model. The empirical results indicate that GSVR could achieve better forecasting performance than v-SVR in shor-term volatility forecasting, while v-SVR has superior forecasting performance in long-term volatility forecasting.
Fourth, TSK fuzzy model is applied to traditional GARCH type model. TSK based nonlinear GARCH model (TSK-GARCH) and TSK nonlinear combined forecasting model are established, respectively. The parameters and structure of TSK fuzzy model is determined by ANFIS. Empirical results indicate that TSK based volatility models provide better volatility forecasts than their benchmark models.
In this study, grey forecasting theory, support vector machine theory and fuzzy inference technology are applied to the traditional financial volatility models and nonlinear financial volatility models are established. Empirical results on Chinese financial markets show that these theories and methods can improve out-of-sample forecasting performance of traditional financial volatility models. The study has important theory and practice value for modeling and forecasting of financial volatility models.
1、将最小二乘支持向量机应用于CARRX模型,建立基于最小二乘支持向量机的非线性CARRX模型(LSSVR-CARRX),通过对沪深300指数的实证研究,发现LSSVR-CARRX模型的样本外预测能力优于CARRX模型。LSSVR-CARRX模型能够在长期预测中很好地刻画极差波动率的变动趋势,而CARRX模型对中短期极差波动率的预测准确度较高。
2、以GM-GARCH类模型为基础,分别将SVRGM模型、RGM预测模型与GARCH模型、EGARCH模型相结合,以减少误差项的随机性和非线性因素。实证结果表明,SVRGM-GARCH模型及RGM-EGARCH模型均比GM-GARCH类模型有更好的波动率预测能力,适合于短期波动率预测。
3、以极差替代收益的标准差来度量波动率,运用灰色支持向量机预测模型(GSVR)预测深市基金波动率,并将v支持向量机作为基准方法。实证结果表明,在中短期预测中,GSVR模型的基金波动率预测效果好于v-SVR模型,而在长期预测中,v-SVR模型则有更好的预测表现。
4、将TSK模糊模型应用于GARCH类模型,建立基于TSK的非线性GARCH模型(TSK-GARCH)及TSK非线性组合预测模型,采用ANFIS方法确定TSK模糊模型的结构、调整模型的参数。实证研究表明,基于TSK的波动率模型比基准模型供了更好的波动率预测值。
本研究将灰色预测理论、支持向量机理论及模糊推理技术应用于传统金融波动率模型中,建立非线性金融波动率模型。对中国金融市场的实证研究表明,这些理论能够有效地提高传统金融波动率模型的样本外预测性能。这一研究对金融波动率的建模及预测具有重要的理论和实际应用价值。
High return and high risk appear simultaneously in financial markets. The risk in financial assets is usually measured by volatility in the modern finance theory. Volatility plays an important role in securities valuation, portfolio optimization, risk management, and hedge investment strategies. Therefore, it is popular for economists to estimate and forecast volatility. Under certain conditions, the traditional financial volatility models have been successfully used for forecasting volatility of assets return. To improve the forecasting accuracy of these models, in this study, grey forecasting theory, support vector machine theory and fuzzy inference technology are combined with the traditional financial volatility models, respectively. The main content of this dissertation is as follows:
First, least squares support vector machine is applied to CARRX model and LSSVR based nonlinear CARRX model is established (LSSVR-CARRX). The empirical research on Hushen 300 index shows that LSSVR-CARRX model performs better than CARRX model in out-of-sample volatility forecasting. LSSVR-CARRX model captures the varying trend of range volatility better in long-term forecasting, and CARRX model has relatively accurate range volatility forecasts in short- and middle-term forecasting.
Second, based on GM-GARCH type model, this study integrates SVRGM with GARCH model and Residual GM(1,1) model with EGARCH model, respectively, to reduce the stochastic and nonlinearity of the error term sequence. Empirical results indicate that SVRGM-GARCH model and RGM-EGARCH model outperform their benchmark models in forecasting volatility of Shenzhen stock index returns, respectively and are applicable to short-term volatility forecasting.
Third, volatility is measured using range instead of return’s standard deviation. Then grey support vector regression (GSVR) is applied to forecasting the volatility of Shenzhen fund market and v-SVR is the benchmark model. The empirical results indicate that GSVR could achieve better forecasting performance than v-SVR in shor-term volatility forecasting, while v-SVR has superior forecasting performance in long-term volatility forecasting.
Fourth, TSK fuzzy model is applied to traditional GARCH type model. TSK based nonlinear GARCH model (TSK-GARCH) and TSK nonlinear combined forecasting model are established, respectively. The parameters and structure of TSK fuzzy model is determined by ANFIS. Empirical results indicate that TSK based volatility models provide better volatility forecasts than their benchmark models.
In this study, grey forecasting theory, support vector machine theory and fuzzy inference technology are applied to the traditional financial volatility models and nonlinear financial volatility models are established. Empirical results on Chinese financial markets show that these theories and methods can improve out-of-sample forecasting performance of traditional financial volatility models. The study has important theory and practice value for modeling and forecasting of financial volatility models.
引文
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