通胀预期:金融市场隐含信息的视角
|
摘要
通胀预期在宏观经济政策的制定和执行中具有重要作用。相较传统的通胀信息提取方法,从金融资产价格中提取隐含的通胀信息具有即时性、前瞻性、真实性等优点。本文构建了三因子高斯仿射动态利率期限结构模型——名义-实际利率期限结构模型,通过对该模型的推导,成功地获得了名义债和真实债的解析定价公式,以及名义收益率、真实收益率、通货膨胀预期、通货膨胀风险溢酬和凸性调整Jensen项的解析表达与实证解读。
Inflation expectation plays a significant role in macro-economic policy making and operability. Compared with the inflation information got by traditional methods, the inflation information implied in financial asset price possesses many good qualities such as instantaneity, forward looking, accuracy and higher frequency. We construct a Gaussian model-Real-Nominal Term Structure Model. Under the No-arbitrage condition, the form of pricing kernel and risk price were set and analysis formulas of nominal and real bonds are deduced. Guided by Fisher Equation, we obtained the Real Rate, Inflation Expectation, Inflation Risk Premium and Jensen Term analytically.
Inflation expectation plays a significant role in macro-economic policy making and operability. Compared with the inflation information got by traditional methods, the inflation information implied in financial asset price possesses many good qualities such as instantaneity, forward looking, accuracy and higher frequency. We construct a Gaussian model-Real-Nominal Term Structure Model. Under the No-arbitrage condition, the form of pricing kernel and risk price were set and analysis formulas of nominal and real bonds are deduced. Guided by Fisher Equation, we obtained the Real Rate, Inflation Expectation, Inflation Risk Premium and Jensen Term analytically.
引文
[1]Ang, A., G. Bekaert, and M. Wei, “The Term Structure of Real Rates and Expected Inflation”, The Journal of Finance, 2008,63(2),797—849.
[2]Ang, A., and M. Piazzesi, “A No-Arbitrage Vector Auto-regression of Term Structure Dynamics with Macroeconomic and Latent Variables”, Journal of Monetary economics, 2003, 50(4),745—787.
[3]Benninga, S., and A. Protopapadakis, “Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure”, The Journal of Political Economy, 1983, 91 (5),856—867.
[4]Bernanke, B. S.,“Long-Term Interest Rates: A Speech at the Annual Monetary/Macroeconomics Conference: The Past and Future of Monetary Policy, Sponsored by Federal Reserve Bank of San Francisco, San Francisco, California, March 1,2013”, Bio/technolgy, 2013,5(10), 1010—1010.
[5]Brédart, A., and S. Dolbeault, “Tips from TIPS: The Informational Content of Treasury Inflation-Protected Security Prices”, SSRN,2016.
[6]Burmeister, E., K. D.Wall, and J. D. Hamilton, “Estimation of Unobserved Expected Monthly Inflation Using Kalman Filtering”, Journal of Business & Economic Statistics, 1986, 4(2),147—160.
[7]Christensen, J. H., J. A. Lopez, and G. D. Rudebusch, “Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields”, Journal of Money, Credit and Banking, 2010,42(s1), 143—178.
[8]Christensen, J. H., F. X. Diebold, and G. D. Rudebusch, “The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models”, Journal of Econometrics, 2011, 164(1), 4—20.
[9]Clarida, R., J. Gali, and M. Gertler, “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory”, Quarterly Journal of Economics, 2000, 115 (1), 147—180.
[10]Cochrane, J., and M. Piazzesi, “Decomposing the Yield Curve”, In AFA 2010 Atlanta Meetings Paper, 2009.
[11]Cox, J. C., J. E. Ingersoll Jr., and S. A. Ross, “A Theory of the Term Structure of Interest Rates”, Econometrica: Journal of the Econometric Society, 1985, 53 (2), 385—407.
[12]Dai, Q., and K. J. Singleton, “Specification Analysis of Affine Term Structure Models”, The Journal of Finance, 2000,55(5), 1943—1978.
[13]Diebold, F. X., G. D. Rudebusch, and S. BoraganAruoba, “The Macro-Economy and the Yield Curve: A Dynamic Latent Factor Approach”, Journal of Econometrics, 2006, 131(1), 309—338.
[14]Diebold, F. X., L. Ji, and C. Li, “A Three-Factor Yield Curve Model: Non-Affine Structure, Systematic Risk Sources, and Generalized Duration”, Pier Working Paper Archive, 2006(6—017).
[15]Duffee, G. R., “Term Premia and Interest Rate Forecasts in Affine Models”, The Journal of Finance, 2002, 57(1),405—443.
[16]Duffee, G. R., “Information in (and not in) the Term Structure”, Review of Financial Studies, 2011, 24(9),2895—2934.
[17]范龙振、张国庆,“仿射模型,广义仿射模型与上交所利率期限结构”,《管理工程学报》,2005年第3期,第97—101页。
[18]Fama, E. F., “Short-Term Interest Rates as Predictors of Inflation”, The American Economic Review, 1975, 65(3),269—282.
[19]Fisher, I.,“Appreciation and Interest”, American Economic Association,1896.
[20]Gürkaynak,R. S., B. Sack, and J. H. Wright, “The TIPS Yield Curve and Inflation Compensation”, American Economic Journal Macroeconomics, 2010, 2(1),70—92.
[21]Hamilton, J. D., “Uncovering Financial Market Expectations of Inflation”, The Journal of Political Economy, 1985, 93 (6), 1224—1241.
[22]Huizinga, J., and F. S. Mishkin, “Monetary Policy Regime Shifts and the Unusual Behavior of Real Interest Rates”, Frederic Mishkin, 1985,24 (1), 231—274.
[23]Joslin, S., M. Priebsch, and K.J. Singleton, “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks”, The Journal of Finance, 2014,69( 3),1197—1233.
[24]Joyce, M. A., P. Lildholdt, and S. Sorensen, “Extracting Inflation Expectations and Inflation Risk Premia from the Term Structure: A Joint Model of the UK Nominal and Real Yield Curves”, Journal of Banking &Finance, 2010,34(2), 281—294.
[25]李宏瑾、钟正生、李晓嘉,“利率期限结构,通货膨胀预测与实际利率”,《世界经济》,2010年第10期,第120—138页。
[26]刘雪燕、张敬庭,“中国通货膨胀预期和Ex-ante实际利率的测度”,《数量经济技术经济研究》, 2008年第7期,第128—137页。
[27]Mundell, R. A., “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates”, Canadian Journal of Economics and Political Science, 1963, 29 (4), 475—485.
[28]Quah, D., and S. P. Vahey, “Measuring Core Inflation”, The Economic Journal, 1995, 105 (432), 1130—1144.
[29]Rose, A. K., “Is the Real Interest Rate Stable?”, The Journal of Finance, 1988, 43(5), 1095—1112.
[30]石柱鲜,“中国主要宏观经济变量与利率期限结构的关系:基于VAR-ATSM模型的分析”,《世界经济》, 2008年第3期,第53—59页。
[31]孙皓、石柱鲜,“中国利率期限结构中的宏观经济风险因素分析”,《经济评论》, 2011年第3期,第36—42页。
[32]Tobin, J., “Money and Economic Growth”, Econometrica: Journal of the Econometric Society, 1965, 33(4), 671—684.
[33]姚余栋、谭海鸣,“中国金融市场通胀预期——基于利率期限结构的量度”,《金融研究》, 2011年第6期,第61—70页。
[34]曾耿明、牛霖琳,“中国实际利率与通胀预期的期限结构——基于无套利宏观金融模型的研究”,《金融研究》,2013年第1期,第24—37页。
[35]张燃、李宏瑾、崔兰清,“仿射利率期限结构模型与中国宏观经济预期”,《金融与经济》,2011年第4期,第10—14页。
[36]郑振龙,“资产价格隐含信息分析框架:目标、方法与应用”,《经济学动态》,2012年第3期,第33—40页。
(1)1另外,-Σ×λtdW(t)若改写形式为-Σ×ΛtdW(t)且记Λt=Σ-1×λt,便得到了实质仿射模型(Essential Affine Model),这是更为学者们所熟悉的风险价格设定形式。本文为计量方便运用简约设定,那么λt中暗含左乘的Σ-1矩阵。因此,可以注意到在定价核的推导中将会出现的Σ×Σ,仅为保证形式上的一致性。
[2]Ang, A., and M. Piazzesi, “A No-Arbitrage Vector Auto-regression of Term Structure Dynamics with Macroeconomic and Latent Variables”, Journal of Monetary economics, 2003, 50(4),745—787.
[3]Benninga, S., and A. Protopapadakis, “Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure”, The Journal of Political Economy, 1983, 91 (5),856—867.
[4]Bernanke, B. S.,“Long-Term Interest Rates: A Speech at the Annual Monetary/Macroeconomics Conference: The Past and Future of Monetary Policy, Sponsored by Federal Reserve Bank of San Francisco, San Francisco, California, March 1,2013”, Bio/technolgy, 2013,5(10), 1010—1010.
[5]Brédart, A., and S. Dolbeault, “Tips from TIPS: The Informational Content of Treasury Inflation-Protected Security Prices”, SSRN,2016.
[6]Burmeister, E., K. D.Wall, and J. D. Hamilton, “Estimation of Unobserved Expected Monthly Inflation Using Kalman Filtering”, Journal of Business & Economic Statistics, 1986, 4(2),147—160.
[7]Christensen, J. H., J. A. Lopez, and G. D. Rudebusch, “Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields”, Journal of Money, Credit and Banking, 2010,42(s1), 143—178.
[8]Christensen, J. H., F. X. Diebold, and G. D. Rudebusch, “The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models”, Journal of Econometrics, 2011, 164(1), 4—20.
[9]Clarida, R., J. Gali, and M. Gertler, “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory”, Quarterly Journal of Economics, 2000, 115 (1), 147—180.
[10]Cochrane, J., and M. Piazzesi, “Decomposing the Yield Curve”, In AFA 2010 Atlanta Meetings Paper, 2009.
[11]Cox, J. C., J. E. Ingersoll Jr., and S. A. Ross, “A Theory of the Term Structure of Interest Rates”, Econometrica: Journal of the Econometric Society, 1985, 53 (2), 385—407.
[12]Dai, Q., and K. J. Singleton, “Specification Analysis of Affine Term Structure Models”, The Journal of Finance, 2000,55(5), 1943—1978.
[13]Diebold, F. X., G. D. Rudebusch, and S. BoraganAruoba, “The Macro-Economy and the Yield Curve: A Dynamic Latent Factor Approach”, Journal of Econometrics, 2006, 131(1), 309—338.
[14]Diebold, F. X., L. Ji, and C. Li, “A Three-Factor Yield Curve Model: Non-Affine Structure, Systematic Risk Sources, and Generalized Duration”, Pier Working Paper Archive, 2006(6—017).
[15]Duffee, G. R., “Term Premia and Interest Rate Forecasts in Affine Models”, The Journal of Finance, 2002, 57(1),405—443.
[16]Duffee, G. R., “Information in (and not in) the Term Structure”, Review of Financial Studies, 2011, 24(9),2895—2934.
[17]范龙振、张国庆,“仿射模型,广义仿射模型与上交所利率期限结构”,《管理工程学报》,2005年第3期,第97—101页。
[18]Fama, E. F., “Short-Term Interest Rates as Predictors of Inflation”, The American Economic Review, 1975, 65(3),269—282.
[19]Fisher, I.,“Appreciation and Interest”, American Economic Association,1896.
[20]Gürkaynak,R. S., B. Sack, and J. H. Wright, “The TIPS Yield Curve and Inflation Compensation”, American Economic Journal Macroeconomics, 2010, 2(1),70—92.
[21]Hamilton, J. D., “Uncovering Financial Market Expectations of Inflation”, The Journal of Political Economy, 1985, 93 (6), 1224—1241.
[22]Huizinga, J., and F. S. Mishkin, “Monetary Policy Regime Shifts and the Unusual Behavior of Real Interest Rates”, Frederic Mishkin, 1985,24 (1), 231—274.
[23]Joslin, S., M. Priebsch, and K.J. Singleton, “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks”, The Journal of Finance, 2014,69( 3),1197—1233.
[24]Joyce, M. A., P. Lildholdt, and S. Sorensen, “Extracting Inflation Expectations and Inflation Risk Premia from the Term Structure: A Joint Model of the UK Nominal and Real Yield Curves”, Journal of Banking &Finance, 2010,34(2), 281—294.
[25]李宏瑾、钟正生、李晓嘉,“利率期限结构,通货膨胀预测与实际利率”,《世界经济》,2010年第10期,第120—138页。
[26]刘雪燕、张敬庭,“中国通货膨胀预期和Ex-ante实际利率的测度”,《数量经济技术经济研究》, 2008年第7期,第128—137页。
[27]Mundell, R. A., “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates”, Canadian Journal of Economics and Political Science, 1963, 29 (4), 475—485.
[28]Quah, D., and S. P. Vahey, “Measuring Core Inflation”, The Economic Journal, 1995, 105 (432), 1130—1144.
[29]Rose, A. K., “Is the Real Interest Rate Stable?”, The Journal of Finance, 1988, 43(5), 1095—1112.
[30]石柱鲜,“中国主要宏观经济变量与利率期限结构的关系:基于VAR-ATSM模型的分析”,《世界经济》, 2008年第3期,第53—59页。
[31]孙皓、石柱鲜,“中国利率期限结构中的宏观经济风险因素分析”,《经济评论》, 2011年第3期,第36—42页。
[32]Tobin, J., “Money and Economic Growth”, Econometrica: Journal of the Econometric Society, 1965, 33(4), 671—684.
[33]姚余栋、谭海鸣,“中国金融市场通胀预期——基于利率期限结构的量度”,《金融研究》, 2011年第6期,第61—70页。
[34]曾耿明、牛霖琳,“中国实际利率与通胀预期的期限结构——基于无套利宏观金融模型的研究”,《金融研究》,2013年第1期,第24—37页。
[35]张燃、李宏瑾、崔兰清,“仿射利率期限结构模型与中国宏观经济预期”,《金融与经济》,2011年第4期,第10—14页。
[36]郑振龙,“资产价格隐含信息分析框架:目标、方法与应用”,《经济学动态》,2012年第3期,第33—40页。
(1)1另外,-Σ×λtdW(t)若改写形式为-Σ×ΛtdW(t)且记Λt=Σ-1×λt,便得到了实质仿射模型(Essential Affine Model),这是更为学者们所熟悉的风险价格设定形式。本文为计量方便运用简约设定,那么λt中暗含左乘的Σ-1矩阵。因此,可以注意到在定价核的推导中将会出现的Σ×Σ,仅为保证形式上的一致性。