Sensitivity analysis is important for its own sake and also in combination with diagnostic testing. We consider the question how to use sensitivity statistics in practice, in particular how to judge whether sensitivity is large or small. For this purpose we distinguish between absolute and relative sensitivity and highlight the context-dependent nature of any sensitivity analysis. Relative sensitivity is then applied in the context of forecast combination and sensitivity-based weights are introduced. All concepts are illustrated through the European yield curve. In this context it is natural to look at sensitivity to autocorrelation and normality assumptions. Different forecasting models are combined with equal, fit-based and sensitivity-based weights, and compared with the multivariate and random walk benchmarks. We show that the fit-based weights and the sensitivity-based weights are complementary. For long-term maturities the sensitivity-based weights perform better than other weights.
{"title":"Practical Use of Sensitivity in Econometrics with an Illustration to Forecast Combinations","authors":"J. Magnus, A. Vasnev","doi":"10.2139/ssrn.2229548","DOIUrl":"https://doi.org/10.2139/ssrn.2229548","url":null,"abstract":"Sensitivity analysis is important for its own sake and also in combination with diagnostic testing. We consider the question how to use sensitivity statistics in practice, in particular how to judge whether sensitivity is large or small. For this purpose we distinguish between absolute and relative sensitivity and highlight the context-dependent nature of any sensitivity analysis. Relative sensitivity is then applied in the context of forecast combination and sensitivity-based weights are introduced. All concepts are illustrated through the European yield curve. In this context it is natural to look at sensitivity to autocorrelation and normality assumptions. Different forecasting models are combined with equal, fit-based and sensitivity-based weights, and compared with the multivariate and random walk benchmarks. We show that the fit-based weights and the sensitivity-based weights are complementary. For long-term maturities the sensitivity-based weights perform better than other weights.","PeriodicalId":112822,"journal":{"name":"ERN: Interest Rate Forecasts (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130517058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the impact of ambiguous information regarding future interest rates on bond prices. A simple bond-pricing model with ambiguity aversion shows that positive bond uncertainty premiums exist, and the interest rate ambiguity affects the term structure of interest rates and yield volatilities. Consistent with the theory, empirical measures of interest rate ambiguity based on the Survey of Professional Forecasters data significantly predict U.S. Treasury bond returns, explain variation in term spreads and yield volatility, and bond yields asymmetrically respond to good and bad news from the Federal Reserve. Results are robust to alternative empirical specifications and out-of-sample forecasts.
{"title":"Ambiguous Information about Interest Rates and Bond Uncertainty Premiums","authors":"Hwagyun Kim","doi":"10.2139/ssrn.2567568","DOIUrl":"https://doi.org/10.2139/ssrn.2567568","url":null,"abstract":"This paper studies the impact of ambiguous information regarding future interest rates on bond prices. A simple bond-pricing model with ambiguity aversion shows that positive bond uncertainty premiums exist, and the interest rate ambiguity affects the term structure of interest rates and yield volatilities. Consistent with the theory, empirical measures of interest rate ambiguity based on the Survey of Professional Forecasters data significantly predict U.S. Treasury bond returns, explain variation in term spreads and yield volatility, and bond yields asymmetrically respond to good and bad news from the Federal Reserve. Results are robust to alternative empirical specifications and out-of-sample forecasts.","PeriodicalId":112822,"journal":{"name":"ERN: Interest Rate Forecasts (Topic)","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123099839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We test the out-of-sample predictive power for one-year bond excess returns for a variety of models that have been proposed in the literature. We find that these models perform well in sample, but have worse out-of-sample performance than the historical sample mean. We write the one-year excess return on a n-maturity bond at time t + 1 as the difference between n times the n-maturity bond yield at time t, and the sum of n 1 times the (n 1)-maturity bond yield at time t + 1 and the one-year bond yield at time t. Instead of forecasting returns directly, we forecast bond yields and replace them in the bond excess return definition. We use two bond yield forecasting methods: a random walk and a dynamic Nelson-Siegel approach proposed by Diebold and Li (2006). An investor who used a simple random walk on yields would have predicted bond excess returns with outof-sample R-squares of up to 15%, while a dynamic Nelson-Siegel approach would have produced out-of-sample R-squares of up to 30%.
{"title":"Out-of-Sample Predictability of Bond Returns","authors":"Luiz Paulo Fichtner, Pedro Santa-clara","doi":"10.2139/ssrn.2226169","DOIUrl":"https://doi.org/10.2139/ssrn.2226169","url":null,"abstract":"We test the out-of-sample predictive power for one-year bond excess returns for a variety of models that have been proposed in the literature. We find that these models perform well in sample, but have worse out-of-sample performance than the historical sample mean. We write the one-year excess return on a n-maturity bond at time t + 1 as the difference between n times the n-maturity bond yield at time t, and the sum of n 1 times the (n 1)-maturity bond yield at time t + 1 and the one-year bond yield at time t. Instead of forecasting returns directly, we forecast bond yields and replace them in the bond excess return definition. We use two bond yield forecasting methods: a random walk and a dynamic Nelson-Siegel approach proposed by Diebold and Li (2006). An investor who used a simple random walk on yields would have predicted bond excess returns with outof-sample R-squares of up to 15%, while a dynamic Nelson-Siegel approach would have produced out-of-sample R-squares of up to 30%.","PeriodicalId":112822,"journal":{"name":"ERN: Interest Rate Forecasts (Topic)","volume":"82 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131451973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The interest rate market has been expanding immensely for thirty years, both in term of volumes and diversity of traded contracts. The growing complexity of derivatives has implied a need for sophisticated models in order to price and hedge these products. Three main approaches can be distinguished in interest rates modeling. Short-rate models model the dynamics of the term structure of interest rates by specifying the dynamics of a single rate (the spot rate or the instantaneous spot rate) from which the whole term structure at any point in time can be calculated. The prices of derivatives in these models are quite involved functions of the underlying process which is being modeled. This fact makes these models difficult to calibrate. However the short rate process is easy to follow and hence implementation is straightforward.Unlike short rate models the class of Market Models is formulated in terms of market rates which are directly related to tradable assets. Thus they exhibit better calibration properties than short rate models. However they are high dimensional by construction and tedious to implement.In 1999, Hunt, Kennedy and Pelsser introduced the class of Markov-Functional Models (MFM) aiming at developing models which could match as many market prices as Market Models while maintaining the efficiency of short rate models in calculating derivative prices.After a general overview of the two dominant paradigms in section III, this report will focus on the class of Markov-functional models. Section IV presents the general framework. Then several issues related to the implementation of a one-factor MFM model are analyzed in section V. Finally we will display in section VI some numerical results of the simulations of this one-factor model.
{"title":"Implementation of a One-Factor Markov-Functional Interest Rate Model","authors":"Baptiste Truchot","doi":"10.2139/ssrn.2732518","DOIUrl":"https://doi.org/10.2139/ssrn.2732518","url":null,"abstract":"The interest rate market has been expanding immensely for thirty years, both in term of volumes and diversity of traded contracts. The growing complexity of derivatives has implied a need for sophisticated models in order to price and hedge these products. Three main approaches can be distinguished in interest rates modeling. Short-rate models model the dynamics of the term structure of interest rates by specifying the dynamics of a single rate (the spot rate or the instantaneous spot rate) from which the whole term structure at any point in time can be calculated. The prices of derivatives in these models are quite involved functions of the underlying process which is being modeled. This fact makes these models difficult to calibrate. However the short rate process is easy to follow and hence implementation is straightforward.Unlike short rate models the class of Market Models is formulated in terms of market rates which are directly related to tradable assets. Thus they exhibit better calibration properties than short rate models. However they are high dimensional by construction and tedious to implement.In 1999, Hunt, Kennedy and Pelsser introduced the class of Markov-Functional Models (MFM) aiming at developing models which could match as many market prices as Market Models while maintaining the efficiency of short rate models in calculating derivative prices.After a general overview of the two dominant paradigms in section III, this report will focus on the class of Markov-functional models. Section IV presents the general framework. Then several issues related to the implementation of a one-factor MFM model are analyzed in section V. Finally we will display in section VI some numerical results of the simulations of this one-factor model.","PeriodicalId":112822,"journal":{"name":"ERN: Interest Rate Forecasts (Topic)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127180077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A good description of the dynamics of interest rates is crucial to price derivatives and to hedge corresponding risk. Interest rate modelling in an unstable macroeconomic context motivates one factor models with time varying parameters. In this paper, the local parameter approach is introduced to adaptively estimate interest rate models. This method can be generally used in time varying coefficient parametric models. It is used not only to detect the jumps and structural breaks, but also to choose the largest time homogeneous interval for each time point, such that in this interval, the coeffcients are statistically constant. We use this adaptive approach and apply it in simulations and real data. Using the three month treasure bill rate as a proxy of the short rate, we nd that our method can detect both structural changes and stable intervals for homogeneous modelling of the interest rate process. In more unstable macroeconomy periods, the time homogeneous interval can not last long. Furthermore, our approach performs well in long horizon forecasting.
{"title":"Adaptive Interest Rate Modelling","authors":"Mengmeng Guo, W. Härdle","doi":"10.2139/ssrn.2894265","DOIUrl":"https://doi.org/10.2139/ssrn.2894265","url":null,"abstract":"A good description of the dynamics of interest rates is crucial to price derivatives and to hedge corresponding risk. Interest rate modelling in an unstable macroeconomic context motivates one factor models with time varying parameters. In this paper, the local parameter approach is introduced to adaptively estimate interest rate models. This method can be generally used in time varying coefficient parametric models. It is used not only to detect the jumps and structural breaks, but also to choose the largest time homogeneous interval for each time point, such that in this interval, the coeffcients are statistically constant. We use this adaptive approach and apply it in simulations and real data. Using the three month treasure bill rate as a proxy of the short rate, we nd that our method can detect both structural changes and stable intervals for homogeneous modelling of the interest rate process. In more unstable macroeconomy periods, the time homogeneous interval can not last long. Furthermore, our approach performs well in long horizon forecasting.","PeriodicalId":112822,"journal":{"name":"ERN: Interest Rate Forecasts (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116917294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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