This paper studies the nonparametric identification and estimation of projected pricing kernels implicit in European option prices and underlying asset returns using conditional moment restrictions. The proposed series estimator avoids computing ratios of estimated risk-neutral and physical densities. Instead, we consider efficient estimation based on the conditional Euclidean empirical likelihood or continuously-updated GMM criterion, which takes into account the informativeness of option prices of varying strike prices beyond observed conditioning variables. In a second step, we convert the implied probabilities into predictive densities by matching the informative part of cross-sections of option prices. Empirically, pricing kernels tend to be U-shaped in the S&P 500 index return given high levels of the VIX, and call and ATM options are more informative about their payoff than put and OTM options.
{"title":"Efficient Estimation of Pricing Kernels and Market-Implied Densities","authors":"Jeroen Dalderop","doi":"10.2139/ssrn.3853347","DOIUrl":"https://doi.org/10.2139/ssrn.3853347","url":null,"abstract":"This paper studies the nonparametric identification and estimation of projected pricing kernels implicit in European option prices and underlying asset returns using conditional moment restrictions. The proposed series estimator avoids computing ratios of estimated risk-neutral and physical densities. Instead, we consider efficient estimation based on the conditional Euclidean empirical likelihood or continuously-updated GMM criterion, which takes into account the informativeness of option prices of varying strike prices beyond observed conditioning variables. In a second step, we convert the implied probabilities into predictive densities by matching the informative part of cross-sections of option prices. Empirically, pricing kernels tend to be U-shaped in the S&P 500 index return given high levels of the VIX, and call and ATM options are more informative about their payoff than put and OTM options.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84933280","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 examines the effects of futures trading on jump risk in the Bitcoin market. Based on 5-minute high-frequency data, we use a nonparametric method to detect Lévy-type jumps in Bitcoin prices and document that there are both big and small jumps, and the intensity and size of jump are time-varying. We then investigate the changes of these jump risk measures after the Bitcoin futures introduction and find that the jump size of big and small jumps decreases while the big jump intensity increases. Furthermore, we examine whether greater futures-trading activity, proxied by trading volume and open interest, is associated with greater spot market jump risk. It is found that there exists a bidirectional causality between unexpected futures-trading volume and spot market jump risk. Unexpected open interest Granger causes jump risk, but the reverse is not true.
{"title":"Futures-Trading Activity and Jump Risk: Evidence From the Bitcoin Market","authors":"Chuanhai Zhang, Huan Ma, Xiaosai Liao","doi":"10.2139/ssrn.3729476","DOIUrl":"https://doi.org/10.2139/ssrn.3729476","url":null,"abstract":"This paper examines the effects of futures trading on jump risk in the Bitcoin market. Based on 5-minute high-frequency data, we use a nonparametric method to detect Lévy-type jumps in Bitcoin prices and document that there are both big and small jumps, and the intensity and size of jump are time-varying. We then investigate the changes of these jump risk measures after the Bitcoin futures introduction and find that the jump size of big and small jumps decreases while the big jump intensity increases. Furthermore, we examine whether greater futures-trading activity, proxied by trading volume and open interest, is associated with greater spot market jump risk. It is found that there exists a bidirectional causality between unexpected futures-trading volume and spot market jump risk. Unexpected open interest Granger causes jump risk, but the reverse is not true.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86971842","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 study examines the nonparametric instrumental variable model with discrete instruments and explores the partial identification and estimation of the target parameter, which is a linear functional of the structural function. We include numerous target parameters, such as the difference between the values of the structural function at two different points and the average effect of a hypothetical policy change. Informative bounds on the target parameter are derived using the control function approach and shape restrictions. Illustrative examples demonstrate that shape restrictions have identification power. The lower and upper bounds are estimated using the sieve method and we show that our estimator is computationally convenient and consistent. An empirical application illustrates the usefulness of our method.
{"title":"Partial Identification of Discrete Instrumental Variable Models using Shape Restrictions","authors":"Takuya Ishihara","doi":"10.2139/ssrn.3711861","DOIUrl":"https://doi.org/10.2139/ssrn.3711861","url":null,"abstract":"This study examines the nonparametric instrumental variable model with discrete instruments and explores the partial identification and estimation of the target parameter, which is a linear functional of the structural function. We include numerous target parameters, such as the difference between the values of the structural function at two different points and the average effect of a hypothetical policy change. Informative bounds on the target parameter are derived using the control function approach and shape restrictions. Illustrative examples demonstrate that shape restrictions have identification power. The lower and upper bounds are estimated using the sieve method and we show that our estimator is computationally convenient and consistent. An empirical application illustrates the usefulness of our method.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75332335","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}
Abstract We provide a model-free framework for studying the dynamics of the state vector and its risk prices. Specifically, we derive a frequency domain decomposition of the unconditional asset return premium in a general setting with a log-affine stochastic discount factor (SDF). Importantly, we show that the cospectrum between returns and the SDF only displays frequency dependencies through the state vector and that its dynamics and risk prices can be inferred from covariances between asset (portfolio) returns, that is, from the cross-section. Empirically, we find low and high-frequency state vector risk to be differentially priced for US equities.
{"title":"Frequency Dependent Risk","authors":"A. Neuhierl, R. T. Varneskov","doi":"10.2139/ssrn.3260167","DOIUrl":"https://doi.org/10.2139/ssrn.3260167","url":null,"abstract":"Abstract We provide a model-free framework for studying the dynamics of the state vector and its risk prices. Specifically, we derive a frequency domain decomposition of the unconditional asset return premium in a general setting with a log-affine stochastic discount factor (SDF). Importantly, we show that the cospectrum between returns and the SDF only displays frequency dependencies through the state vector and that its dynamics and risk prices can be inferred from covariances between asset (portfolio) returns, that is, from the cross-section. Empirically, we find low and high-frequency state vector risk to be differentially priced for US equities.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74588177","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 attempts to address the issue of borrower heterogeneity when modelling a borrower’s mortgage loan termination behaviors (default and prepayment) by applying a nonparametric spatial model to a traditional competing-risks loan hazard model. In this spatial competing-risks hazard model, all of the parameters are allowed but not forced to vary across space. Using a sample of 30-year fixed-rate subprime mortgage loans for home purchase, this study finds a substantial level of spatial variation in a borrower’s responsiveness to interest rate change and housing equity change in exercising the default or prepayment option. Further analysis indicates that the observed spatial variation is associated with different levels of resistance to negative shocks, financial literacy, and financial constraints.
{"title":"Spatial Heterogeneity in the Borrowers' Mortgage Termination Decision – a Nonparametric Approach","authors":"Lu Fang, Henry J. Munneke","doi":"10.2139/ssrn.3611291","DOIUrl":"https://doi.org/10.2139/ssrn.3611291","url":null,"abstract":"This paper attempts to address the issue of borrower heterogeneity when modelling a borrower’s mortgage loan termination behaviors (default and prepayment) by applying a nonparametric spatial model to a traditional competing-risks loan hazard model. In this spatial competing-risks hazard model, all of the parameters are allowed but not forced to vary across space. Using a sample of 30-year fixed-rate subprime mortgage loans for home purchase, this study finds a substantial level of spatial variation in a borrower’s responsiveness to interest rate change and housing equity change in exercising the default or prepayment option. Further analysis indicates that the observed spatial variation is associated with different levels of resistance to negative shocks, financial literacy, and financial constraints.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87866400","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 Gini-Frisch bounds partially identify the constant slope coefficient in a linear equation when the explanatory variable suffers from classical measurement error. This paper generalizes these quintessential bounds to accommodate nonparametric heterogenous effects. It provides suitable conditions under which the main insights that underlie the Gini-Frisch bounds apply to partially identify the average marginal effect of an error-laden variable in a nonparametric nonseparable equation. To this end, the paper puts forward a nonparametric analogue to the standard "forward" and "reverse" linear regression bounds. The nonparametric forward regression bound generalizes the linear regression "attenuation bias" due to classical measurement error.
{"title":"Nonparametric Gini-Frisch Bounds","authors":"Karim Chalak","doi":"10.2139/ssrn.3547097","DOIUrl":"https://doi.org/10.2139/ssrn.3547097","url":null,"abstract":"The Gini-Frisch bounds partially identify the constant slope coefficient in a linear equation when the explanatory variable suffers from classical measurement error. This paper generalizes these quintessential bounds to accommodate nonparametric heterogenous effects. It provides suitable conditions under which the main insights that underlie the Gini-Frisch bounds apply to partially identify the average marginal effect of an error-laden variable in a nonparametric nonseparable equation. To this end, the paper puts forward a nonparametric analogue to the standard \"forward\" and \"reverse\" linear regression bounds. The nonparametric forward regression bound generalizes the linear regression \"attenuation bias\" due to classical measurement error.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81470932","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 article proposes a test for the conditional superior predictive ability (CSPA) of a family of forecasting methods with respect to a benchmark. The test is functional in nature: under the null hypothesis, the benchmark’s conditional expected loss is no more than those of the competitors, uniformly across all conditioning states. By inverting the CSPA tests for a set of benchmarks, we obtain confidence sets for the uniformly most superior method. The econometric inference pertains to testing conditional moment inequalities for time series data with general serial dependence, and we justify its asymptotic validity using a uniform non-parametric inference method based on a new strong approximation theory for mixingales. The usefulness of the method is demonstrated in empirical applications on volatility and inflation forecasting.
{"title":"Conditional Superior Predictive Ability","authors":"Jia Li, Z. Liao, R. Quaedvlieg","doi":"10.2139/ssrn.3536461","DOIUrl":"https://doi.org/10.2139/ssrn.3536461","url":null,"abstract":"\u0000 This article proposes a test for the conditional superior predictive ability (CSPA) of a family of forecasting methods with respect to a benchmark. The test is functional in nature: under the null hypothesis, the benchmark’s conditional expected loss is no more than those of the competitors, uniformly across all conditioning states. By inverting the CSPA tests for a set of benchmarks, we obtain confidence sets for the uniformly most superior method. The econometric inference pertains to testing conditional moment inequalities for time series data with general serial dependence, and we justify its asymptotic validity using a uniform non-parametric inference method based on a new strong approximation theory for mixingales. The usefulness of the method is demonstrated in empirical applications on volatility and inflation forecasting.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81616718","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}
Multivariate Adaptive Regression Spline (MARS) is a simple and powerful non-parametric technique that automatizes the selection of non-linear terms in regression models. Non-linearities and spatial effects are natural characteristics in numerous spatial hedonic pricing models. In this paper, we propose using the MARS data-driven methodology combined with the Instrumental Variables method in order to account for potential non-linearities and spatial effects in hedonic models. Using a large data set of more than 6,000 dwellings in Hamburg and about 17,000 in St. Petersburg, we confirm the presence of both effects (non-linearities and spatial autocorrelation). The results also show that there is a non-linear effect of the prices of neighboring houses on the price of each house. High prices for neighboring houses have a lower impact on the house price than low prices of neighboring houses. Finally, an extensive Monte Carlo exercise evaluates the ability of MARS to incorporate the correct spatial spillover terms in spatial regression models simultaneously including at same time non-linear effects.
{"title":"The MARS Algorithm in the Spatial Framework: Non-Linearities and Spatial Effects in Hedonic Models","authors":"F. López, K. Kholodilin","doi":"10.2139/ssrn.3520600","DOIUrl":"https://doi.org/10.2139/ssrn.3520600","url":null,"abstract":"Multivariate Adaptive Regression Spline (MARS) is a simple and powerful non-parametric technique that automatizes the selection of non-linear terms in regression models. Non-linearities and spatial effects are natural characteristics in numerous spatial hedonic pricing models. In this paper, we propose using the MARS data-driven methodology combined with the Instrumental Variables method in order to account for potential non-linearities and spatial effects in hedonic models. Using a large data set of more than 6,000 dwellings in Hamburg and about 17,000 in St. Petersburg, we confirm the presence of both effects (non-linearities and spatial autocorrelation). The results also show that there is a non-linear effect of the prices of neighboring houses on the price of each house. High prices for neighboring houses have a lower impact on the house price than low prices of neighboring houses. Finally, an extensive Monte Carlo exercise evaluates the ability of MARS to incorporate the correct spatial spillover terms in spatial regression models simultaneously including at same time non-linear effects.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85914048","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 augment the usual regression discontinuity design model by considering an endogenously chosen cutoff, perhaps chosen to maximize certain criterion that the treatment provider has. This regime faces the challenge that, conditional on realization of the cutoff, observations are no longer i.i.d. We develop conditions under which an asymptotic expansion of the locally linear estimator contains a bias term caused by the endogeneity of order op(h2 +1/√nh). The lower order bias justifies the usual optimal bandwidth selection and bias correction procedures in this setting, though it places constraints on the maximal degree of undersmoothing.
{"title":"Nonparametric Regression with Stochastic Boundary and Regression Discontinuity with Endogenous Cutoff","authors":"Jiafeng Chen","doi":"10.2139/ssrn.3510899","DOIUrl":"https://doi.org/10.2139/ssrn.3510899","url":null,"abstract":"We augment the usual regression discontinuity design model by considering an endogenously chosen cutoff, perhaps chosen to maximize certain criterion that the treatment provider has. This regime faces the challenge that, conditional on realization of the cutoff, observations are no longer i.i.d. We develop conditions under which an asymptotic expansion of the locally linear estimator contains a bias term caused by the endogeneity of order op(h2 +1/√nh). The lower order bias justifies the usual optimal bandwidth selection and bias correction procedures in this setting, though it places constraints on the maximal degree of undersmoothing.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76395414","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}
Our main objective is to test for evidence of information asymmetry in the mortgage servicing market. Does the sale of mortgage servicing rights (MSR) by the initial lender to a second servicing institution unveil any residual asymmetric information? We analyze the originator’s selling choice of MSR using a large sample of U.S. mortgages that were privately securitized during the period of January 2000 to December 2013 (more than 5 million observations). Our econometric methodology is mainly non-parametric and the main test for the presence of information asymmetry is driven by kernel density estimation techniques (Su and Spindler, 2013). We also employ the non-parametric testing procedure of Chiappori and Salanie (2000). For robustness, we present parametric tests to corroborate our results after controlling for observable risk characteristics, for econometric misspecification error, and for endogeneity issues using instrumental variables. Our empirical results provide strong support for the presence of second-stage asymmetric information in the mortgage servicing market.
{"title":"Nonparametric Testing for Information Asymmetry in the Mortgage Servicing Market","authors":"Helmi Jedidi, G. Dionne","doi":"10.2139/ssrn.3351417","DOIUrl":"https://doi.org/10.2139/ssrn.3351417","url":null,"abstract":"Our main objective is to test for evidence of information asymmetry in the mortgage servicing market. Does the sale of mortgage servicing rights (MSR) by the initial lender to a second servicing institution unveil any residual asymmetric information? We analyze the originator’s selling choice of MSR using a large sample of U.S. mortgages that were privately securitized during the period of January 2000 to December 2013 (more than 5 million observations). Our econometric methodology is mainly non-parametric and the main test for the presence of information asymmetry is driven by kernel density estimation techniques (Su and Spindler, 2013). We also employ the non-parametric testing procedure of Chiappori and Salanie (2000). For robustness, we present parametric tests to corroborate our results after controlling for observable risk characteristics, for econometric misspecification error, and for endogeneity issues using instrumental variables. Our empirical results provide strong support for the presence of second-stage asymmetric information in the mortgage servicing market.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79128278","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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