Non-Parametric and Flexible Time Series Estimators

The estimation of the probability of default based on information on the individual customer or the company is an important part of credit screening, i.e., judging the credit standing. It is essential for the establishment of a rating or for measuring credit risk to estimate the probability that a company will end in financial difficulties within a given period, for example, one year. Also, here nonparametric applications prove to be flexible tools in estimating the desired default probability without arbitrary assumptions. In this chapter we will give a brief overview of the various approaches for non- and semiparametric estimates of conditional probabilities.

[1]  Jianqing Fan,et al.  Nonlinear Time Series : Nonparametric and Parametric Methods , 2005 .

[2]  J. Duan THE GARCH OPTION PRICING MODEL , 1995 .

[3]  P. Robinson Robust Nonparametric Autoregression , 1984 .

[4]  W. Cleveland Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[5]  Critères d'ergodicité de quelques modèles à représentation markovienne , 1992 .

[6]  E. Mammen,et al.  Bootstrap of kernel smoothing in nonlinear time series , 2002 .

[7]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[8]  Christian M. Hafner,et al.  Estimating high-frequency foreign exchange rate volatility with nonparametric ARCH models , 1998 .

[9]  J. Zakoian Threshold heteroskedastic models , 1994 .

[10]  R. Engle Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[11]  G. Collomb Propriétés de convergence presque complète du prédicteur à noyau , 1984 .

[12]  E. Mammen,et al.  ESTIMATION IN AN ADDITIVE MODEL WHEN THE COMPONENTS ARE LINKED PARAMETRICALLY , 2002, Econometric Theory.

[13]  W. Härdle,et al.  Robust and Nonlinear Time Series Analysis , 1984 .

[14]  Peter Bossaerts,et al.  A TEST OF A GENERAL EQUILIBRIUM STOCK OPTION PRICING MODEL , 1993 .

[15]  R. Engle,et al.  Semiparametric ARCH Models , 1991 .

[16]  Allan W. Gregory A Nonparametric Test for Autoregressive Conditional Heteroscedasticity: A Markov-Chain Approach , 1989 .

[17]  P. Vieu Order Choice in Nonlinear Autoregressive Models , 1995 .

[18]  Jianqing Fan,et al.  Efficient Estimation of Conditional Variance Functions in Stochastic Regression , 1998 .

[19]  C. Gouriéroux,et al.  Qualitative threshold arch models , 1992 .

[20]  S. Turnbull,et al.  Pricing foreign currency options with stochastic volatility , 1990 .

[21]  N. Touzi,et al.  Option Hedging And Implied Volatilities In A Stochastic Volatility Model , 1996 .

[22]  C. J. Stone,et al.  Consistent Nonparametric Regression , 1977 .

[23]  D. Sondermann Hedging of non-redundant contingent claims , 1985 .

[24]  Wolfgang Karl Härdle,et al.  Local polynomial estimators of the volatility function in nonparametric autoregression , 1997 .

[25]  Mark H. A. Davis,et al.  Applied Stochastic Analysis , 1991 .

[26]  H. Tong,et al.  On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations , 1985, Advances in Applied Probability.

[27]  P. Robinson NONPARAMETRIC ESTIMATORS FOR TIME SERIES , 1983 .

[28]  W. Härdle,et al.  A Review of Nonparametric Time Series Analysis , 1997 .

[29]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[30]  Jens Perch Nielsen,et al.  Nonparametric Autoregression with Multiplicative Volatility and Additive mean , 1999 .

[31]  Ruey S. Tsay,et al.  Nonlinear Additive ARX Models , 1993 .

[32]  Ruey S. Tsay,et al.  Functional-Coefficient Autoregressive Models , 1993 .

[33]  Wolfgang Karl Härdle,et al.  Nonparametric Vector Autoregression , 1998 .

[34]  James B. Wiggins Option values under stochastic volatility: Theory and empirical estimates , 1987 .

[35]  W. Härdle Applied Nonparametric Regression , 1991 .

[36]  W. Härdle,et al.  Nonparametric Estimation in a Stochastic Volatility Model , 1998 .

[37]  Michael G. Akritas,et al.  Recent Advances and Trends in Nonparametric Statistics , 2003 .

[38]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[39]  Wolfgang K. Härdle,et al.  Discrete time option pricing with flexible volatility estimation , 2000, Finance Stochastics.

[40]  Jiirgen Franke Nonlinear and Nonparametric Methods for Analyzing Financial Time Series , 1999 .

[41]  I. McKeague,et al.  Identification of Nonlinear Time Series from First Order Cumulative Characteristics , 1994 .

[42]  A. Mokkadem SUR UN MODÉLE AUTORÉGRESSIF NON LINÉAIRE, ERGODICITÉ ET ERGODICITÉ GÉOMÉTRIQUE , 1987 .

[43]  Daniel B. Nelson CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[44]  J. Zakoian,et al.  Threshold Arch Models and Asymmetries in Volatility , 1993 .