Location of Repository

Multivariate kernel regression is an important tool for investigating the relationship between a response and a set of explanatory variables. It is generally accepted that the performance of a kernel regression estimator largely depends on the choice of bandwidth rather than the kernel function. This nonparametric technique has been employed in a number of empirical studies including the state-price density estimation pioneered by Aït-Sahalia and Lo (1998). However, the widespread usefulness of multivariate kernel regression has been limited by the difficulty in computing a data-driven bandwidth. In this paper, we present a Bayesian approach to bandwidth selection for multivariate kernel regression. A Markov chain Monte Carlo algorithm is presented to sample the bandwidth vector and other parameters in a multivariate kernel regression model. A Monte Carlo study shows that the proposed bandwidth selector is more accurate than the rule-of-thumb bandwidth selector known as the normal reference rule according to Scott (1992) and Bowman and Azzalini (1997). The proposed bandwidth selection algorithm is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow-Debreu securities. When applying the proposed method to the S&P 500 index options and the DAX index options, we find that for short-maturity options, the proposed Bayesian bandwidth selector produces an obviously different state-price density from the one produced by using a subjective bandwidth selector discussed in Aït-Sahalia and Lo (1998).Black-Scholes formula, Likelihood, Markov chain Monte Carlo, Posterior density.

OAI identifier:

Provided by:
Research Papers in Economics

- (1995). A bandwidth selector for bivariate kernel regression.
- (2006). A Bayesian approach to bandwidth selection for multivariate kernel density estimation.
- (1996). A brief survey of bandwidth selection for density estimation.
- (1987). A comparison of cross-validation techniques in density estimation.
- (1997). A nonparametric model of term structure dynamics and the market price of interest rate risk.
- (2000). American options with stochastic dividends and volatility: a nonparametric investigation.
- (1990). Applied Nonparametric Regression.
- (1997). Applied Smoothing Techniques for Data Analysis.
- (1998). Arbitrage opportunities in arbitrage-free models of bond pricing.
- (1994). Cross-validation of multivariate densities.
- (2002). Estimating state-price densities with nonparametric regression.
- (2004). Estimation of hyperbolic di®usion using the Markov chain Monte Carlo simulation method.
- (2004). Exchange rates and interest rates: can term structure models explain currency movements.
- (2006). Financial crashes as endogenous jumps: estimation, testing and forecasting.
- (2001). Goodness-of-¯t tests for kernel regression with an application to option implied volatilities.
- (2000). How far are automatically chosen regression estimators 22from their optimum?
- (1997). Inference concerning the number of factors in a multivariate nonparametric relationship.
- (1995). Kernel Smoothing.
- (1997). Likelihood analysis of non-Gaussian measurement time series.
- (2000). Local polynomial ¯tting. In
- (1996). Markov chain concepts related to sampling algorithms.
- (2000). Multivariate and semiparametric kernel regression.
- (1992). Multivariate Density Estimation: Theory, Practice, and Visualization.
- (1994). Multivariate plug-in bandwidth selection.
- (2001). Non-linear error correction and the e±cient market hypothesis: the case of German dual-class shares.
- (2003). Nonlinear aspects of capital market integration and real interest rate equalization.
- (1998). Nonparametric estimation of state-price densities implicit in ¯nancial asset prices.
- (2003). Nonparametric option pricing under shape restrictions.
- (2000). Nonparametric risk management and implied risk aversion.
- (2005). Nonparametric speci¯cation testing for continuous-time models with applications to term structure of interest rates.
- (2006). Nonparametric state price density estimation using constrained least squares and the bootstrap.
- (2003). Plug-in bandwidth selectors for bivariate kernel density estimation.
- (2000). Portfolio performance measurement using APM-free kernel models.
- (1997). Pricing mortgage-backed securities in a multifactor interest rate environment: a multivariate density estimation approach.
- (2002). Simulated likelihood estimation of di®usions with an application to exchange rate dynamics in incomplete markets.
- (1998). Stochastic volatility: likelihood inference and comparison with ARCH models.
- (1996). Testing continuous-time models of the spot interest rate.
- (2000). Variance estimation and bandwidth selection for kernel regression. In

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.