On Quantile Estimator in Volatility Model with Non-negative Error Density and Bayesian Perspective

Stochastic volatility models are of great importance in the field of mathematical finance, especially for accurately explaining the dynamics of financial derivatives. A quantile-based estimator for the location parameter of a stochastic volatility model is proposed by solving an optimization problem. In this chapter, the asymptotic distribution of the estimator is derived without assuming that the density function of the noise is positive around the corresponding population quantile. We also discuss a Bayesian approach to the quantile estimation problem and establish a result regarding the nature of the posterior distribution.