Bayesian Analysis of the Box-Cox Transformation in Stochastic Volatility Models

Abstract

In the paper, we consider the Box-Cox transformation of financial time series in Stochastic Volatility models. Bayesian approach is applied to make inference about the Box-Cox transformation parameter (λ). Using daily data (quotations of stock indices), we show that in the Stochastic Volatility models with fat tails and correlated errors (FCSV), the posterior distribution of parameter λ strongly depends on the prior assumption about this parameter. In the majority of cases the values of λ close to 0 are more probable a posteriori than the ones close to 1.

Bayesian Portfolio Selection with MSV Models

“…Now, we consider a SV process based on the spectral decomposition of the matrix S t (see [11]). That is…”

“…In the JSV model the structure of the conditional covariance matrix is based on two separate latent variables. The next specification uses three separate latent processes (see [11]). In the definition of the JSV model we replace p 11 by a process p 11,t with value in (0,1].…”

Bayesian Value-at-Risk and Expected Shortfall for a Large Portfolio (Multi- and Univariate Approaches)

“…In practice, the logarithmic return rates r t+1,i = ln (S t+1,i /S t,i ) = ln (R t:t+1,i + 1) are the quantities being modelled. They can take any real value, easily aggregate over time, and modelling them can be more justified in view of the data; see [10]. Using the logarithmic return rates we can rewrite (2) and (4) as:…”