In this paper, we review the most common specifications of discrete-time stochasticvolatility (SV) models and illustrate the major principles of corresponding MarkovChain Monte Carlo (MCMC) based statistical inference. We provide a hands-on approachwhich is easily implemented in empirical...

Measuring and modeling financial volatility is the key to derivative pricing, asset allocation and risk management. The recent availability of high-frequency data allows for refined methods in this field. In particular, more precise measures for the daily or lower frequency volatility can be...

GARCH models are widely used in financial econometrics. However, we show by mean of a simple simulation example that the GARCH approach may lead to a serious model misspecification if the assumption of stationarity is violated. In particular, the well known integrated GARCH effect can be...

Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomialtrees (IBT) models capture the variations of the implied volatility known as \volatility smile". They provide a discrete...

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and...

In this paper we propose a Libor model with a high-dimensional speciallystructured system of driving CIR volatility processes. A stablecalibration procedure which takes into account a given local correlationstructure is presented. The calibration algorithm is FFT based, so fastand easy to implement.

The volatility implied by observed market prices as a function of the strikeand time to maturity form an Implied Volatility Surface (IV S). Practicalapplications require reducing the dimension and characterize its dynamicsthrough a small number of factors. Such dimension reduction is...

High-dimensional regression problems which reveal dynamic behavior are typicallyanalyzed by time propagation of a few number of factors. The inference on thewhole system is then based on the low-dimensional time series analysis. Such highdimensional problems occur frequently in many different...

A primary goal in modelling the implied volatility surface (IVS) for pricing andhedging aims at reducing complexity. For this purpose one fits the IVS each dayand applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of...

The Black-Scholes formula, one of the major breakthroughs of modern finance,allows for an easy and fast computation of option prices. But some of its assumptions, like constant volatility or log-normal distribution of asset prices,do not find justification in the markets. More complex models,...