In Japanese stock markets, there are two kinds of breaks, i.e., nighttime and lunch break, where we have no trading, entailing inevitable increase of variance in estimating daily volatility via naive realized variance (RV). In order to perform a much more stabilized estimation, we are concerned...

We propose simple sequential calibration for an asset price model driven by piecewise Lévy processes, for which simulation methods and Greeks formulas are available. The proposed methods are easy to implement and consist of fitting a sequence of Lévy processes to a return series such that they...

In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicabilityin the context of the volatility smile of multiple assets. Our formulation is based upona linear combination of independent univariate Lévy processes and can easily be calibratedto a set of...

The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform...

Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the...