We discuss the local asymptotic behavior of the likelihood function associated with all the four characterizing parameters ([alpha],[beta],[delta],[mu]) of the Meixner Lévy process under high-frequency sampling scheme. We derive the optimal rate of convergence for each parameter and the Fisher...

The main purpose of this article is to propose computational methods for Greeks and the multidimensional density estimation for an asset price dynamics model defined with time-changed Brownian motions. Our approach is based on an application of the Malliavin integration-by-parts formula on the...

The purpose of this paper is to derive the Greeks formulas of Delta, Gamma, Vega and Theta for derivative securities with both continuous and discontinuous payoff structures under asset price dynamics described by stable and tempered stable processes with presentation of their practical...

We address the problem of gradient estimation with respect to four characterizing parameters of the Meixner distribution and Lévy process. With the help of the explicit marginal probability density function, the likelihood ratio method is directly applicable, while unbiased estimators may...

Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise series representation is the only exact simulation method for the tempered stable process and has...

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...