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...

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...

In this paper, we develop a multivariate risk-neutral Levy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Levy processes and can easily be calibrated to 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...

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...