In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility...

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In...

There appears to be a consensus that the recent instability in global financial markets may be attributable in part to the failure of financial modeling. More specifically, it is alleged that current risk models have failed to properly assess the risks associated with large adverse stock price...

In this article, we introduce two new six-parameter processes based on time-changing tempered stable distributions and develop an option pricing model based on these processes. This model provides a good fit to observed option prices. To demonstrate the advantages of the new processes, we...

The purpose of this paper is to introduce a stochastic volatility model for option pricing that exhibits Lévy jump behavior. For this model, we derive the general formula for a European call option. A well known particular case of this class of models is the Bates model, for which the jumps are...

There appears to be a consensus that the recent instability in global financial markets may be attributable in part to the failure of financial modeling. More specifically, current risk models have failed to properly assess the risks associated with large adverse stock price behavior. In this...

There is considerable empirical evidence that financial returns exhibit leptokurtosis and nonzero skewness. As a result, alternative distributions for modelling a time series of the financial returns have been proposed. A family of distributions that has shown considerable promise for modelling...

In this paper we will introduce a hybrid option pricing model that combines the classical tempered stable model and regime switching by a hidden Markov chain. This model allows the description of some stylized phenomena about asset return distributions that are well documented in financial...

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts...

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In...