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 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...

This paper investigates the use of the asymptotic Heston solution in locally risk minimizing hedging. The asymptotic Heston solution is presented along with issues that are relevant to its use. Comparison between the exact and asymptotic Heston hedges are made using both simulated and real...

In this paper we derive asymptotic expansions for Australian options in the case of low volatility using the method of matched asymptotics. The expansion is performed on a volatility scaled parameter. We provides a solution for up to third order. In case that there is no drift in the underlying,...

We study the hedging problem for European-style options written on crude-oil futures. Locally risk-minimizing hedging strategies are derived under the assumption that the dynamics of crude-oil futures are described by a Merton-type jump-diffusion. These are then tested empirically using...