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 work we apply asymptotic analysis on compound options, American options, Asian options, and variance (or volatility) contracts in the context of stochastic volatility models. Singular perturbations are used mainly. A singular-regular perturbation is applied on Asian option problems....

In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal...

In the study of finance, likelihood based or moment based methods are frequently used to estimate parameters for various kinds of models given the sampled return data. While the former method is not robust, the latter one suffers from loss of efficiency and high noise-to-signal ratio in the...