This article surveys recent developments to estimate and test continuous-time models in finance using discrete observations on the underlying asset price or derivative securities' prices. Both parametric and nonparametric methods are described. All these methods share a common focus on the...

In various agent-based models the stylized facts of financial markets (unit-roots, fat tails and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even...

Multifractal processes reproduce some of the stylised features observed in financial time series, namely heavy tails found in asset returns distributions, and long-memory found in volatility. Multifractal scaling cannot be assumed, it should be established; however, this is not a straightforward...

Numerous heavy-tailed distributions are used for modeling financial data and in problems related to the modeling of economics processes. These distributions have higher peaks and heavier tails than normal distributions. Moreover, in some situations, we cannot observe complete information about...