Research Group "Stochastic Algorithms and Nonparametric Statistics"

The research group contributes to the following application oriented research topics of WIAS:

Calibration of stock and interest rate models

Calibration of realistic stock and interest rate models is of prime importance. While standard interest rate products such as caps and swaptions can be priced (quasi-) analytically in a simple Libor market model, it is impossible to match cap and swaption volatility smiles and skews observed in the markets using this model. Therefore a more appropriate Libor rate model with a feasible calibration procedure is of main importance for banks in order to price various interest rate derivatives in their trading books. [>> more]

Image processing

Image processing tools based on modern mathematical algorithms enable a bulk of applications in the medical sciences. They range from image enhancement to automatic image analysis. [>> more]

Pricing of American options

Derivatives of complex structured financial instruments with early exercise features (American style products) are important instruments traded at financial markets. Such products give the holder the right to exercise a cash-flow or a stream of cash-flows at any date before expiry. For example, an investor who holds a certain loan may buy an option to swap his floating interest rate payments with fixed rate payments specified in the contract. [>> more]

Static and dynamic simulation in process engineering

Static and dynamic process simulation has become an indispensable tool for design, analysis, and operation of complex plants in the process engineering industry. Here initial value problems for large-scale systems of differential and algebraic equations (DAEs) have to be solved. The simulation concept developed at WIAS is based on divide-and-conquer techniques and exploits the modular structure of the process models. The DAE system is solved with block-structured Newton-type methods. The simulation concept has been implemented in the Block Oriented Process Simulator BOP and has been successfully used in different industrial applications. [>> more]

Volatility estimation and risk management

The valuation and risk assessment of financial products requires appropriate analysis of the characteristics involved in the modeling. Particular examples are volatility and characteristics of extreme events. Usually the models under consideration are multi-dimensional and have time dependent parameters. [>> more]