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

Calibration and risk assesment of stock and interest rate models

Calibration of realistic stock and interest rate models is of prime importance. While standard Libor 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. Moreover, after the financial crisis the Libor rate could not be considered risk free anymore. [>> more]

Computational neuroscience and medical imaging

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

Phase transition and hysteresis in the context of storage problems

Phase transitions and hysteresis are characteristics of energy storage problems. The aim is to formulate and analyse a thermodynamical model which discribes the storage problem. [>> more]

Static and dynamic simulation in process engineering

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

Valuation of complex structured instruments in financial and energy markets

Derivatives of complex structured financial instruments with early exercise features (e.g. American style products and energy swing options) are important instruments traded at financial and energy markets. Such products give the holder the right to exercise a cash-flow or energy unit or a stream of cash-flows (energy units) 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]


Further application topics where the institute has expertise in:

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]