Instrument Analytics is the very heart and the historical beginning of UnRisk software products. A fast and robust valuation of instruments under various models is the foundation for more elaborate solutions, like risk management and counterparty credit risk.
This is the backbone and work horse of our solutions. Written in C++ it covers:
- Model Calibration: Parameter identification, in such a volatile environment the financial markets offer, is hard task. UnRisk calibration is based on advanced regularization methods to overcome difficulties arising from noisy, unreliable data and to solve even ill-posed inverse problems efficiently.
- Valuation: For the solution of the forward problem (valuation) UnRisk chooses among different methods including the solution of PDEs with Finite Difference/Finite Element schemes, the solution of SDEs with (Quasi-) Monte-Carlo methods as well as direct integration methods like Adaptive Integration and Fourier based techniques.
Highlights of the used methods include:
- Finite differences schemes with special attention to upwinding techniques. Upwinding schemes need to be applied to cure the instabilities occurring if partial differential equations arising from mean reversion models are discretized.
- To reduce the number of discretization points in the discretization process of PDEs and to further speed up the calculations the finite element method is used. Emphasis is laid on the assembling process of the global matrices and the incorporation of boundary conditions. Similar to the finite difference technique stabilization terms are added if the finite element method is applied to convection-diffusion-reaction problems.
- For higher dimensional models Monte Carlo schemes are applied. To reduce the number of paths, and therefore the computation time, variance reduction techniques are applied. For several tasks the Quasi Monte Carlo utilizing low discrepancy sequences instead of pseudo random numbers is the method of choice.
- To incorporate early exercise features into the valuation of instruments requiring larger numbers of risk factors the least squares Monte Carlo method is used.
- In order to speed up the calibration process very fast valuation of vanilla instruments need to be performed. For these cases Cosine-Fourier based methods are used.