The book covers many topics relevant in quantitative finance from a practitioner's point of view, backed with the mathematical knowledge the authors collected when solving complex technical and financial problems with their advanced cross-sectoral mathematical schemes - for blast furnaces, telescopes, combustion engines ... and quantitative finance, implemented in UnRisk for bank proof derivative and risk analytics.
Highlights of the book are
- an intensive discussion of inverse problems arising in model calibration and a discussion of strategies to cure instabilities due to ill-posedness
- an overview of optimization methods to target the various problems where optimization plays a key role in the financial industry like parameter estimation and portfolio optimization
- an analysis of tree methods and why they should not be used
- finite difference and finite elements schemes and their stabilization for the partial differential equations arising when contingent claims are priced under Hull&White, Black Karasinsky, Heston or other models
- Monte Carlo and Quasi Monte Carlo methods and their application to American/Bermudan callable instruments using Least Squares Monte Carlo
- numerical methods based on characteristic functions
- an introduction to the most important copulas
- an introduction to risk management and a discussion of the different methods to calculate important risk measures
- a chapter on parallelization strategies for problems arising in quantitative finance like calibration and instrument valuation
- a short discussion how the different topics/methods covered (calibration-valuation-risk management) can be embedded into large software systems with market data support, user role models and audit support
I can imagine how tired they are - in the last weeks they were working flat out on creating the last chapters without compromising the quality, although Q3-12 was an exciting and intense time for UnRisk. New customers and users selected it for new uses. NewUnRisk shows amazing results ... because of the deep algorithmic design of Andreas and Michael ...