Inverse Problems in Finance
Jorge Passamani Zubelli
A crucial step in precifying financial instruments is the calibration of the underlying model. As mathematical models for financial instruments get more sophisticated, for example by incorporating stochastic volatility, the need for efficient and robust calibration techniques becomes apparent. It turns out that most calibration problems, such as for example the local volatility in generalized Black-Scholes models, is an ill-posed one. Such problems thus fall into the realm of the mathematical theory of inverse problems. The latter being an interdisciplinary field with impact in areas ranging from medical imaging to geophysics.
In this talk we shall survey some of the main techniques from inverse problems as they apply to quantitative finances.