In this talk, I will briefly describe the financial engineering problems we have been working on (derivatives valuation, model calibration, portfolio liquidation, etc.), with the focus being on the inversion of holomorphic characteristic functions and the Hilbert transform in financial engineering applications. Analytic characteristic functions naturally arise in financial engineering, as well as many statistical and engineering applications. We explore the analyticity of such characteristic functions and propose highly efficient inversion schemes. In particular, a Hilbert transform representation is obtained for the distribution function. The schemes are very easy to implement. One does not need to rely on commercial numerical packages. Despite the simplicity, they are highly accurate, with exponentially decaying errors. Moreover, they admit explicit and computable error estimates that only depend on the given characteristic function. Multiple values of the desired quantity can be computed simultaneously using the fast Fourier transform. We illustrate the effectiveness of the schemes with financial engineering examples, including options valuation, as well as Monte Carlo simulation of Lvy processes with analytic characteristic functions.
Reception immediately following outside of 202 Transportation Building.