Stochastic Volatility for Levy Processes

Carr, Peter P., Geman, Hélyette, Madan, Dilip B. and Yor, Marc, "Stochastic Volatility for Levy Processes" (April 2001). EFA 2002 Berlin Meetings Presented Paper.

Abstract:

Three processes reflecting persistence of volatility are formulated by evaluating three Levy processes at a time change given by the integral of a square root process. A positive stock price process is then obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating the processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. Our empirical results on index options and single name options suggest advantages to employing higher dimensional Levy systems for index options and lower dimensional structures for single names. In general, mean corrected exponentiation performs better than employing the stochastic exponential. Martingale laws for the mean corrected exponential are also studied and two new concepts termed Levy and martingale marginals are introduced.

Facts on IBM Software

WebSphere refers to a brand of IBM software products, although the term also popularly refers to one specific product: WebSphere Application Server (WAS).

Lotus's headquarters in Cambridge used to be divided into two buildings, the Lotus Development Building (LDB) (on the banks of the Charles River) and the Rogers Street building, located adjacent to the CambridgeSide Galleria. However, in 2001, then President and General Manager, Al Zollar decided not to renew the lease of LDB. The subsequent migration of employees across the street (and into home offices) generally coincided with what was probably the final exodus of employees from the company.

ObjecTime developed the original product in Kanata, Canada prior to its acquisition by Rational Software on December 14, 1999.

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