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Seminar
Department of Systems Engineering and Engineering Management
The Chinese
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Title |
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Functional Ito calculus
and applications to path-dependent options |
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Speaker |
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Prof. Rama Cont |
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Department of Industrial Engineering and Operations
Research |
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Date |
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Dec. 22nd, 2010 (Wednesday) |
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Time |
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5:00 p.m. - 6:00 p.m. |
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Venue |
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Room 513 |
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William M.W. Mong Engineering
Building |
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(Engineering Building Complex Phase 2) |
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CUHK |
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Abstract:
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We develop an extension of the Ito calculus for to
path-dependent functionals of a semimartingale,
using a notion of non-anticipative functional derivative proposed by B. Dupire. The key ingredient is a functional Ito formula,
which is used to derive an explicit martingale representation formula for
square integrable martingales. Regular functionals of a semimartingale
S which have the local martingale property are characterized as solutions of
a functional equation, for which a uniqueness result is given. This result is used to derive: (a) a universal pricing equation for path-dependent
derivatives, which is shown to be a functional equation whose coefficients
involve the local characteristics of the stochastic process S describing the
price of the underlying asset. (b) a general formula for the hedging strategy of a
path-dependent contingent claim and (c) a numerical method for
computing this hedging strategy. By contrast with methods based on Malliavin calculus, this representation is based on
non-anticipative quantities which may be computed pathwise
and leads to simple simulation-based estimators for computing hedging
strategies for path-dependent options. |
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Biography:
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Prof. Rama Cont is currently Directeur
de Recherche CNRS, Laboratoire
de Probabilités et Modeles
Aléatoires, Paris, France, and associate professor
and director of Center for Financial Engineering at the Department of
Industrial Engineering and Operations Research, Columbia University, New
York. His research interests include computational finance,
stochastic modeling of financial markets, Lévy
processes and applications,
Prof. Rama Cont is one of the leading scholars in quantitative finance and has published more than 40 papers in the field. He serves in the editorial boards of various scientific journals such as SIAM Journal of Financial Mathematics, Operations Research, Quantitative Finance and International Journal of Theoretical and Applied Finance. He is also editor in chief of the Encyclopedia of Quantitative Finance published by Johns Wiley, which is an essential reference work providing comprehensive and up-to-date coverage of all aspects of quantitative modeling in finance. |
************************* ALL ARE WELCOME ************************
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Host |
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Prof. |
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Tel |
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(852)2609-8237 |
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Enquiries |
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Prof. Nan Chen or Prof. Sean X. Zhou |
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Department of Systems Engineering and Engineering
Management |
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CUHK |
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