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- Title
Stochastic flow approach to Dupire’s formula.
- Authors
Jourdain, B.
- Abstract
The equivalent probabilistic formulation of Dupire’s PDE is the put-call duality equality. In local volatility models including exponential Lévy jumps, we give a direct probabilistic proof for this result based on stochastic flow arguments. This approach also enables us to check the equivalent probabilistic formulation of various generalizations of Dupire’s PDE recently obtained by Pironneau [C. R. Acad. Sci. Paris Ser. I 344(2) 127–133 ()] by the adjoint equation technique in the case of complex options.
- Subjects
STOCHASTIC analysis; MATHEMATICAL models of finance; MATHEMATICAL analysis; STOCHASTIC processes; FINANCIAL management; NUMERICAL analysis; BUSINESS mathematics; MATHEMATICAL models in business; MATHEMATICAL models of industrial management
- Publication
Finance & Stochastics, 2007, Vol 11, Issue 4, p521
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-007-0042-8