
From Local Volatility to Local Levy Models
Yor, Marc; Madan, Dilip B.; Carr, Peter; Geman, Hélyette (2004), From Local Volatility to Local Levy Models, Quantitative Finance, 4, 5, p. 581-588
View/ Open
Type
Article accepté pour publication ou publiéDate
2004-10Journal name
Quantitative FinanceVolume
4Number
5Publisher
Routledge
Pages
581-588
Metadata
Show full item recordAbstract (EN)
We define the class of local Lévy processes. These are Lévy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded option prices of all strikes and maturities. The local Lévy processes generalize the class of local volatility models. Closed forms for local speed functions for a variety of cases are also presented. Numerical methods for recovery are also described.Subjects / Keywords
Levy processes; Derivatives securities; Random walks (mathematics); Volatility (finance); Options (finance)Related items
Showing items related by title and author.
-
Geman, Hélyette; Carr, Peter; Madan, Dilip B.; Yor, Marc (2003-07) Article accepté pour publication ou publié
-
Yor, Marc; Madan, Dilip B.; Carr, Peter; Geman, Hélyette (2007) Article accepté pour publication ou publié
-
Geman, Hélyette; Madan, Dilip B. (2004) Chapitre d'ouvrage
-
Geman, Hélyette; Madan, Dilip B.; Pliska, Syanley R. (2002) Ouvrage
-
Madan, Dilip B.; Geman, Hélyette (2005) Chapitre d'ouvrage