This paper presents a very general option pricing formula incorporating both the Lévy process methodology and the level dependent volatility approach. Since the classical Black-Scholes equation is replaced by a pseudo differential equation, an approximate solution to the pricing problem is obtained throughout the construction of a parametrix by means of the pseudo differential calculus. Some examples are provided and the implications in terms of the volatility smile are studied.

Option pricing under generalized Lévy processes with state dependent parameters

AGLIARDI, ROSSELLA
2011

Abstract

This paper presents a very general option pricing formula incorporating both the Lévy process methodology and the level dependent volatility approach. Since the classical Black-Scholes equation is replaced by a pseudo differential equation, an approximate solution to the pricing problem is obtained throughout the construction of a parametrix by means of the pseudo differential calculus. Some examples are provided and the implications in terms of the volatility smile are studied.
Proceedings of the 8th international Conference on Applied Financial Economics
559
564
Agliardi R.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/105335
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