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.File in questo prodotto:
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