Option pricing under model involving slow growth volatility

Abstract

In this paper, we present a new model of the European option price, it is about a model involving slow growth volatility. The SGV model (slow growth volatility model) is the name of the new model considered in this manuscript. The mathematical analysis shows that one has to resort to a degenerate parabolic equation, the resolution of which gives the price of the European option as a function of the time, the price of the underlying asset and the instantaneous volatility.

Keywords:

• option pricing
• CEV model
• degenerate parabolic equations
• finite difference methods

2000 AMS Subject Classifications :

• 35K10
• 35K65
• 65L12
• 91G60

Acknowledgements

The authors would like to thank the anonymous referee for his valuable comments and suggestions to improve the quality of the paper. This work was partly supported by the Volkswagen Foundation through Grant number I/79315, by the French-Moroccan Project A.I number M.A/05/115 and by the Hassan II Academy of Science and Technology.