Modyfikacja geometrycznego ruchu Browna oparta na czasie przebywania. Wycena instrumentów pochodnych, implikowana zmienność – badania symulacyjne
Modified geometric Brownian motion – occupation time approach. Derivative pricing, implied volatility – simulations

Summary/Abstract: The paper presents a new model for the evolution of stock prices. The proposed model uses geometric Brownian motion functionals based on windowed relative occupation time. The model preserves market completeness and introduces a dependency of derivative prices and thus implied volatility from historical stock prices. It also allows to reproduce a rich family of implied volatility surfaces.

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