Modified geometric Brownian motion – occupation time approach. Derivative pricing, implied volatility – simulations Cover Image

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

Author(s): Tadeusz Czernik, Daniel Iskra
Subject(s): Economy
Published by: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Keywords: derivative instruments; pricing; implied volatility; stochastic processes

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.

  • Issue Year: 2014
  • Issue No: 371
  • Page Range: 75-87
  • Page Count: 13