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Title: Fitting a Heston's stochastic volatility model to the option quotes on the Warsaw stock exchange Authors:  Katarzyna Brzozowska-Rup - Kielce University of Technology (Poland) [presenting]
Antoni Leon Dawidowicz - Jagiellonian University (Poland)
Abstract: Estimating volatility from the underlying asset price history for discrete observations plays a key role in modelling and exploring financial data. Sequential Monte Carlo methods demonstrate considerable benefits for option pricing. Although the problem is hardly new, Monte Carlo methods have been extensively used in option pricing and it is worth it to review and expand them. The main focus is on Hestons models of stochastic volatility which uses data on an underlying market index and the prices of options written on that index. The most important property in this model is the assumption that the asset price and the volatility process are correlated. Further modifications of the model are still possible. The proposed generalisation consists in considering variables in the current and past time in the equation expressing the evolution of the asset price process. This process is not Markovian but more natural from the practical point of view. The pricing methodology is based on the maximum likelihood estimation combined with the particle filter. To facilitate the discussion simulated and real data from the Warsaw Stock Exchange are employed.