Abstract:
Two models with uncertain volatility and the Heston model are considered. For the European type option, Bellman equations are obtained for calculating the range of fair prices in the case of models with uncertain volatility, as well as for calculating the fair price in the case of the Heston model. For comparison, the boundary value problem solution method, the Monte Carlo method and the method based on recurrent formulas on a binary tree are used. An obvious advantage of Bellman equations is their invariance with respect to methods of approximating continuous models. The main conclusion is that models with uncertain volatility are an adequate replacement for the Heston model in cases where it is necessary to calculate the range of fair prices of a European type option.
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