DYNAMIC PROBABILISTIC FORECASTING WITH UNCERTAINTY

Fred Espen Benth, Gleda Kutrolli () and Silvana Stefani ()
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Fred Espen Benth: Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway
Gleda Kutrolli: Department of Statistics and Quantitative Methods, University of Milano - Bicocca, Piazza dell’Ateneo Nuovo, 1 - 20126, Milano, Italy
Silvana Stefani: Department of Statistics and Quantitative Methods, University of Milano - Bicocca, Piazza dell’Ateneo Nuovo, 1 - 20126, Milano, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 06n07, 1-18

Abstract: In this paper, we introduce a dynamical model for the time evolution of probability density functions incorporating uncertainty in the parameters. The uncertainty follows stochastic processes, thereby defining a new class of stochastic processes with values in the space of probability densities. The purpose is to quantify uncertainty that can be used for probabilistic forecasting. Starting from a set of traded prices of equity indices, we do some empirical studies. We apply our dynamic probabilistic forecasting to option pricing, where our proposed notion of model uncertainty reduces to uncertainty on future volatility. A distribution of option prices follows, reflecting the uncertainty on the distribution of the underlying prices. We associate measures of model uncertainty of prices in the sense of Cont.

Keywords: Probability density; model uncertainty; risk measure; volatility; option prices; stochastic processes in Banach space (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0219024921500345

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