Dynamic Probabilistic Forecasting with Uncertainty

37 Pages Posted: 24 Jun 2019

See all articles by Fred Espen Benth

Fred Espen Benth

University of Oslo

Gleda Kutrolli

University of Milano-Bicocca

Silvana Stefani

University of Milano-Bicocca

Date Written: June 18, 2019

Abstract

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 such as FTSEMIB, FTSE100 and S&P500 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 context of Cont (2006). As a further application we look at the Sharpe ratio and the VaR measure of market risk as well, proposing some decision rules for investors, regulators and risk managers.

Keywords: probability density, model uncertainty, risk measure, volatility, option prices

JEL Classification: G2

Suggested Citation

Benth, Fred Espen and Kutrolli, Gleda and Stefani, Silvana, Dynamic Probabilistic Forecasting with Uncertainty (June 18, 2019). Available at SSRN: https://ssrn.com/abstract=3405890 or http://dx.doi.org/10.2139/ssrn.3405890

Fred Espen Benth (Contact Author)

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Gleda Kutrolli

University of Milano-Bicocca ( email )

Piazza dell'Ateneo Nuovo
Milano, MI 20126
Italy
0264481 (Phone)

Silvana Stefani

University of Milano-Bicocca ( email )

Piazza dell'Ateneo Nuovo, 1
Milano, MI Milano 20126
Italy
20099 (Fax)

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