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P.I.: Silvia Muzzioli
Budget : € 50.000,00 Euro
Funded by: University of Modena and Reggio Emilia
National Departments involved: Department of Economics, University of Modena and Reggio Emilia and Department of Physics, Informatics and Mathematics.
International Departments involved: Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Ghent (Belgium).
Abstract
Abstract
Since the onset of the global financial crisis it has been apparent that the fundamental assumptions underlying the mathematical and financial models used in evaluation and risk management can no longer be considered valid. There is a need to work on model assumptions, the analysis of the model proposed from an economic perspective and the computational methods put in place.
The aim of the project is to combine mathematical, statistical and economic tools in order to study and provide solutions to the modelling of the asymmetry of risk in financial markets, by also looking at the macroeconomic impact of the risk measures. Volatility treats increases and decreases in the underlying asset returns symmetrically and precludes the disentanglement of positive and negative stock price movements (good and bad news). To this end we intend to investigate both model-free and model-based techniques explicitly accounting for asymmetry in stock price movements, in order to model the moments of the underlying asset distribution and derive the option prices consistently.
Among model-free methods, we will provide new asymmetry measures based on option prices and investigate the possibility of using fuzzy regression techniques in order to better capture the empirical irregularities in option implied moments. Among model-based methods, we will investigate the potentialities of Kolmogorov partial differential equations (KPDEs) in modelling the volatility dependence on both the underlying asset and past informative averages of the latter attained in a given time-period.
The expected results of the project are important both at the micro and the macro level. At the micro level, we expect investors to improve portfolio trading strategies and risk assessment with the help of the new models proposed. At the macro level, we expect the new models to provide regulators and policymakers with a valid early warning instrument for possible stock market crashes and public debt default events..
Publications
Publications
E. Elyasiani, L. Gambarelli, S. Muzzioli, “Moment risk premia and the cross-section of stock returns in the European stock market”, Journal of Banking and Finance, 111, 2020. 10.1016/j.jbankfin.2019.105732
A. Lanconelli, A. Pascucci, S. Polidoro, Gaussian lower bounds for non-homogeneous Kolmogorov equations with measurable coefficients, Journal of Evolution Equations (2020);
F. Anceschi, S. Polidoro, A survey on the classical theory for Kolmogorov equation, Le Matematiche, Vol. LXXV-I, (2020);
A. Aimi, L. Diazzi, C. Guardasoni, Integral approach to Asian barrier option pricing, IP Conference Proceedings 2116, 450019 (2019).
G. Campisi, S. Muzzioli, “Fundamentalists heterogeneity and the role of the sentiment indicator”, DEMB Working Paper Series n.167
G. Campisi, L. La Rocca, S. Muzzioli, “Assessing skewness in financial markets” - DEMB Working Paper Series n.164
G. Campisi, S. Muzzioli, “Investor sentiment and trading behavior”, DEMB Working Paper Series n.163
Gambarelli, L., Muzzioli, S. (2019) “Risk asymmetry indices in Europe”, DEMB Working Paper n. 157.
G. Campisi, S. Muzzioli, "Construction and properties of volatility indices for Austria, Finland and Spain" - DEMB Working Paper Series n.156.
F. G. Caloia, A. Cipollini, S. Muzzioli, "How do normalization schemes affect net spillovers? A replication of the Diebold and Yilmaz (2012) study", Energy Economics, 84, 2019. https://doi.org/10.1016/j.eneco.2019.104536
F. Anceschi, M. Eleuteri, S. Polidoro, A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients, Communications in Contemporary Mathematics (2019);
F. Anceschi, S. Polidoro, M.A. Ragusa, Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients, Nonlinear Analysis, TMA (2019);
S. Muzzioli, L. Gambarelli, B. De Baets, "Towards a fuzzy index of skewness", In: Fullér R., Giove S., Masulli F. (eds) Fuzzy Logic and Applications. WILF 2018. Lecture Notes in Computer Science, vol 11291. Springer, Cham. https://doi.org/10.1007/978-3-030-12544-8_13
Muzzioli S. (2018) The Future of Fuzzy Sets in Finance: New Challenges in Machine Learning and Explainable AI. In: Fullér R., Giove S., Masulli F. (eds) Fuzzy Logic and Applications. WILF 2018. Lecture Notes in Computer Science, vol 11291. Springer, Cham. https://doi.org/10.1007/978-3-030-12544-8_26
A. Aimi, L. Diazzi, C. Guardasoni, Efficient BEM-Based Algorithm for Pricing Floating Strike Asian Barrier Option (with MAT LABr Code), Axioms 7(2):40 (2018);
A. Aimi, L. Diazzi, C. Guardasoni, Numerical pricing of geometric Asian options with barriers, Math. Meth. Appl. Sci. 120 (2018);
G. Cibelli, S. Polidoro, F. Rossi, Sharp Estimates for Geman–Yor Processes and applications to Arithmetic Average Asian options, Journal des Mathematiques Pures et Appliquees (2018) .
E. Elyasiani, L. Gambarelli, S. Muzzioli, "The Risk-Asymmetry Index as a New Measure of Risk", Multinational Finance Journal, 22 (3/4), 2018, 173-210.
S. Muzzioli, L. Gambarelli, B. De Baets, "Indices for financial market volatility obtained through fuzzy regression", International Journal of Information Technology & Decision Making, 17(6), 2018, 1659-1691. https://doi.org/10.1142/S0219622018500335
Elyasiani, E., Gambarelli, L., Muzzioli, S. (2018) “The properties of a skewness index and its relation with volatility and returns”, DEMB Working Paper n.133.
Elyasiani, E., Gambarelli, L., Muzzioli, S. (2018) “The use of option prices in order to evaluate the skewness risk premium”, DEMB Working Paper n.132.
F.G. Caloia, A. Cipollini, S. Muzzioli, “Asymmetric semi-volatility spillover effects in EMU stock markets”, International Review of Financial Analysis, 57, 2018, 221-230. https://doi.org/10.1016/j.irfa.2018.03.001 (journal impact factor 1.566, n. of citations: scholar 1, Scopus 2, Web of Sciences 0)
F. Anceschi, M. Eleuteri, S. Polidoro, "A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients", Communications in Contemporary Mathematics, in press. DOI:10.1142/S0219199718500578
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