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47 results on '"Taglialatela, Giovanni"'

1. On some hyperbolic equations of third order

Author

Colombini, Ferruccio, Gramchev, Todor, Orrù, Nicola, and Taglialatela, Giovanni

Subjects
Mathematics - Analysis of PDEs, Primary 35L30, Secondary 35G10
Abstract

We give sufficient conditions for the well-posedness in $\mathcal{C}^\infty$ of the Cauchy problem for third order equations with time dependent coefficients.

Published
2021

3. Challenges in approximating the Black and Scholes call formula with hyperbolic tangents

Author

Mininni, Michele, Orlando, Giuseppe, and Taglialatela, Giovanni

Subjects
Quantitative Finance - General Finance, 65-02, 91G20, 91G60
Abstract

In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option's price. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common methods available in literature we discuss the challenges of this approach.

Published
2018

4. Applied Spectral Analysis

Author

Rossa, Fabio Della, Guerrero, Julio, Orlando, Giuseppe, Taglialatela, Giovanni, Mittnik, Stefan, Series Editor, Semmler, Willi, Series Editor, Orlando, Giuseppe, editor, Pisarchik, Alexander N., editor, and Stoop, Ruedi, editor

Published
2021
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5. Embedding Dimension and Mutual Information

Author

Orlando, Giuseppe, Stoop, Ruedi, Taglialatela, Giovanni, Mittnik, Stefan, Series Editor, Semmler, Willi, Series Editor, Orlando, Giuseppe, editor, Pisarchik, Alexander N., editor, and Stoop, Ruedi, editor

Published
2021
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6. Chaos

Author

Orlando, Giuseppe, Stoop, Ruedi, Taglialatela, Giovanni, Mittnik, Stefan, Series Editor, Semmler, Willi, Series Editor, Orlando, Giuseppe, editor, Pisarchik, Alexander N., editor, and Stoop, Ruedi, editor

Published
2021
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7. Bifurcations

Author

Orlando, Giuseppe, Stoop, Ruedi, Taglialatela, Giovanni, Mittnik, Stefan, Series Editor, Semmler, Willi, Series Editor, Orlando, Giuseppe, editor, Pisarchik, Alexander N., editor, and Stoop, Ruedi, editor

Published
2021
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9. Dynamical Systems

Author

Orlando, Giuseppe, Taglialatela, Giovanni, Mittnik, Stefan, Series Editor, Semmler, Willi, Series Editor, Orlando, Giuseppe, editor, Pisarchik, Alexander N., editor, and Stoop, Ruedi, editor

Published
2021
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13. Chaos

Author

Orlando, Giuseppe, primary, Stoop, Ruedi, additional, and Taglialatela, Giovanni, additional

Published
2021
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17. Bifurcations

Author

Orlando, Giuseppe, primary, Stoop, Ruedi, additional, and Taglialatela, Giovanni, additional

Published
2021
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27. A GENERALIZED DERIVATION OF THE BLACK-SCHOLES IMPLIED VOLATILITY THROUGH HYPERBOLIC TANGENTS.

Author

Mininni, Michele, Orlando, Giuseppe, and Taglialatela, Giovanni

Subjects
BLACK-Scholes model, MARKET volatility, APPROXIMATION error, MONTE Carlo method, DECISION making
Abstract

This article extends the previous research on the notion of a standardized call function and how to obtain an approximate model of the Black-Scholes formula via the hyperbolic tangent. Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to derive the implied volatility of options. This is particularly important for traders because it represents the risk of the underlying, and is the main factor in the option price. The approximation error of the suggested solution was estimated and the results compared with the most common methods available in the literature. A new formula was provided to correct some cases of underestimation of implied volatility. Graphic evidence, stress tests and Monte Carlo analysis confirm the quality of the results obtained. Finally, further literature is provided as to why implied volatility is used in decision making. [ABSTRACT FROM AUTHOR]

Published
2022
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31. NECESSARY AND SUFFICIENT CONDITIONS FOR HYPERBOLICITY AND WEAK HYPERBOLICITY OF SYSTEMS WITH CONSTANT MULTIPLICITY, PART I.

Author

TAGLIALATELA, GIOVANNI and VAILLANT, JEAN

Subjects
*PARTIAL differential equations, *CAUCHY problem, *HAMILTONIAN systems, *DIVISIBILITY groups, *LINEAR systems, *MULTIPLICITY (Mathematics)
Abstract

We consider a linear system of partial differential equations, whose principal symbol is hyperbolic with characteristics of constant multiplicities. We define necessary and suffcient invariant condition in order the Cauchy problem to be well-posed in C∞. These conditions generalize the Levi condi- tions for scalar operators. The proof is based on the construction of a new non commutative determinant adapted to this case (and to the holomorphic case). [ABSTRACT FROM AUTHOR]

Published
2019

34. $L^p$-$L^q$ estimates for regularly linear hyperbolic systems

Author

Marcello D'Abbicco, Lucente, Sandra, and Taglialatela, Giovanni

Subjects
35L45, Applied Mathematics, 35B45, Analysis
Abstract

In this paper we establish $L^p-L^q$ estimates for the solution of the strictly hyperbolic first-order linear systems with bounded time-dependent coefficients. In the equation setting, Reissig and others obtained such estimates by using WKB representations of the solutions. Here the crucial point is to find minimal assumptions on the coefficients of the system so that Reissig's approach still works for systems.

Published
2009

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