Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, 1975
IVAR Massabò, A fixed-point theorem fo r single-valued mappings, ecc. 559 Topologia.-A fixed-poin... more IVAR Massabò, A fixed-point theorem fo r single-valued mappings, ecc. 559 Topologia.-A fixed-point theorem fo r single-valued mappings defined on a topological space (*}. Nota di I v a r M a s s a b ò , presen tata (**} dal Socio G. S a n s o n e. RIASSUNTO.-Scopo di questa Nota è quello di mostrare come con la nozione di <pcoerenza, introdotta da Furi e Vignoli [7], si possano ottenere molti dei teoremi sull'esistenza del punto fisso.
In this paper we compare different approaches to computing VaR (Value-at-Risk) for heavy tailed r... more In this paper we compare different approaches to computing VaR (Value-at-Risk) for heavy tailed return series. Using data from the Italian market, we show that almost all the return series present statistically significant skewness and kurtosis. We implement (i) the stable models proposed by Rachev et at. (2000), (ii) an alternative to the Gaussian distributions based on a Generalized Error Distribution and (iii) a nonparametric model proposed by Li (1999). All the models are then submitted to backtest on out-of-sample data in order to assess their forecasting power. We observe that when the percentiles are low, all the models tested produce results that are dominant compared to the standard RiskMetrics model.
Nonlinear multiparametric equations: structure and topological dimension of global branches of solutions
Proceedings of symposia in pure mathematics, 1986
Using a homotopy-theoretical approach via 0-epi maps, we study the connectivity properties and th... more Using a homotopy-theoretical approach via 0-epi maps, we study the connectivity properties and the topological dimension of the solution set of a parametrized family of compact vector fields
On the connectivity properties of the solution set of infinitely-parametrized families of vector fields
We study the connectivity properties of the solution set of a family of compact vector fields par... more We study the connectivity properties of the solution set of a family of compact vector fields parametrized by an infinite dimensional space
This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 5... more This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, we fit a three-regime switching model that allows market parameters to behave differently during economic downturns, with the regimes representative of the tranquil, volatile, and turbulent states. We document that the tranquil regime is the most frequent for the whole period, while the dominant regime is the volatile one for the crisis of 2008 and the turbulent one for the first four months of 2020. We fit the same model to the returns of the Dow Jones Industrial Average index and find that during the same period of investigation, the most frequent regime has been the tranquil one, while the volatile and turbulent regimes share the same frequencies. Additionally, we use a multinomial logit model to describe the probabilities of...
A binomial approximation for two-state Markovian HJM models
Review of Derivatives Research, 2010
This article develops a lattice algorithm for pricing interest rate derivatives under the Heath e... more This article develops a lattice algorithm for pricing interest rate derivatives under the Heath et al. (Econometrica 60:77–105, 1992) paradigm when the volatility structure of forward rates obeys the Ritchken and Sankarasubramanian (Math Financ 5:55–72) condition. In such a framework, the entire term structure of the interest rate may be represented using a two-dimensional Markov process, where one state variable is
Computationally simple lattice methods for option and bond pricing
Decisions in Economics and Finance, 2009
We propose new lattice-based algorithms for option and bond pricing, which rely on computationall... more We propose new lattice-based algorithms for option and bond pricing, which rely on computationally simple trees, i.e., trees with the number of nodes that grows at most linearly in the number of time intervals. Contrary to commonly used methods, the target diffusion is approximated directly, without having to transform the original process into a constant volatility process. The discrete approximating
Bulletin of the American Mathematical Society, 1983
We state, and indicate some of the consequences of, a theorem whose sole assumption is the nonvan... more We state, and indicate some of the consequences of, a theorem whose sole assumption is the nonvanishing of the Leray-Schauder degree of a compact vector field, and whose conclusions yield multidimensional existence, continuation and bifurcation results.
Rendiconti del Seminario Matematico e Fisico di Milano, 1983
SUNTO.-In questa nota si descrivono alcuni risultati sull'esistenza, la struttura topologica ed i... more SUNTO.-In questa nota si descrivono alcuni risultati sull'esistenza, la struttura topologica ed il comportamento globale di rami di soluzioni di equazioni non lineari dipendenti da pifi parametri.
International Journal of Financial Markets and Derivatives, 2010
We develop a pricing algorithm for US-style period-average reset options written on an underlying... more We develop a pricing algorithm for US-style period-average reset options written on an underlying asset which evolves in a Cox-Ross-Rubinstein (CRR) framework. The averaging feature of such an option on the reset period makes the price valuation problem computationally unfeasible because the arithmetic average is not recombining on a CRR tree. To overcome this obstacle, we associate to each node of the lattice belonging to the reset period a set of representative averages chosen among all the effective arithmetic averages attained at that node. On the remaining time to maturity, a US period-average reset option becomes a US standard one and the Barone Adesi-Whaley approximation is used to compute an option value in correspondence to each representative average lain at the end of the reset period.
We propose a model for pricing American-style period-average reset options. Our approach relies o... more We propose a model for pricing American-style period-average reset options. Our approach relies on a binomial tree describing the underlying asset evolution on the reset period. At each node of the tree, we associate a set of representative averages chosen among all the effective averages realized at that node. At the terminal nodes, we associate an option value to each representative average by using the Barone-Adesi and Whaley analytic approximation since, at the end of the reset period, an American period-average reset option becomes a standard American option. Then, we use backward recursion and linear interpolation to compute the option prices.
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