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VaR-Optimal Risk Management in Regime-Switching Jump-Diffusion Models  [PDF]
Alessandro Ramponi
Journal of Mathematical Finance (JMF) , 2013, DOI: 10.4236/jmf.2013.31009

In this paper we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the hedged position in a continuous time, regime-switching jump-diffusion market, by using Fourier Transform methods. However, the analysis of this hedging strategy, as well as the computational technique for its implementation, is fairly general, i.e. it can be applied to any dynamical model for which Fourier transform methods are viable.

Computing Quantiles in Regime-Switching Jump-Diffusions with Application to Optimal Risk Management: a Fourier Transform Approach
Alessandro Ramponi
Quantitative Finance , 2012,
Abstract: In this paper we consider the problem of calculating the quantiles of a risky position, the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transform methods. Furthermore, we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the hedged position and show the impact of jumps and switching regimes on the optimal strategy in a numerical example. However, the analysis of this hedging strategy, as well as the computational technique for its implementation, is fairly general, i.e. it can be applied to any dynamical model for which Fourier transform methods are viable.
On a Transform Method for the Efficient Computation of Conditional VaR (and VaR) with Application to Loss Models with Jumps and Stochastic Volatility
Alessandro Ramponi
Quantitative Finance , 2014, DOI: 10.1007/s11009-015-9446-7
Abstract: In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an elementary optimization problem of convex type in one dimension for which Fast and Fractional Fourier transform can be implemented. An application to univariate loss models driven by L\'{e}vy or stochastic volatility risk factors dynamic is finally reported.
Fourier Transform Methods for Regime-Switching Jump-Diffusions and the Pricing of Forward Starting Options
Alessandro Ramponi
Quantitative Finance , 2011,
Abstract: In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.
A critical review of techniques for Term Structure analysis
Livio Marangio,Alessandro Ramponi,Massimo Bernaschi
Physics , 2000,
Abstract: Fixed income markets share many features with the equity markets. However there are significant differences as well and many attempts have been done in the past to develop specific tools which describe (and possibly forecasts) the behavior of such markets. For instance, a correct pricing of fixed income securities with fixed cache flows requires the knowledge of the {\it term structure} of interest rates. A number of techniques have been proposed for estimating and interpreting the term structure, yet solid theoretical foundations and a comparative assessment of the results produced by these techniques are not available. In this paper we define the fundamental concepts with a mathematical terminology. Besides that, we report about an extensive set of experiments whose scope is to point out the strong and weak points of the most widely used approaches in this field.
Random Time Forward Starting Options
Fabio Antonelli,Alessandro Ramponi,Sergio Scarlatti
Quantitative Finance , 2015,
Abstract: We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options {\bf Random Time Forward Starting (RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.
Gonality and Clifford index of curves on elliptic K3 surfaces with Picard number two
Marco Ramponi
Mathematics , 2015,
Abstract: For any non-zero integer $m$, we compute the gonality and Clifford index of curves on K3 surfaces with Picard group isomorphic to $U(m)$. Here we denote by $U(m)$ the lattice given by the hyperbolic plane $U$ with intersection form multiplied by $m$.
Fenomeni di superfluidità nucleare in stelle di neutroni
Giorgio Gori,F. Ramponi
Bollettino del CILEA , 2003, DOI: 10.1472/bc.v90inovembre.857
Abstract: Viene presentato in questo articolo il lavoro del gruppo di teoria della struttura nucleare dell'Università di Milano riguardante la descrizione dello stato superfluido della materia nella inner crust di una stella di neutroni.
Photonic glass-ceramics: consolidated outcomes and prospects
Brigitte Boulard,Tran T. T. Van,Anna ?ukowiak,Adel Bouajaj,Rogéria Rocha Gon?alves,Andrea Chiappini,Alessandro Chiasera,Wilfried Blanc,Alicia Duran,Sylvia Turrell,Francesco Prudenzano,Francesco Scotognella,Roberta Ramponi,Marian Marciniak,Giancarlo Righini,Maurizio Ferrari
Physics , 2015,
Abstract: Transparent glass-ceramics are nanocomposite materials which offer specific characteristics of capital importance in photonics. This kind of two-phase materials is constituted by nanocrystals embedded in a glass matrix and the respective composition and volume fractions of crystalline and amorphous phase determine the properties of the glass-ceramic. Among these properties transparency is crucial, in particular when confined structures, such as dielectric optical waveguides and optical fibers, are considered, and the number of papers devoted to this topic is continuously increasing. Another important point is the role of the nanocrystals when activated by luminescent species, as rare earth ions, and their effect on the spectroscopic properties of the glass-ceramic. The presence of the crystalline environment around the rare earth ion allows high absorption and emission cross sections, reduction of the non-radiative relaxation thanks to the lower phonon cutoff energy, and tailoring of the ion-ion interaction by the control of the rare earth ion partition. This last point is crucial and still object of intense experimental and theoretical studies. The composition of the glass matrix also impacts the properties of the rare earth ions located in nanoparticles. Moreover, some kinds of nanocrystals can play as effective rare earth sensitizers. Fabrication, assessment and application of glass-ceramic photonic systems, especially waveguides, deserve an appropriate discussion which is the aim of this paper, focused on luminescent glass-ceramics. In this work, a brief historical review, consolidated results and recent advances in this important scientific and technological area will be presented, and some perspectives will be outlined.
Design of Farthest-Point Masks for Image Halftoning
G. Ramponi,C. Moloney,R. Shahidi
EURASIP Journal on Advances in Signal Processing , 2004, DOI: 10.1155/s1687617204403217
Abstract: In an earlier paper, we briefly presented a new halftoning algorithm called farthest-point halftoning. In the present paper, this method is analyzed in detail, and a novel dispersion measure is defined to improve the simplicity and flexibility of the result. This new stochastic screen algorithm is loosely based on Kang's dispersed-dot ordered dither halftone array construction technique used as part of his microcluster halftoning method. Our new halftoning algorithm uses pixelwise measures of dispersion based on one proposed by Kang which is here modified to be more effective. In addition, our method exploits the concept of farthest-point sampling (FPS), introduced as a progressive irregular sampling method by Eldar et al. but uses a more efficient implementation of FPS in the construction of the dot profiles. The technique we propose is compared to other state-of-the-art dither-based halftoning methods in both qualitative and quantitative manners.
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