1,721,061 research outputs found
A note on the complex roots of complex random polynomials
No full textBy using the technique proposed in Ibragimov and Zeitouni, [(1997), Trans. Amer. Math. Soc. 349, 2427{2441], we derive an exact formula for the mean number of complex roots of a complex random polynomial. The explicit evaluation of the average density is obtained in the case of multivariate normal coefficients and its correspondence with the early Hammersley result is shown
Lezioni di finanza matematica
No full textLezioni su alcuni dei concetti alla base della moderna Finanza Matematica: mercati a reddito fisso, analisi del rischio, valutazione di derivati
Computing quantiles in regime-switching jump-diffusions with application to optimal risk management: a Fourier transform approach
No full textIn 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
VaR-Optimal risk management in regime-switching jump-diffusion models
No full textIn this paper we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the hedged po-sition 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 viabl
Adaptive and monotone spline estimation of the cross--sectional term structure of interest rates
No full textA number of numerical methods based on a piecewise polynomial approximation have
been proposed for the estimation of the term structure of interest rates. Some drawbacks
have been pointed out, such as a possible non monotonic estimated discount function
and a highly fluctuating spot and forward rates. In order to overcome these kind of
problems, we study the feasibility of an adaptive regression spline technique which use a
monotone basis together with two alternative knot location procedures: a deterministic
greedy algorithm and its randomized version in a simulated annealing framework. The
features of the proposed method are tested on a set of data
Spread Option Pricing in Regime-Switching Jump Diffusion Models
No full textIn this paper, we consider the problem of pricing a spread option when the underlying assets follow a bivariate regime-switching jump diffusion model. We exploit an approximation technique which is based on the univariate Fourier transform representation of the option price. The method proves to be computationally very effective with respect to benchmark Monte Carlo estimators and permits the use of several kinds of jump models other than the standard Gaussian setting. As a by-product, the exact price of an Exchange Option may be efficiently computed within this framework
Mixture dynamics and regime switching diffusions with application to option pricing
Full text linkIn this paper we present a class of regime switching diffusion models
described by a pair (X(t),Y(t)) ∈ Rn × S, S = {1, 2, . . . , N}, Y(t) being a Markov
chain, for which the marginal probability of the diffusive component X(t) is a given
mixture. Our main motivation is to extend to a multivariate setting the class of
mixture models proposed by Brigo and Mercurio in a series of papers. Furthermore,
a simple algorithm is available for simulating paths through a thinning mechanism.
The application to option pricing is considered by proposing a mixture version for
theMargrabe Option formula and the Heston stochastic volatility formula for a plain
vanilla
Stopping rules for the multistart method when different local minima have different function values
No full textA new estimation method in modal analysis
No full textIn this paper, the modal analysis model, which is made up by a linear combination of complex exponential functions, is considered. The problem of estimating the number of modes as well as the frequencies, decays, amplitudes, and phases and their variability is afforded by means of the condensed distribution of the poles of Padé approximants to the -transform
of the data. This provides a unified framework in which all of these problems can be solved in an almost automatic way. It is
experimentally proved that the results favorably compare with that provided by well-established methods
Selection of importance weights for Monte Carlo estimation of normalizing constants
No full textThis paper concerns the problem of estimating normalizing constants for multivariate densities. We first compare the well known technique of Importance Sampling (IS) with another technique that we call Importance Weighting (IW), which has been recently proposed by Gelfand and Dey (1994). Both techniques require the choice of a suitable density. Whereas it is quite well known that the asymptotic variance of an IS estimator is proportional to the chi-square divergence of the IS density w.r.t. the density of interest, we point out that for the asymptotic variance of the corresponding IW estimator the same results holds, except that the arguments of the divergence are interchanged. This suggests how to adapt to the problem of choosing an IW density procedures which have been already proposed for the choice of the IS density. In particular we show this feature for the algorithms proposed by Geweke (1989) and West (1993). The resulting procedures are illustrated with some examples
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