1,721,005 research outputs found
A characterization for a class of actuarial risk measures
No full textThe idea of coherent risk measures has been introduced by Artzner, Delbaen, Eber, and Heath (1999). We consider a particular class of coherent risk measures used in insurance pricing. These measures are obtained by expansion of TVaR measures. We develop an axiomatic description of these measures
A radial basis function approach to compute the first-passage probability density function in two-dimensional jump-diffusion models for financial and other applications
No full textWe consider the problem of computing the survival (first-passage) probability density function of jump-diffusion models with two stochastic factors. In particular the Fokker–Planck partial integro-differential equation associated to these models is solved using a meshless collocation approach based on radial basis functions (RBF). To enhance the computational efficiency of the method, the calculation of the jump integrals is performed using a suitable Chebyshev interpolation procedure. In addition, the RBF discretization is carried out in conjunction with an ad hoc change of variables, which allows to use radial basis functions with equally spaced centers and at the same time yields an accurate resolution of the gradients of the survival probability density function near the barrier. Numerical experiments are presented showing that the RBF approach is extremely accurate and fast, and performs significantly better than the conventional finite difference method
A very fast and accurate boundary element method for options with moving barrier and time-dependent rebate
No full textThe constant elasticity of variance model: calibration, test and evidence from the Italian equity market
No full textPricing European and American options with two stochastic factors: A highly efficient radial basis function approach
No full textComputing the survival probability density function in jump-diffusion models: A new approach based on radial basis functions
No full textOn the characterization of convex premium priciples
No full textWorking Papers Department of Applied Mathematics University of Venice (IDEAS)142-2006
ISSN: 1828-688
Maximum likelihood estimation of the Heston stochastic volatility model using asset and option prices: an application of nonlinear filtering theory
No full textLet us suppose that the dynamics of the stock prices and of their stochastic variance is described by the Heston model, that is by a system of two stochastic differential equations with a suitable initial condition. The aim of this paper is to estimate the parameters of the Heston model and one component of the initial condition, that is the initial stochastic variance, from the knowledge of the stock and option prices observed at discrete times. The option prices considered refer to an European call on the stock whose prices are described by the Heston model. The method proposed to solve this problem is based on a filtering technique to construct a likelihood function and on the maximization of the likelihood function obtained. The estimated parameters and initial value component are characterized as being a maximizer of the likelihood function subject to some constraints. The solution of the filtering problem, used to construct the likelihood function, is based on an integral representation of the fundamental solution of the Fokker–Planck equation associated to the Heston model, on the use of the wavelet expansions presented in (Fatone et al. in High performance algorithms based on a new wavelet expansion for time dependent acoustic obstacle scattering. Commun. Computat. Phys. (2007), Research Developments in Acoustics, vol. 2, pp. 39–69. Transworld Research Network, Kerala (2005), New wavelet bases made of piecewise polynomial functions: approximation theory, quadrature rules and applications to kernel sparsification and image compression. SIAM J. Sci. Comput. (submitted)) to approximate the integral kernel appearing in the representation formula of the fundamental solution, on a simple truncation procedure to exploit the sparsifying properties of the wavelet expansions and on the use of the fast Fourier transform (FFT). The use of these techniques generates a very efficient and fully parallelizable numerical procedure to solve the filtering problem, this last fact makes possible to evaluate very efficiently the likelihood function and its gradient. As a byproduct of the solution of the filtering problem we have developed a stochastic variance tracking technique that gives very good results in numerical experiments. The maximum likelihood problem used in the estimation procedure is a low dimensional constrained optimization problem, its solution with ad hoc techniques is justified by the computational cost of evaluating the likelihood function and its gradient. We use parallel computing and a variable metric steepest ascent method to solve the maximum likelihood problem. Some numerical examples of the estimation problem using synthetic and real data, that is data relative to an index of the Milano stock exchange (S&PMIB30), obtained with a parallel implementation of the previous numerical method are presented. Very impressive speed up factors are obtained in the numerical examples using the parallel implementation of the numerical method proposed. The website: http://www.econ.univpm.it/pacelli/mariani/finance/w1 contains animations and some auxiliary material that helps the understanding of this paper and makes available to the interested users the computer programs used to produce the numerical experience presented
The Heston stochastic volatility model for single assets and for asset portfolios: parameter estimation and an application to the Italian financial market
No full textWe investigate the performance of the Heston stochastic volatility model in describing the
probability distribution of returns both in the case of single assets and in the case of asset
portfolios. The R. parameters of the Heston model are estimated from observed market prices
using a simple calibration method based on an integral representation of the exact probability
density function of returns derived by Dragulescu and Yakovenko (2002). In the case of multiple
correlated assets, the correlation parameters are obtained using a heuristic procedure based on
a matrix completion algorithm. We present numerical experiments where several stocks traded on
the Italian financial market are considered. We show that, both in the case of single assets and in the case of multiple correlated assets, the Heston model provides an excellent agreement with historical time series data and fits the empirical probability
distribution of returns far better than the lognormal model
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