1,720,961 research outputs found
" A numerical method to price European derivatives based on factor LIBOR Market Model of interest rates"
No full textWe consider the problem of pricing European interest rate derivatives based on the LIBOR Market Model (LMM) with one
driving factor. We derive a closed-form approximation of the transition probability density functions associated to the stochastic
dynamical systems that describe the behaviour of the forward LIBOR interest rates in the LMM. These approximate formulae
are based on a truncated power series expansion of the solutions of the Fokker–Planck equations associated to the LMM. The
approximate probability density functions obtained are used to price European interest rate derivatives using the method of
discounted expectations. The resulting integrals are low dimensional when the most commonly traded European interest rate
derivatives are considered, and they can be computed efficiently using elementary numerical quadrature schemes (i.e. Simpson’s
rule). The algorithm obtained is very well suited for parallel computing and is tested on the problem of pricing several derivatives
including an European swaption and an interest rate spread option. In both cases, the method proposed in this paper appears to
be accurate (i.e. relative error of order 10−2, 10−3, or even 10−4) and approximately between 278 and 63 000 times faster than
previous methods based on the Monte Carlo simulation of the LMM stochastic dynamical systems.
The website http://www.econ.univpm.it/pacelli/ballestra/finance/w2 contains material that helps the understanding of this paper
and makes available to the interested users the computer programs that implement the numerical method proposed
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. © 2012 Elsevier Ltd. All rights reserved
An operator splitting harmonic differential quadrature approach to solve Young's model for life insurance risk
No full textThis paper is concerned with the numerical approximation of a mathematical model for life insurance risk that has been presented quite recently by Young (2007, 2008). In particular, such a model, which consists of a system of several non-linear partial differential equations, is solved using a new numerical method that combines an operator splitting procedure with the differential quadrature (DQ) finite difference scheme. This approach allows one to reduce the partial differential problems to systems of linear equations of very small dimension, so that pricing portfolios of many life insurances becomes a relatively easily task. Numerical experiments are presented showing that the method proposed is very accurate and fast. In addition, the limit behavior of portfolios of life insurances as the number of contracts tends to infinity is investigated. This analysis reveals that the prices of portfolios comprising more than five thousand policies can be accurately approximated by solving a linear partial differential equation derived in Young (2007, 2008). © 2012 Elsevier B.V
A very fast and accurate boundary element method for options with moving barrier and time-dependent rebate
No full textA numerical method to price options with moving barrier and time-dependent rebate is proposed. In particular, using the so-called Boundary Element Method, an integral representation of the barrier option price is derived in which one of the integrand functions is not given explicitly but must be obtained solving a Volterra integral equation of the first kind. This equation is affected by several kinds of singularities, some of which are removed using a suitable change of variables. Then the transformed equation is solved using a low-order finite element method based on product integration. Numerical experiments are carried out showing that the proposed method is extraordinarily fast and accurate. In particular a high level of accuracy is achieved also when the initial price of the underlying asset is close to the barrier, when the barrier and the rebate are not differentiable functions, or when the optionÊs maturity is particularly long. © 2013 IMACS
The evaluation of American options in a stochastic volatility model with jumps: An efficient finite element approach.
No full textWe consider the problem of pricing American options in the framework of a well-known stochastic volatility model with jumps, the Bates model. According to this model the asset price is described by a jump-diffusion stochastic differential equation in which the jump term consists of a Lévy process of compound Poisson type, while the volatility is modeled as a CIR-type process correlated with the asset price. Pricing American options under the Bates model requires to solve a partial integro-differential equation with final condition and boundary conditions prescribed on a free boundary. In this paper a numerical method to solve such a problem is proposed. In particular, first of all, using a Richardson extrapolation technique, the problem is reduced to a problem with fixed boundary. Then the problem obtained is solved using an ad-hoc finite element method which efficiently combines an implicit/explicit time stepping, an operator splitting technique, and a non-uniform mesh of right-angled triangles. Numerical experiments are presented showing that the option pricing algorithm developed in this paper is extremely accurate and fast. In particular it is significantly more efficient than other numerical methods that have recently been proposed for pricing American options under the Bates model
A numerical method to price exotic path dependent options on an underlying described by the Heston stochastic volatility model
No full textWe consider the problem of pricing European exotic path-dependent derivatives on an underlying described by the Heston stochastic volatility model. Lipton has found a closed form integral representation of the joint transition probability density function of underlying price and variance in the Heston model. We give a convenient numerical approximation of this formula and we use the obtained approximated transition probability density function to price discrete path-dependent options as discounted expectations. The expected value of the payoff is calculated evaluating an integral with the Monte Carlo method using a variance reduction technique based on a suitable approximation of the transition probability density function of the Heston model. As a test case, we evaluate the price of a discrete arithmetic average Asian option, when the average over n = 12 prices is considered, that is when the integral to evaluate is a 2n = 24 dimensional integral. We show that the method proposed is computationally efficient and gives accurate results
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
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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