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31
Non-Uniform Random Variate Generation
, 1986
"... This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorith ..."
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Cited by 1006 (25 self)
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This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.
Random variate generation for exponentially and polynomially tilted stable distributions
- ACM Transactions on Modeling and Computer Simulation 19, Article
, 2009
"... Abstract. We develop exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions. The algorithms, which generalize Kanter’s method, are uniformly fast over all choices of the tilting and stable parameters. The key to the solution is a new distributio ..."
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Cited by 16 (2 self)
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Abstract. We develop exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions. The algorithms, which generalize Kanter’s method, are uniformly fast over all choices of the tilting and stable parameters. The key to the solution is a new distribution which we call Zolotarev’s distribution. We also present a novel double rejection method that is useful whenever densities have an integral representation involving an auxiliary variable.
Efficient, almost exact simulation of the Heston stochastic volatility model
- International Journal of Theoretical and Applied Finance
, 2010
"... Efficient, almost exact simulation of the Heston stochastic volatility model A. van Haastrecht1 2 and A.A.J. Pelsser3. ..."
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Cited by 12 (1 self)
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Efficient, almost exact simulation of the Heston stochastic volatility model A. van Haastrecht1 2 and A.A.J. Pelsser3.
An Improved Ziggurat Method to Generate Normal Random Samples
"... The ziggurat is an efficient method to generate normal random samples. It is shown that the standard Ziggurat fails a commonly used test. An improved version that passes the test is intro-duced. Flexibility is enhanced by using a plug-in uniform random number generator. An efficient double-precision ..."
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Cited by 5 (0 self)
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The ziggurat is an efficient method to generate normal random samples. It is shown that the standard Ziggurat fails a commonly used test. An improved version that passes the test is intro-duced. Flexibility is enhanced by using a plug-in uniform random number generator. An efficient double-precision version of the ziggurat algorithm is developed that has a very high period.
The Double CFTP method
, 2010
"... Abstract. We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z L = V Y + (1 − V)Z, where V ∈ [0, 1] and Y are independent, and L = denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give ..."
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Cited by 5 (2 self)
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Abstract. We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z L = V Y + (1 − V)Z, where V ∈ [0, 1] and Y are independent, and L = denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give an algorithm that can be automated under the condition that we have a source capable of generating independent copies of Y, and that V has a density that can be evaluated in a black box format. The method uses a doubling trick for inducing coalescence in coupling from the past. Applications include exact samplers for many Dirichlet means, some two-parameter Poisson–Dirichlet means, and a host of other distributions related to occupation times of Bessel bridges that can be described by stochastic fixed point equations. Keywords and phrases. Random variate generation. Perpetuities. Coupling from the past. Random partitions. Stochastic recurrences. Stochastic fixed point equations. Distribution theory. Markov chain Monte Carlo. Simulation. Expected time analysis. Bessel bridge. Poisson-Dirichlet. Dirichlet means.
A Simple Gamma Random Number Generator for Arbitrary Shape Parameters
"... This paper proposes an improved gamma random generator. In the past, a lot of gamma random number generators have been proposed, and depending on a shape parameter (say, alpha) they are roughly classified into two cases: (i) alpha lies on the interval (0,1) and (ii) alpha is greater than 1, where al ..."
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Cited by 3 (0 self)
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This paper proposes an improved gamma random generator. In the past, a lot of gamma random number generators have been proposed, and depending on a shape parameter (say, alpha) they are roughly classified into two cases: (i) alpha lies on the interval (0,1) and (ii) alpha is greater than 1, where alpha=1 can be included in either case. In addition, Cheng and Feast (1980) extended the gamma random number generator in the case where alpha is greater than 1/n, where n denotes an arbitrary positive number. Taking n as a decreasing function of alpha, in this paper we propose a simple gamma random number generator with shape parameter alpha greater than zero. The proposed algorithm is very simple and shows quite good performance.
Design Flaws in the Implementation of the Ziggurat and Monty Python methods (and some remarks on Matlab
, 2006
"... Ziggurat and Monty Python are two fast and elegant methods proposed by Marsaglia and Tsang to transform uniform random variables to random variables with normal, exponential and other common probability distributions. While the proposed methods are theoretically correct, we show that there are va ..."
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Cited by 2 (0 self)
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Ziggurat and Monty Python are two fast and elegant methods proposed by Marsaglia and Tsang to transform uniform random variables to random variables with normal, exponential and other common probability distributions. While the proposed methods are theoretically correct, we show that there are various design flaws in the uniform pseudo random number generators (PRNG's) of their published implementations for both the normal and Gamma distributions [1, 2, 3]. These flaws lead to non-uniformity of the resulting pseudo-random numbers and consequently to noticeable deviations of their outputs from the required distributions. In addition, we show that the underlying uniform PRNG of the published implementation of Matlab's randn, which is also based on the Ziggurat method, is not uniformly distributed with correlations between consecutive pairs. Also, we show that the simple linear initialization of the registers in matlab's randn may lead to non-trivial correlations between output sequences initialized with di#erent (related or even random unrelated) seeds. These, in turn, may lead to erroneous results for stochastic simulations.
Unsupervised blind deconvolution
- Proceedings of the AMOS Technical Conference, 9-13 September 2013, Maui
, 2013
"... To reduce the influence of atmospheric turbulence on images of space-based objects we are developing a maximum a posteriori deconvolution approach. In contrast to techniques found in the literature, we are focusing on the statistics of the point-spread function (PSF) instead of the object. We incorp ..."
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Cited by 2 (1 self)
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To reduce the influence of atmospheric turbulence on images of space-based objects we are developing a maximum a posteriori deconvolution approach. In contrast to techniques found in the literature, we are focusing on the statistics of the point-spread function (PSF) instead of the object. We incorporated statistical information about the PSF into multi-frame blind deconvolution. Theoretical constraints on the average PSF shape come from the work of D. L. Fried while for the univariate speckle statistics we rely on the gamma distribution adopted from radar/laser speckle studies of J. W. Goodman. Our aim is to develop deconvolution strategy which is reference-less, i.e., no calibration PSF is required, extendable to longer exposures, and applicable to imaging with adaptive optics. The theory and resulting deconvolution framework were validated using simulations and real data from the 3.5m telescope at the Starfire Optical Range (SOR) in New Mexico. 1.
Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility
, 2012
"... The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility ..."
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Cited by 2 (0 self)
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The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a Bayesian learning approach combined with an efficient particle filter is employed. It not only allows for comparison of both nested and non-nested models, but also generates all quantities necessary for sequential model analysis. Empirical investigation using S&P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find substantial evidence for jump clustering, in particular, after the recent financial crisis in 2008, even though parameters driving dynamics of the jump intensity
MALLIAVIN CALCULUS FOR LEVY MARKETS AND NEW SENSITIVITIES
"... Abstract. We present a method to apply the Malliavin calculus to calculate sensitivities for exponential Levy models built from the Variance Gamma and Normal Inverse Gaussian processes. We also present new sensitivities for these processes. The calculation of the sensitivities is based on a finite d ..."
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Abstract. We present a method to apply the Malliavin calculus to calculate sensitivities for exponential Levy models built from the Variance Gamma and Normal Inverse Gaussian processes. We also present new sensitivities for these processes. The calculation of the sensitivities is based on a finite dimensional Malliavin calculus and we compare the results with finite difference calculations. This is done using Monte Carlo methods. For European call and digital options we compare the simulation results with exact calculation of sensitivities using Fourier transform methods. The Malliavin method outperforms the finite difference method especially when payoff has serious discontinuities.
