On the Bessel Distribution and Related Problems

Yuan, Lin; Kalbfleisch, John D.

doi:10.1023/a:1004152916478

Cited by 64 publications

(51 citation statements)

References 11 publications

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“…With an accurate initial solution, this root finding procedure will converge in only a few iterations. Yuan [32] gives numerical evidence for the fact that the noncentral chi-square distribution "converges" to a normal distribution when non-centrality parameter c or random number a increase in value. A number of normal approximations to the noncentral chi-square distribution have been developed, see Johnson and Kotz [16] for a review.…”

Section: Enhanced Direct Inversion Proceduresmentioning

confidence: 99%

A Low-Bias Simulation Scheme for the Sabr Stochastic Volatility Model

Chen

Oosterlee

Weide

2012

Int. J. Theor. Appl. Finan.

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The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

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Section: Enhanced Direct Inversion Proceduresmentioning

confidence: 99%

A Low-Bias Simulation Scheme for the Sabr Stochastic Volatility Model

Chen

Oosterlee

Weide

2012

Int. J. Theor. Appl. Finan.

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“…To state our main result, we need to recall the definition of the Bessel distribution, which we denote by BES(ν, z), with parameter ν > −1 and z > 0 (see Yuan and Kalbfleisch [32] for a study of this distribution). The BES(ν, z) distribution is supported on the nonnegative integers with probability mass function…”

Section: Remark 21mentioning

confidence: 99%

“…Devroye [13] proposed and analyzed fast acceptance-rejection algorithms for sampling Bessel random variables; Iliopoulos et al [20] also proposed acceptance-rejection algorithms, using properties of the Bessel law studied in Yuan and Kalbfleisch [32]. However, with acceptance-rejection methods, small changes in parameter values can produce abrupt changes in the samples generated.…”

Section: Simulation Of Xmentioning

confidence: 99%

Gamma expansion of the Heston stochastic volatility model

Glasserman

Kim²

2009

Finance Stoch

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We derive an explicit representation of the transitions of the Heston stochastic volatility model and use it for fast and accurate simulation of the model. Of particular interest is the integral of the variance process over an interval, conditional on the level of the variance at the endpoints. We give an explicit representation of this quantity in terms of infinite sums and mixtures of gamma random variables. The increments of the variance process are themselves mixtures of gamma random variables. The representation of the integrated conditional variance applies the Pitman-Yor decomposition of Bessel bridges. We combine this representation with the Broadie-Kaya exact simulation method and use it to circumvent the most time-consuming step in that method.

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“…are independent. See Yuan and Kalbfleisch (2000) for properties of the Bessel distribution. The distribution of X 1 is determined by its Laplace transform: for u ≥ 0,…”

Section: Stochastic Volatility Modelmentioning

confidence: 99%

Beta approximations for bridge sampling

Glasserman

Kim

2008

2008 Winter Simulation Conference

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We consider the problem of simulating X conditional on the value of X +Y , when X and Y are independent positive random variables. We propose approximate methods for sampling (X|X +Y ) by approximating the fraction (X/z|X + Y = z) with a beta random variable. We discuss applications to Lévy processes and infinitely divisible distributions, and we report numerical tests for Poisson processes, tempered stable processes, and the Heston stochastic volatility model.

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On the Bessel Distribution and Related Problems

Cited by 64 publications

References 11 publications

A Low-Bias Simulation Scheme for the Sabr Stochastic Volatility Model

A Low-Bias Simulation Scheme for the Sabr Stochastic Volatility Model

Gamma expansion of the Heston stochastic volatility model

Beta approximations for bridge sampling

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