Conditional Sampling for Barrier Option Pricing under the LT Method

Achtsis, Nico; Cools, Ronald; Nuyens, Dirk

doi:10.1137/110855909

Cited by 28 publications

(25 citation statements)

References 21 publications

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“…Note that we have A 1 > 0 for 1 ≤ ≤ d because the elements of the eigenvector u 1 are all positive. For approximate integration with quadrature, we generate randomized QMC or MC samples x (1) , . .…”

Section: Numerical Experiments: Application To Option Pricingmentioning

confidence: 99%

High dimensional integration of kinks and jumps—Smoothing by preintegration

Griewank

Kuo

Leövey

et al. 2018

Journal of Computational and Applied Mathematics

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We show how simple kinks and jumps of otherwise smooth integrands over R d can be dealt with by a preliminary integration with respect to a single well chosen variable. It is assumed that this preintegration, or conditional sampling, can be carried out with negligible error, which is the case in particular for option pricing problems. It is proven that under appropriate conditions the preintegrated function of d − 1 variables belongs to appropriate mixed Sobolev spaces, so potentially allowing high efficiency of Quasi Monte Carlo and Sparse Grid Methods applied to the preintegrated problem. The efficiency of applying Quasi Monte Carlo to the preintegrated function are demonstrated on a digital Asian option using the Principal Component Analysis factorisation of the covariance matrix.

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Section: Numerical Experiments: Application To Option Pricingmentioning

confidence: 99%

High dimensional integration of kinks and jumps—Smoothing by preintegration

Griewank

Kuo

Leövey

et al. 2018

Journal of Computational and Applied Mathematics

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“…So we refer to this the variable push-out (VPO) smoothing method, and callμ sm the smoothed estimate. Achtsis et al (2013a) used a similar idea to price barrier options under the LT method. Their motivation was to make the sampling scheme compatible with the LT method.…”

Section: The Variable Push-out Methodsmentioning

confidence: 99%

An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering

Wang

2020

Comput Econ

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Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the performance of the QMC method. This paper develops an integrated method that overcomes the challenges of the high dimensionality and discontinuities concurrently. For this purpose, a smoothing method is proposed to remove the discontinuities for some typical functions arising from financial engineering. To make the smoothing method applicable for more general functions, a new path generation method is designed for simulating the paths of the underlying assets such that the resulting function has the required form. The new path generation method has an additional power to reduce the effective dimension of the target function. Our proposed method caters for a large variety of model specifications, including the Black-Scholes, exponential normal inverse Gaussian Lévy, and Heston models. Numerical experiments dealing with these models show that in the QMC setting the proposed smoothing method in combination with the new path generation method can lead to a dramatic variance reduction for pricing exotic options with discontinuous payoffs and for calculating options' Greeks. The investigation on the effective dimension and the related characteristics explains the significant enhancement of the combined procedure.

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“…The function f (Z Z Z) is then sampled using the transformation Z Z Z = Qz z z for a carefully chosen orthogonal matrix Q. This means that in (1) and (2) we take, for k = 0, . .…”

Section: The Lt Methods For Heston Under Log Pricesmentioning

confidence: 99%

“…In previous work [1] we have introduced a conditional sampling method to deal with barrier conditions in the Black-Scholes setting that can be used in combination with a good path construction method like the LT method. In that paper we have shown that such a scheme always performs better than the unconditional method.…”

Section: Introductionmentioning

confidence: 99%

Conditional Sampling for Barrier Option Pricing Under the Heston Model

Achtsis¹,

Cools²,

Nuyens³

2013

Springer Proceedings in Mathematics &Amp; Statistics

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We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path and then conditionally modifying its marginals to fulfill the barrier condition(s). We show that this method is unbiased and never does worse than the unconditional algorithm. In addition, the conditioning is combined with a root finding method to also force positive payouts. The effectiveness of this method is shown by extensive numerical results.

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Conditional Sampling for Barrier Option Pricing under the LT Method

Cited by 28 publications

References 21 publications

High dimensional integration of kinks and jumps—Smoothing by preintegration

High dimensional integration of kinks and jumps—Smoothing by preintegration

An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering

Conditional Sampling for Barrier Option Pricing Under the Heston Model

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