Conditional Sampling for Barrier Option Pricing Under the Heston Model

Achtsis, Nico; Cools, Ronald; Nuyens, Dirk

doi:10.1007/978-3-642-41095-6_9

Cited by 18 publications

(23 citation statements)

References 14 publications

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“…One may write that W 1 (t) =ρB 1 (t) + ρB 2 (t) and W 2 (t) = B 2 (t), whereρ = 1 − ρ 2 , B 1 (t) and B 2 (t) are two independent standard Brownian motions. We use the Euler-Maruyama scheme to discretize the asset paths in log-space (Achtsis et al, 2013b), resulting in…”

Section: Extension To Heston Modelmentioning

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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Section: Extension To Heston Modelmentioning

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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“…We pair the weighted Sobolev space with randomly shifted lattice rules; the complete theory can be found in [13]. Randomly shifted lattice rules approximate the integral (1) by…”

Section: Randomly Shifted Lattice Rulesmentioning

confidence: 99%

“…An interlaced polynomial lattice rule with interlacing factor α ≥ 2, with irreducible modulus polynomial of degree m, and with n = 2 m points in s dimensions, can be constructed by a CBC algorithm such that, for all λ ∈ (1/α, 1],…”

Section: Setting 3: Smooth Integrands In the Unit Cubementioning

confidence: 99%

“…In the option pricing application, see e.g., [2,28,29], none of the settings is applicable due to the presence of a kink. We discuss the strategy of smoothing by preintegration [38], which is similar to the method known as conditional sampling [1]. In the maximum likelihood application [49], the change of variables plays a crucial role in a similar way to importance sampling for Monte Carlo methods.…”

Section: Introductionmentioning

confidence: 99%

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Hot New Directions for Quasi-Monte Carlo Research in Step with Applications

Kuo

Nuyens

2018

Springer Proceedings in Mathematics &Amp; Statistics

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This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube [0, 1] s and in R s , and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension s under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when s is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications. * Frances Y. Kuo ( ):

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“…As conditional expectations always reduce the variance of a random variable, this trick can also be useful in a Monte Carlo setting as well. In this sense, the method is similar to the one proposed in [1,2], who also reduce the variance of a (Q)MC estimator of a barrier option prices by clever transformation of the integrand coupled with identification of the region of positive payoff values in terms of the integration variables. The approach presented here is different since we really focus on the smoothing aspect (obtaining lower variance as a welcome by-product), whereas the previous approach is really focused on the variance, obtaining a smoother integrand as a by-product.…”

Section: Introductionmentioning

confidence: 99%

Smoothing the payoff for efficient computation of Basket option prices

Bayer

Siebenmorgen

Tempone

2017

Quantitative Finance

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Abstract. We consider the problem of pricing basket options in a multivariate BlackScholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.

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Conditional Sampling for Barrier Option Pricing Under the Heston Model

Cited by 18 publications

References 14 publications

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

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

Hot New Directions for Quasi-Monte Carlo Research in Step with Applications

Smoothing the payoff for efficient computation of Basket option prices

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