Computable Error Bounds of Laplace Inversion for Pricing Asian Options

Song, Yingda; Cai, Ning; Kou, Steven

doi:10.1287/ijoc.2017.0805

Cited by 25 publications

(5 citation statements)

References 28 publications

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“…It is well known that the inversion of a Laplace transform is an ill-posed problem, for which several techniques have been proposed to alleviate the numerical issues. We invite the interested reader to refer to the paper of Song et al (2018) for more details. We believe that similar techniques can be applied in our case, which we leave as an interesting project for future research.…”

Section: T Echnical Papermentioning

confidence: 99%

Full‐fledged SABR Through Markov Chains

Cui¹,

Kirkby²,

Nguyen³

2019

Wilmott

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We present a general purpose technique for the efficient and accurate valuation of options in the shifted stochastic alpha, beta, rho (shifted‐SABR) model which includes SABR as a special case. The method is based on a novel double‐layer continuous‐time Markov chain from which closed form matrix expressions for European options are derived. We also propose a recursive risk‐neutral valuation technique for pricing discretely monitored path‐dependent options, and use it to price Bermudian and barrier options. In addition, we provide single Laplace transform formulae for discretely monitored arithmetic Asian options. Numerical experiments confirm the accuracy and efficiency of the proposed method, which is suitable for practical use.

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Section: T Echnical Papermentioning

confidence: 99%

Full‐fledged SABR Through Markov Chains

Cui¹,

Kirkby²,

Nguyen³

2019

Wilmott

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“…Mijatović and Pistorius (2013) proposed the CTMC approximation in the context of barrier option pricing. It has recently been widely applied in the options pricing literature (e.g., Cai et al., 2015; Cui et al., 2018; Song et al., 2018). Conventionally, CTMC approximations are constructed on nonuniform grids to accelerate computation; that is, the grids are designed to be dense around the critical points and sparse elsewhere.…”

Section: Introductionmentioning

confidence: 99%

A general approximation method for optimal stopping and random delay

Chen

Song

2023

Mathematical Finance

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This study examines the continuous‐time optimal stopping problem with an infinite horizon under Markov processes. Existing research focuses on finding explicit solutions under certain assumptions of the reward function or underlying process; however, these assumptions may either not be fulfilled or be difficult to validate in practice. We developed a continuous‐time Markov chain (CTMC) approximation method to find the optimal solution, which applies to general reward functions and underlying Markov processes. We demonstrated that our method can be used to solve the optimal stopping problem with a random delay, in which the delay could be either an independent random variable or a function of the underlying process. We established a theoretical upper bound for the approximation error to facilitate error control. Furthermore, we designed a two‐stage scheme to implement our method efficiently. The numerical results show that the proposed method is accurate and rapid under various model specifications.

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“…Based on the same principles, Cui et al (2018) simplified to a single Laplace transform with respect to the strike, with consequent significant complexity and computational cost reductions. Song et al (2018) derived computable bounds for the error in the Laplace transform inversion guaranteeing its accuracy.…”

Section: Introductionmentioning

confidence: 99%

Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions

Das

Tsai

Kyriakou

et al. 2022

Operations Research

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On Modeling the Probability Distribution of Stochastic Sums In the “Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions,” Das, Tsai, Kyriakou, and Fusai propose an efficient methodology for approximating the unknown probability distribution of a weighted stochastic sum or time integral. Resulting from earlier contributions based on continuous-time Markov chain approximations of one-dimensional Markov processes is the Laplace transform of the unknown distribution available in exponential matrix form. In this paper, the authors develop a bona fide Pearson curve-fitting approach to this distribution based on the moments, which they recover from the derivatives of the Laplace transform. Motivated by the computational hurdles toward this, they derive computationally efficient closed-form expressions for the derivatives of the matrix exponential. They then apply to pricing average-based options.

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Computable Error Bounds of Laplace Inversion for Pricing Asian Options

Cited by 25 publications

References 28 publications

Full‐fledged SABR Through Markov Chains

Full‐fledged SABR Through Markov Chains

A general approximation method for optimal stopping and random delay

Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions

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