A General Computation Scheme for a High-Order Asymptotic Expansion Method

Takahashi, Akihiko; Takehara, Kohta; Toda, Masashi

doi:10.2139/ssrn.1761792

Cited by 15 publications

(24 citation statements)

References 14 publications

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“…Following [87] and [96], this section briefly describes an asymptotic expansion method in a general diffusion setting.…”

Section: Asymptotic Expansion In General Diffusion Settingmentioning

confidence: 99%

“…This section follows [96] to introduce a computational scheme for the asymptotic expansion, which is an alternative to the direct calculation method for the conditional expectations given in [95].…”

Section: Computational Schemementioning

confidence: 99%

“…Although the asymptotic expansion up to the fifth order is known to be sufficiently accurate for option pricing (e.g. [81], [95], [96], [108], [109]), one of the main criticisms against the method would be that the approximate density function admits negative values typically at its tails that is, some region of the deep Out-of-The-Money (OTM), which could create an arbitrage opportunity in option trading. Also, even if the domain of a true density is restricted to be positive, the domain of its approximation may include negative values unless an appropriate boundary condition is assigned.…”

Section: Improvement Scheme For Asymptotic Expansionmentioning

confidence: 99%

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Asymptotic Expansion Approach in Finance

Takahashi

2015

Springer Proceedings in Mathematics &Amp; Statistics

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This paper provides a survey on an asymptotic expansion approach to valuation and hedging problems in finance. The asymptotic expansion is a widely applicable methodology for analytical approximations of expectations of certain Wiener functionals. Hence not only academic researchers but also practitioners have been applying the scheme to a variety of problems in finance such as pricing and hedging derivatives under high-dimensional stochastic environments. The present note gives an overview of the approach.

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“…Following [87] and [96], this section briefly describes an asymptotic expansion method in a general diffusion setting.…”

Section: Asymptotic Expansion In General Diffusion Settingmentioning

confidence: 99%

Section: Computational Schemementioning

confidence: 99%

Section: Improvement Scheme For Asymptotic Expansionmentioning

confidence: 99%

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Asymptotic Expansion Approach in Finance

Takahashi

2015

Springer Proceedings in Mathematics &Amp; Statistics

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“…Although the asymptotic expansion up to the fifth order is known to be sufficiently accurate for option pricing (e.g. [37], [49], [50], [51]), one of the main criticisms against the method would be that the approximate density function admits negative values typically at its tails that is, some region of the deep Out-of-The-Money (OTM), which could create an arbitrage opportunity in option trading. Also, even if the domain of a true density is restricted to be positive, the domain of its approximation may include negative values unless an appropriate boundary condition is assigned.…”

Section: Introductionmentioning

confidence: 99%

A new improvement scheme for approximation methods of probability density functions

Takahashi¹,

Tsuzuki²

2016

JCF

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This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in best approximation in an inner product space. Moreover, we applies "Dykstra's cyclic projections algorithm" for its implementation. Numerical examples for application to an asymptotic expansion method in option pricing demonstrate the effectiveness of our scheme under Black-Scholes and SABR models.

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“…An effective method for overcoming this problem is an asymptotic expansion scheme, which is a unified method in order to achieve accurate approximations of option prices and Greeks in multidimensional models. (For example, please see Kunitomo & Takahashi, ; Takahashi, , ; Takahashi & Yoshida, , ; Takahashi, Takehara, & Toda, , ; Yoshida, , for the detail.) We also remark that the mathematical foundation of this method relies on Watanabe theory in Malliavin calculus.…”

Section: Introductionmentioning

confidence: 99%

Pricing Multiasset Cross‐Currency Options

Shiraya

Takahashi

2012

Journal of Futures Markets

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This study develops a general pricing method for multiasset cross‐currency options, whose underlying asset consists of multiple different assets, and the evaluation currency is different from the ones used in the most liquid market of each asset; the examples include cross‐currency options, cross‐currency basket options, and cross‐currency average options. Moreover, in practice, fast calibration is necessary in the option markets relevant for the underlying assets and the currency, which is also achieved in this study. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:1–19, 2014

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A General Computation Scheme for a High-Order Asymptotic Expansion Method

Cited by 15 publications

References 14 publications

Asymptotic Expansion Approach in Finance

Asymptotic Expansion Approach in Finance

A new improvement scheme for approximation methods of probability density functions

Pricing Multiasset Cross‐Currency Options

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