Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

Zhang, Bowen; Oosterlee, Cornelis W.

doi:10.1137/110853339

Cited by 92 publications

(61 citation statements)

References 22 publications

(55 reference statements)

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“…Although the distribution of σ ( T ) is known, the distribution of T 0 σ 2 (s )d s needs to be approximated. We propose a method based on a Fourier technique, which was already employed for Asian options in [15] . In Section 3 , this derivation is presented in detail.…”

Section: Sabr Monte Carlo Simulationmentioning

confidence: 99%

“…We first restrict the integration range to [ a , b ]. The calculation of integration boundaries a and b follows the cumulant-based approach as described in [15,20] . After truncation of the integral, we have…”

Section: Cdf Of Sabr's Time-integrated Variancementioning

confidence: 99%

“…, (n q / 2 + 1) and with n q the number of terms in the quadrature. This was the approach taken in [15] , with computational complexity O ( n q N 2 ). Piecewise linear approximation.…”

Section: Analytic Solution Based Onmentioning

confidence: 99%

“…(22) as stated in [15] , the error can be bounded by O ((2 n q ) −m /m ) for an m -times differentiable integrand, with n q the number of quadrature terms. When m is bounded, we achieve algebraic convergence while, otherwise, the error converges exponentially with respect to n q .…”

Section: Y (T )mentioning

confidence: 99%

“…The approximation of the cumulative distribution function (CDF) of the time-integrated variance is obtained by applying a recursive procedure, as described in [15] , which was originally developed to price arithmetic Asian options. The derivation is based on the definition of the characteristic function of the time-integrated variance and the use of Fourier inversion techniques.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Leitao

Grzelak

Oosterlee

2017

Applied Mathematics and Computation

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a b s t r a c tIn this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan's analytic formula for short maturities that may be employed for model calibration purposes.

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Section: Sabr Monte Carlo Simulationmentioning

confidence: 99%

Section: Cdf Of Sabr's Time-integrated Variancementioning

confidence: 99%

“…, (n q / 2 + 1) and with n q the number of terms in the quadrature. This was the approach taken in [15] , with computational complexity O ( n q N 2 ). Piecewise linear approximation.…”

Section: Analytic Solution Based Onmentioning

confidence: 99%

Section: Y (T )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Leitao

Grzelak

Oosterlee

2017

Applied Mathematics and Computation

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Efficient pricing of path‐dependent interest rate derivatives

Silva,

Baczynski,

Vicente

2024

Appl Stoch Models Bus & Ind

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Interest rate derivative pricing is a critical aspect of fixed‐income markets, where efficient methods are essential. This study introduces a novel approach to pricing path‐dependent interest rate derivatives within a broad class of affine jumps. The study's particular setting is the Fourier‐cosine series (COS) method adaptation, which offers an accurate and computationally efficient method for pricing interest rate derivatives. The Fourier‐cosine series approach can be used to compute probability density functions and option pricing with a linear computing complexity and exponential convergence rate. The lack of a quick and precise pricing technique for Asian interest rate options in diverse fixed‐income market scenarios is a research gap that is being addressed. This approach closes this gap by providing quasi‐closed and closed‐form equations for a range of density and characteristic functions, resulting in precise pricing. The results demonstrate the versatility of the COS method in interest rate markets. Similar to what has been previously reported for stock options, the numerical findings demonstrate the extreme precision and computing speed of the pricing and hedging estimations provided here. This method is an innovative approach to interest rate derivative pricing, offering researchers and practitioners a powerful tool for efficiently calculating prices and calibrating options across strikes and maturities.

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Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options

Choi

2018

Journal of Futures Markets

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Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black–Scholes–Merton (BSM) models, such as the basket, spread, and Asian options. The option price is expressed as a quadrature integration of analytic multi‐asset BSM prices under a single Brownian motion. Then the state space is rotated in such a way that the quadrature requires much coarser nodes than it would otherwise or low varying dimensions are reduced. The accuracy and efficiency of the method is illustrated through various numerical experiments.

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Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

Cited by 92 publications

References 22 publications

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Efficient pricing of path‐dependent interest rate derivatives

Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options

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