The COS method for option valuation under the SABR dynamics

Have, Z. Van der; Oosterlee, Cornelis W.

doi:10.1080/00207160.2017.1290438

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…The reason for working with the characteristic function is twofold. First, the conditional probability p(x|x 0 ) is only known analytically in very few special cases, while analytic expressions for the characteristic function are more widely known (e.g., Black-Scholes-Merton [17], Heston [18]) or can be approximated (e.g., SABR [15,19]). Second, the function is more stable in the Fourier domain for small time steps due to the uncertainty principle.…”

Section: B Fourier Options Pricingmentioning

confidence: 99%

“…We now discuss the numerical evaluation of the single asset formula in Eq. (19). The multi-asset extension is straightforward.…”

Section: Discretizationmentioning

confidence: 99%

“…In the single asset case, we compare the convergence of the Monte Carlo algorithm in the number of samples to the Fourier method [Eq. (19)] and the direct method [Eq. ( 13)] in the number of interpolation points.…”

Section: A the Single Asset Casementioning

confidence: 99%

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A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Kastoryano¹,

Pancotti²

2022

Preprint

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Section: B Fourier Options Pricingmentioning

confidence: 99%

“…We now discuss the numerical evaluation of the single asset formula in Eq. (19). The multi-asset extension is straightforward.…”

Section: Discretizationmentioning

confidence: 99%

See 1 more Smart Citation

A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Kastoryano¹,

Pancotti²

2022

Preprint

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“…For example, Deng et al [31] used the 1D COS method for equity-indexed annuity products under general exponential Lévy models; Alonso-García et al [32] extended the 1D COS method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdraw benefit riders. The latest research on Fourier transform was given by Zhang et al [33], Chan [34], Zhang and Liu [35], Have and Oosterlee [36], Shimizu and Zhang [37], Tour [38], Zhang [39], and Wang et al [40].…”

Section: Introductionmentioning

confidence: 99%

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Yong

Guan

et al. 2019

Mathematics

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Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

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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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The COS method for option valuation under the SABR dynamics

Cited by 6 publications

References 35 publications

A highly efficient tensor network algorithm for multi-asset Fourier options pricing

A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Efficient pricing of path‐dependent interest rate derivatives

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