Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs

Fernández, José Luis Fernández; Ferreiro, A.; Garcia-Rodriguez, Jose; Leitao, Álvaro; López-Salas, José G.; Vázquez, Carlos

doi:10.1016/j.matcom.2013.05.007

Cited by 14 publications

(8 citation statements)

References 23 publications

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“…Almost all research using stochastic techniques reports issues with performance. GPU technology has been applied with simulated annealing to speed up the calibration [13], however a speed of 9.7 hours with one GPU is still too slow for real-time use.…”

Section: Stochastic Optimisation Methodsmentioning

confidence: 99%

Full and fast calibration of the Heston stochastic volatility model

Cui

Rollin

Germano

2017

European Journal of Operational Research

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This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston characteristic function and modify it to avoid discontinuities caused by branch switchings of complex functions. Using this representation, we obtain the analytical gradient of the price of a vanilla option with respect to the model parameters, which is the key element of all variants of the objective function. The interdependency between the components of the gradient enables an efficient implementation which is around ten times faster than a numerical gradient. We choose the Levenberg-Marquardt method to calibrate the model and do not observe multiple local minima reported in previous research. Two-dimensional sections show that the objective function is shaped as a narrow valley with a flat bottom. Our method is the fastest calibration of the Heston model developed so far and meets the speed requirement of practical trading.

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Section: Stochastic Optimisation Methodsmentioning

confidence: 99%

Full and fast calibration of the Heston stochastic volatility model

Cui

Rollin

Germano

2017

European Journal of Operational Research

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“…The usage of the “least squares Monte Carlo” in predicting the payoffs for American style options has been successfully shown by Longstaff and Schwartz (2001). Fernández et al (2013) used Monte Carlo simulations to calibrate the parameters for static and dynamic Stochastic Alpha, Beta, Rho models. The probability of optimal usage of hybridisation of parametric option pricing models such as the Black–Scholes–Merton and Monte Carlo Simulation versus nonparametric machine learning models has been tested by Das and Padhy (2017).…”

Section: Findings and Discussionmentioning

confidence: 99%

Research in market-calibrated option pricing analysis

Singh

Bhardwaj

Sharma

et al. 2019

QRFM

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Purpose This paper aims to consolidate and review the literature in the field of market-calibrated option pricing analysis. By doing so, the paper brings out the gaps in the extant literature and makes suggestions for future researchers in the field. Design/methodology/approach The methodology used in this research is inspired by the works of Ferreira et al. (2016), Jabbour (2013), Lage Junior and Godinho Filho (2010), Seuring (2013) and Sharma et al. (2018). A total of 1,500 papers written on the pricing of options globally are collated from the Web of Science ranging across 2010-2018. Findings Most of the research papers present mathematical proposals to value options; without calibrating it with real market data points. The authors bring out five important gaps in the extant literature. Originality/value This is arguably the first study that consolidates the literature in the field of market calibrated option pricing analysis with a view to suggest directions for future researchers.

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“…Some examples are used in [11], and differential evolution and particle swar are used in [15]. These methods are too computationally expensive for real-time use as [16], which employs GPU computations to calibrate options using an SV model called SABR, and it took 421.72 s to calibrate 12 instruments with a tolerance of 10 −2 using 2 NVIDIA Geforce GTX470 GPUs.…”

Section: Calibration Challengesmentioning

confidence: 99%

SWIFT Calibration of the Heston Model

Romo¹,

Ortiz-Gracia

2021

Mathematics

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In the present work, the SWIFT method for pricing European options is extended to Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The proposed calibration machinery appears to be extremely fast, in particular for a single expiry and multiple strikes, outperforming the state-of-the-art method we compare it with. Further, the a priori knowledge of SWIFT parameters makes a reliable and practical implementation of the presented calibration method possible. A wide range of stress, speed and convergence numerical experiments is carried out, with deep in-the-money, at-the-money and deep out-of-the-money options for very short and very long maturities.

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Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs

Cited by 14 publications

References 23 publications

Full and fast calibration of the Heston stochastic volatility model

Full and fast calibration of the Heston stochastic volatility model

Research in market-calibrated option pricing analysis

SWIFT Calibration of the Heston Model

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