Evaluation of gas sales agreements with indexation using tree and least-squares Monte Carlo methods on graphics processing units

Dong, Wenfeng; Kang, Boda

doi:10.1080/14697688.2020.1775283

Cited by 4 publications

(2 citation statements)

References 31 publications

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“…The parameters for the Clewlow-Strickland model are the same used by Dong and Kang [14] (see Table (6)). Tables (7) and ( 8) report the numerical results for different values of M and for different parameter configurations.…”

Section: The Clewlow-strickland Modelmentioning

confidence: 99%

“…Finally, it is worth mentioning the works of Dong and Kang [13,14] who study a particular type of swing contracts that include a moving average feature, by means of a two-dimensional trinomial tree and least squares Monte Carlo methods. To conclude this review, we also mention the research on the dynamic hedging of moving average options of Warin [27].…”

Section: Introductionmentioning

confidence: 99%

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Moving average options: Machine Learning and Gauss-Hermite quadrature for a double non-Markovian problem

Goudenège¹,

Molent²,

Zanette³

2021

Preprint

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Evaluating moving average options is a tough computational challenge for the energy and commodity market as the payoff of the option depends on the prices of a certain underlying observed on a moving window so, when a long window is considered, the pricing problem becomes high dimensional. We present an efficient method for pricing Bermudan style moving average options, based on Gaussian Process Regression and Gauss-Hermite quadrature, thus named GPR-GHQ. Specifically, the proposed algorithm proceeds backward in time and, at each time-step, the continuation value is computed only in a few points by using Gauss-Hermite quadrature, and then it is learned through Gaussian Process Regression. We test the proposed approach in the Black-Scholes model, where the GPR-GHQ method is made even more efficient by exploiting the positive homogeneity of the continuation value, which allows one to reduce the problem size. Positive homogeneity is also exploited to develop a binomial Markov chain, which is able to deal efficiently with medium-long windows. Secondly, we test GPR-GHQ in the Clewlow-Strickland model, the reference framework for modeling prices of energy commodities. Finally, we consider a challenging problem which involves double non-Markovian feature, that is the rough-Bergomi model. In this case, the pricing problem is even harder since the whole history of the volatility process impacts the future distribution of the process. The manuscript includes a numerical investigation, which displays that GPR-GHQ is very accurate and it is able to handle options with a very long window, thus overcoming the problem of high dimensionality.

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Section: The Clewlow-strickland Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%