Forecasting Commodity Markets Volatility: HAR or Rough?

Alfeus, Mesias; Nikitopoulos, Christina Sklibosios

doi:10.2139/ssrn.3520500

Cited by 5 publications

(9 citation statements)

References 10 publications

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“…Note that the ability to approximate the continuation value of LS for large values of M is limited by the use of a polynomial of small degree, a limitation imposed by the large size of the problem. The results presented in Table (4) have similar properties to those of Table (2), however, we observe that BC loses accuracy in this case.…”

Section: The Black-scholes Modelsupporting

confidence: 66%

“…Tables (2), ( 3) and ( 4) report the results for LS, GPR-GHQ, and BC for different values of M , by changing the numerical parameters of the methods. Specifically, ( 2) is referred to T = 0.2, while Table ( 4) is referred to T = 1.0.…”

Section: The Black-scholes Modelmentioning

confidence: 99%

“…Since moving average options are also used in the energy markets, we also test the GPR-GHQ method in the Clewlow-Strickland model for prices of energy commodities, which is able to match the forward curve and also provides mean reversion. [2] show that the volatility in the commodity market is rough, therefore we also consider the rough-Bergomi model, introduced by Bayer et al [3], which is a promising rough volatility model in quantitative finance. This latter model is particularly interesting as the underlying is as a process with fractional stochastic volatility.…”

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 Black-scholes Modelsupporting

confidence: 66%

Section: The Black-scholes Modelmentioning

confidence: 99%

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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“…Example 1. For (τ, s) ∈ ∆ T 2 , assume that the kernel K(τ, s) ∈ L(H) is given on the form K(τ, s) = (τ − s) −η A, where η ∈ (0, 1 2 ) and A ∈ L(H). Furthermore, for any α ∈ (0, 1 2 ) such that α > η, consider an α-Hölder continuous trajectory of an H-valued Q-Wiener process W .…”

Section: The Next Proposition Shows the Relation Between The Space Of...mentioning

confidence: 99%

“…X = I (W ). This tells us in particular that when we have constructed a Wiener processes on a probability space (Ω, F, P), and according to Kolmogorov's continuity theorem 3 found the set N c ⊂ Ω of full measure such that for each ω ∈ N c the mapping t → W (ω, t) has α−Hölder continuous trajectories for α ∈ (0, 1 2 ), then the trajectory…”

Section: The Next Proposition Shows the Relation Between The Space Of...mentioning

confidence: 99%

Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications

Benth¹,

Harang²

2020

Preprint

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We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals of deterministic kernels with respect to the Hölder continuous trajectories of Hilbertvalued Gaussian processes. To this end, we extend the Volterra sewing lemma from [18] to the two dimensional case, in order to construct two dimensional operator-valued Volterra integrals of Young type. We prove that the covariance operator associated to infinite dimensional Volterra processes can be represented by such a two dimensional integral, which extends the current notion of representation for such covariance operators. We then discuss a series of applications of these results, including the construction of a rough path associated to a Volterra process driven by Gaussian noise with possibly irregular covariance structures, as well as a description of the irregular covariance structure arising from Gaussian processes time-shifted along irregular trajectories. Furthermore, we consider an infinite dimensional fractional Ornstein-Uhlenbeck process driven by Gaussian noise, which can be seen as an extension of the volatility model proposed by Rosenbaum et al. in [13].

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The Changing Dynamics of Commodity Markets Volatility: Evidence from Major Commodity Indices

Trivedi,

Inamdar,

Baid

et al. 2023

Political Economy of Development in the Global South Post-Covid-19 Pandemic

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Forecasting Commodity Markets Volatility: HAR or Rough?

Cited by 5 publications

References 10 publications

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

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

Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications

The Changing Dynamics of Commodity Markets Volatility: Evidence from Major Commodity Indices

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