A Two-Factor Cointegrated Commodity Price Model with an Application to Spread Option Pricing

Farkas, Walter; Gourier, Elise; Huitema, Robert; Necula, Ciprian

doi:10.2139/ssrn.2679218

Cited by 5 publications

(14 citation statements)

References 48 publications

(21 reference statements)

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“…We employed the continuous time model of cointegrated commodity prices developed in Farkas et al [6] and conducted a simulation study for a cointegrated system of three commodities. We calculated the prices of several spread options and found that cointegration significantly influences these prices.…”

Section: Discussionmentioning

confidence: 99%

“…Before proceeding to the simulation study, in this section we present for the sake of completeness, a short description of the model developed in Farkas et al [6].…”

Section: Outline Of the Modelmentioning

confidence: 99%

“…In this work we employ the continuous time model of cointegrated commodity prices developed by the authors in Farkas et al [6] in order to conduct a simulation study for assessing the impact of cointegration on spread options. In our model, commodity prices are non-stationary and several cointegration relations are allowed amongst them, capturing long-run equilibrium relationships.…”

mentioning

confidence: 99%

“…Although they explicitly take into account cointegration between prices, the cointegrated systems generated by these two models are not covering the whole range of possible number of cointegration relations, but allow for none or for exactly n − 1 relations to exist between the n prices. In Farkas et al [6] we propose an easy-to-use, yet comprehensive, model for a system of cointegrated commodity prices that retains the exponential affine structure of previous approaches and allows, in the same time, for an arbitrary number of cointegration relationships.…”

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confidence: 99%

“…In Sect. 2 we briefly describe the model proposed in Farkas et al [6] and point out some qualitative aspects regarding the dynamics of the system. Section 3 is devoted to an extensive simulation study focused on computing spread options prices and on assessing the impact of cointegration on pricing spread options.…”

mentioning

confidence: 99%

See 4 more Smart Citations

The Impact of Cointegration on Commodity Spread Options

Farkas

Gourier

Huitema

et al. 2016

Innovations in Derivatives Markets

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In this work we explore the implications of cointegration in a system of commodity prices on the premiums of options written on various spreads on the futures prices of these commodities. We employ a parsimonious, yet comprehensive model for cointegration in a system of commodity prices. The model has an exponential affine structure and is flexible enough to allow for an arbitrary number of cointegration relationships. We conduct an extensive simulation study on pricing spread options. We argue that cointegration creates an upward sloping term structure of correlation, that in turn lowers the volatility of spreads and consequently the price of options on them.

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Section: Discussionmentioning

confidence: 99%

“…Before proceeding to the simulation study, in this section we present for the sake of completeness, a short description of the model developed in Farkas et al [6].…”

Section: Outline Of the Modelmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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The Impact of Cointegration on Commodity Spread Options

Farkas

Gourier

Huitema

et al. 2016

Innovations in Derivatives Markets

Self Cite

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Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

Ackooij¹,

Escobar

Glanzer

et al. 2019

Comput Manag Sci

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The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. However, also this approach has its limitations, since quite often the models for costs and revenues are subject to model error. Under a prudent valuation, the possible model error should be incorporated into the calculation. In this paper, we consider the valuation of a power plant under ambiguity of probability models for costs and revenues. The valuation is done by stochastic dynamic programming and on top of it, we use a dynamic ambiguity model for obtaining the prudent minimax valuation. For the valuation of the power plant under model ambiguity we introduce a distance based on the Wasserstein distance. Another highlight of this paper is the multiscale approach, since decision stages are defined on a weekly basis, while the random costs and revenues appear on a much finer scale. The idea of bridging stochastic processes is used to link the weekly decision scale with the finer simulation scale. The applicability of the introduced concepts is broad and not limited to the motivating valuation problem.

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Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework

2019

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One of the peculiarities of power and gas markets is the delivery mechanism of forward contracts. The seller of a futures contract commits to deliver, say, power, over a certain period, while the classical forward is a financial agreement settled on a maturity date. Our purpose is to design a Heath-Jarrow-Morton framework for an additive, mean-reverting, multicommodity market consisting of forward contracts of any delivery period. Even for relatively simple dynamics, we face the problem of finding a density between a risk-neutral measure Q, such that the prices of traded assets like forward contracts are true Q-martingales, and the real world probability P, under which forward prices are mean-reverting. By assuming that forward prices can be represented as affine functions of a universal source of randomness, we can completely characterize the models which prevent arbitrage opportunities. In this respect, we prove two results on the martingale property of stochastic exponentials. The first allows to validate measure changes made of two components: an Esscher-type density and a Girsanov transform with stochastic and unbounded kernel. The second uses a different approach and works for the case of continuous density. We show how this framework provides an explicit way to describe a variety of models by introducing, in particular, a generalized Lucia-Schwartz model and a cross-commodity cointegrated market.

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A Two-Factor Cointegrated Commodity Price Model with an Application to Spread Option Pricing

Cited by 5 publications

References 48 publications

The Impact of Cointegration on Commodity Spread Options

The Impact of Cointegration on Commodity Spread Options

Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework

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