A Two-Factor Model for Commodity Prices and Futures Valuation

Ribeiro, Diana; Hodges, Sarah

doi:10.2139/ssrn.498802

Cited by 24 publications

(19 citation statements)

References 24 publications

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“…A natural direction for future research is to investigate the trading strategies under a multi-factor or time-varying mean-reverting spot price model. To this end, we include here some references that discuss the pricing aspect of futures under such models, for example, Detemple and Osakwe (2000), Lu and Zhu (2009), Zhu and Lian (2012), Mencía and Sentana (2013) for VIX futures, Schwartz (1997), Ribeiro and Hodges (2004) for commodities, and Monoyios and Sarno (2002) for equity index futures. It is also of practical interest to develop similar optimal multiple stopping approaches to trading commodities under mean-reverting spot models (Leung et al , 2014, and credit derivatives trading (Leung and Liu 2012).…”

Section: Resultsmentioning

confidence: 99%

Speculative Futures Trading under Mean Reversion

Leung

et al. 2016

Asia-Pac Financ Markets

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This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck, Cox-Ingersoll-Ross, or exponential OrnsteinUhlenbeck model. The futures term structure is derived and its connection to futures price dynamics is examined. For each futures contract, we describe the evolution of the roll yield, and compute explicitly the expected roll yield. For the futures trading problem, we incorporate the investor's timing option to enter or exit the market, as well as a chooser option to long or short a futures upon entry. This leads us to formulate and solve the corresponding optimal double stopping problems to determine the optimal trading strategies. Numerical results are presented to illustrate the optimal entry and exit boundaries under different models. We find that the option to choose between a long or short position induces the investor to delay market entry, as compared to the case where the investor pre-commits to go either long or short.

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Section: Resultsmentioning

confidence: 99%

Speculative Futures Trading under Mean Reversion

Leung

et al. 2016

Asia-Pac Financ Markets

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“…, n) futures and forward prices were considered separately in Hyndman [22] where we employed a version of the flows method. Examples of models covered by Assumptions 1-3 which incorporate factors that are not all Gaussian include the models of Ribeiro and Hodges [35] and Heston [18] as well as the continuous version of Björk and Landén [1].…”

Section: Assumptionmentioning

confidence: 99%

A forward–backward SDE approach to affine models

Hyndman

2009

Math Finan Econ

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We consider factor models for interest rates and asset prices where the riskneutral dynamics of the factors process is modelled by an affine diffusion. We characterize the factors process and bond price in terms of forward-backward stochastic differential equations (FBSDEs), prove an existence and uniqueness theorem which gives the solution explicitly, and characterize the bond price as an exponential affine function of the factors in a new way. Our approach unifies the results, based on stochastic flows, of Elliott and van der Hoek (Finance Stoch 5: [511][512][513][514][515][516][517][518][519][520][521][522][523][524][525] 2001) with the approach, based on the Feynman-Kac formula, of Duffie and Kan (Math Finance 6(4): 1996), and addresses a mistake in the approach of Elliott and van der Hoek (Finance Stoch 5:511-525, 2001). We extend our results on the bond price to consider the futures and forward price of a risky asset or commodity.Keywords Affine models · Forward-backward stochastic differential equations · Stochastic flows · Bond price · Futures price · Forward price JEL Classification E43 · G12 · G13 Mathematics Subject Classification (2000) 60G35 · 60H20 · 60H30 · 91B28 · 91B70

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“…This implies that if the initial spot-price is very low when compared to the long-run mean price, the forward curve does not reach steady-state equilibrium within a realistic length of time. This result diverges from the analysis of the forward curve provided by Routledge et al (2000) and Ribeiro and Hodges (2004b). The other drawback is that the spot-price distribution is left skewed, which is not a desirable property in commodity price distributions.…”

Section: Resultsmentioning

confidence: 56%

“…The empirical calibration of the two-factor models developed by Schwartz (1997), Nielsen and Schwartz (2004) and Ribeiro and Hodges (2004b) show that there is a very strong correlation between the spot price and the convenience yield dynamics, particularly in the oil market and industrial metals. This motivates the question of whether a two-factor model is essential to capture the commodity spot-price movements or if an arbitrage-free single-factor model would explain much of the empirical behavior.…”

Section: Introductionmentioning

confidence: 99%

A contango-constrained model for storable commodity prices

Ribeiro

Hodges

2005

J. Fut. Mark.

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This article presents a model of commodity price dynamics under the riskneutral measure where the spot price switches between two distinct stochastic processes depending on whether or not inventory is being held. Specifically, the drift of the spot price is equal to the cost of carry when the stock is positive. Conversely, whenever the drift of the spot price is less than the cost of carry, no inventory is being held.

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A Two-Factor Model for Commodity Prices and Futures Valuation

Cited by 24 publications

References 24 publications

Speculative Futures Trading under Mean Reversion

Speculative Futures Trading under Mean Reversion

A forward–backward SDE approach to affine models

A contango-constrained model for storable commodity prices

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