Abstract:Abstract. The goal of this survey is to review the major idiosyncrasies of the commodity markets and the methods which have been proposed to handle them in spot and forward price models. We devote special attention to the most idiosyncratic of all: electricity markets. Following a discussion of traded instruments, market features, historical perspectives, recent developments and various modeling approaches, we focus on the important role of other energy prices and fundamental factors in setting the power price… Show more
“…This is a special case of a formula in [7,6] which conveniently rewrites the integral of the product of an exponential, a univariate Gaussian density and Gaussian cdf as a simple bivariate Gaussian cdf (which collapses again to a univariate cdf when integrating over (−∞, ∞) as above). In this case, we obtain the following closed-form expression:…”
Section: 2mentioning
confidence: 99%
“…While such approaches may be successful for capturing price spikes and overall price distributions, they rarely capture the complicated dependence structure between price, load and other factors, which is equally vital for hedging purposes in practice. Hence, we instead favor the category often known as 'structural' models, as reviewed for example in the recent survey paper of [6]. In such a model, power price is written as a function of several underlying supply and demand factors, and its dynamics are therefore not specified directly through an SDE (stochastic differential equation), but produced indirectly as a result of the dynamics chosen for the factors.…”
Abstract. Energy companies with commitments to meet customers' daily electricity demands face the problem of hedging load and price risk. We propose a joint model for load and price dynamics, which is motivated by the goal of facilitating optimal hedging decisions, while also intuitively capturing the key features of the electricity market. Driven by three stochastic factors including the load process, our power price model allows for the calculation of closed-form pricing formulas for forwards and some options, products often used for hedging purposes. Making use of these results, we illustrate in a simple example the hedging benefit of these instruments, while also evaluating the performance of the model when fitted to the Texas electricity market.
“…This is a special case of a formula in [7,6] which conveniently rewrites the integral of the product of an exponential, a univariate Gaussian density and Gaussian cdf as a simple bivariate Gaussian cdf (which collapses again to a univariate cdf when integrating over (−∞, ∞) as above). In this case, we obtain the following closed-form expression:…”
Section: 2mentioning
confidence: 99%
“…While such approaches may be successful for capturing price spikes and overall price distributions, they rarely capture the complicated dependence structure between price, load and other factors, which is equally vital for hedging purposes in practice. Hence, we instead favor the category often known as 'structural' models, as reviewed for example in the recent survey paper of [6]. In such a model, power price is written as a function of several underlying supply and demand factors, and its dynamics are therefore not specified directly through an SDE (stochastic differential equation), but produced indirectly as a result of the dynamics chosen for the factors.…”
Abstract. Energy companies with commitments to meet customers' daily electricity demands face the problem of hedging load and price risk. We propose a joint model for load and price dynamics, which is motivated by the goal of facilitating optimal hedging decisions, while also intuitively capturing the key features of the electricity market. Driven by three stochastic factors including the load process, our power price model allows for the calculation of closed-form pricing formulas for forwards and some options, products often used for hedging purposes. Making use of these results, we illustrate in a simple example the hedging benefit of these instruments, while also evaluating the performance of the model when fitted to the Texas electricity market.
“…In recent times, stochastic models of commodity futures prices have played a central role in evaluating commodity-related securities among academics and practitioners, such as Schwartz (1997), Schwartz and Smith (2000), Sorensen (2002), Cortazar and Schwartz (2003), Cortazar and Naranjo (2006), Mirantes, Poblacion and Serna (2012), Carmona and Coulon (2014), and et al. A detailed survey of these types of models is written by Pirrong (2011).…”
“…Long-side options in futures markets depend totally on the idiosyncrasies of each commodity's exchange traded structure. The survey paper by Carmona and Coulon (2013) demonstrates the appropriate model for a commodity varies highly depending on storability, instantaneous utility, and alternatives. At expiration, a CBOT agricultural futures contract does not deliver the physical grains but an artificial instrument called the shipping certificate that entitles its holder to demand loading of the grains from a warehouse at any time.…”
This paper studies the market phenomenon of non-convergence between futures and spot prices in the grains market. We postulate that the positive basis observed at maturity stems from the futures holder's timing options to exercise the shipping certificate delivery item and subsequently liquidate the physical grain. In our proposed approach, we incorporate stochastic spot price and storage cost, and solve an optimal double stopping problem to give the optimal strategies to exercise and liquidate the grain. Our new models for stochastic storage rates lead to explicit no-arbitrage prices for the shipping certificate and associated futures contract. We calibrate our models to empirical futures data during the periods of observed non-convergence, and illustrate the premium generated by the shipping certificate.
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