Forward Prices Research Articles

Iron ore spot price volatility and change in forward pricing mechanism

To examine the impact of the change in forward pricing mechanism on the volatility of iron ore spot prices, we model the iron ore daily price of Platts IODEX from October 7, 2008 to September 21, 2012. The identified iron ore spot price tends to be less volatile after the introduction of quarterly pricing mechanism. Our main approaches are as follows: (i) to decompose the spot price of Platts IODEX into two subsamples and relate the result of the structural break to the date of the switch in the iron ore forward pricing mechanism; (ii) to apply the EGARCH (1, 1) model to simultaneously capture the long memory and the asymmetric effect on the volatility of the iron ore spot price; and (iii) to delineate the news impact curve to further interpret the asymmetric effect.

Equilibrium forward risk premiums in electricity markets

This paper develops an equilibrium electricity forward pricing model which explicitly accounts for constrained capacity. The model is able to reproduce the price spikes observed in wholesale electricity markets using reasonable parameter values. The equilibrium forward premium, defined as the forward price minus the expected spot price, decreases in spot price variance when the expected spot price is less than the retail price, but increases in spot price variance when the expected spot price is greater than the retail price. The forward premium is an increasing function of the ratio of the expected spot price to the retail price.

Predicting realized volatility for Nord Pool forward prices by including volatility spillover and covariance effects

In this study, the current literature on volatility prediction in financial electricity markets is extended by incorporating volatility spillover and covariance effects. This is done using the concept of realized volatility and covariance with three financial electricity contracts traded at the Nord Pool exchange. A recently developed robust method to separate the total variation into continuous and jump components is applied. The results indicate that volatility spillover and covariance effects are clearly present in the three different contracts. The prediction accuracy is improved significantly when utilizing a multivariate framework (vector autoregressions) rather than a univariate one.

Analysis of the Iberian Power Forward Price Formation

<?Pub Dtl=""?> The price formation of the Iberian Energy Derivatives Market—the power futures market—starting in July 2006, is assessed until November 2011, through the evolution of the difference between forward and spot prices in the delivery period (“ex-post forward risk premium”) and the comparison with the forward generation costs from natural gas (“clean spark spread”). The premium tends to be positive in all existing mechanisms (futures, Over-the-Counter and auctions for catering part of the last resort supplies). Since year 2011, the values are smaller due to regulatorily recognized prices for coal power plants. The power futures are strongly correlated with European gas prices. The spreads built with prompt contracts tend also to be positive. The biggest ones are for the month contract, followed by the quarter contract and then by the year contract. Therefore, gas fired generation companies can maximize profits trading with contracts of shorter maturity.

Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes

This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled directly in stationarity. Second, stochastic volatility is regarded as a key factor for modelling energy spot prices. Third, the model allows for the possibility of jumps and extreme spikes and, lastly, it features great flexibility in terms of modelling the autocorrelation structure and the Samuelson effect. We provide a detailed analysis of the probabilistic properties of VMLV processes and show how they can capture many stylised facts of energy markets. Further, we derive forward prices based on our new spot price models and discuss option pricing. An empirical example based on electricity spot prices from the European Energy Exchange confirms the practical relevance of our new modelling framework.

Public Disclosure of Forward Contracts and Revelation of Proprietary Information

Financial executives of firms engaged in forward contracting have raised concerns that mandated disclosure of those contracts would reveal proprietary information to rival firms. This paper considers the basis for those concerns in the framework of a duopoly in which one privately informed producer enters the forward market prior to production. In choosing its forward position, the firm considers the effects of that position on the forward price and second stage product market competition with its rival. Two regimes are considered: mandated disclosure and no disclosure. Under the former, the contracting firm faces a tension between exploiting its information advantage in the forward market and attempting to influence the production decision of its rival. On average, in equilibrium, the contracting firm gains a first-mover advantage, but at the cost of revealing its private information to its rival and extracting less expected gains from uninformed forward market participants. In contrast, with no disclosure, the contracting firm cannot influence rival firm beliefs, but extracts more expected gains from its private information in both the forward and product markets. On balance, the contracting firm prefers no disclosure. Moreover, parameterizations exist such that the rival also prefers that regime. These findings explain the opposition of respondents to draft proposals of Statement of Financial Standards No. 133.

The forward pricing function of industrial metal futures – evidence from cointegration and smooth transition regression analysis

The prices of internationally traded metals have experienced wild swings and increased volatility in recent years. The relationship between spot and futures prices is an important topic in this context, as the current period’s price of a futures contract should be an unbiased estimator of next period’s spot price under the joint assumption of risk neutrality and rationality. Taking as a basis data from the Dow Jones UBS Commodity Index, which uses metals traded on the London Metal Exchange and US exchanges, this study adopts nonlinear smooth transition models to analyze whether the forward spread is a leading indicator of future spot price movements. Our findings suggest that such a price discovery function can in most cases only be identified in periods of low volatility or small previous spreads. Moreover, the underlying dynamics are captured best by the use of a logistic transition function.

The forward premium in electricity futures

Understanding the nature of the forward premium is particularly crucial, but rather elusive, for a non-storable commodity such as wholesale electricity. Whilst forward prices emerge as the expectation of spot plus, or minus, an ex ante premium for risk, the manifestation and empirical analysis must focus upon realised ex post premiums. This presents modelling requirements to control for shocks to the spot expectation as well as the endogeneity of ex post premia with spot price outcomes. In addition, because electricity is a derived commodity in the sense that market prices are often set by technologies that convert gas or coal into power, it is an open question whether much of the premia in power may actually be a pass-through of the premia in gas (or coal). Using a four dimensional VAR model we are able to distinguish fundamental and behavioural aspects of price formation in both the daily and monthly forward premia from the British market. We present new evidence on daily and seasonal sign reversals, associated with demand cycles, the greater importance of behavioural adaptations in the risk premia than fundamental or spot market risk measures, and the substantial fuel risk pass-through. We also show the value of a nonlinear specification in this context. • Futures for electricity are analysed through forward premia on expected spot prices. • These premia differ by time of day (peak and off-peak) and according to many drivers. • Behavioural drivers play a greater part in the peak periods. • Fundamental drivers are more influential in off-peak periods.

Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

Exact Forward in Monte-Carlo

We look at how to reproduce a nearly exact forward price in Monte-Carlo with a term structure of interest rates or a term structure of dividends, in the case of the Black-Scholes model, as well as the local volatility and stochastic volatility models.

A Square-Root T Hedging Rule for Nonstorable Products

This note derives a hedging rule under the assumption of noisy forward prices. Forward prices are assumed to be noisy due to non-storability of the underlying product and the resulting lack of carry arbitrage. The minimum-variance hedge ratio increases nonlinearly with decreasing time to maturity of the forward contract, as more information about the expected spot price arrives and the forward price becomes less noisy. If the noise component follows a process similar to a random walk, the precision of the forward price increases as a square-root function of the remaining trading time. By setting the initial hedge ratio according to hypothetically efficient prices, a producer overhedges and the minimum-variance hedge is not achieved.

Momentum and Reversion in Risk Neutral Martingale Probabilities

A time homogeneous, purely discontinuous, parsimonous Markov martingale model is proposed for the risk neutral dynamics of equity forward prices. Transition probabilities are in the variance gamma class with spot dependent parameters. Markov chain approximations give access to option prices. The model is estimated on option prices across strike and maturity for five days at a time. Properties of the estimated processes are described via an analysis of return quantiles, momentum functions that measure the response of tail probabilities to such moves. Momentum and reversion are also addressed via the construction of reverse conditional expectations. Term structures for the moments of marginal distributions support a decay in skewenss and excess kurtosis with maturity at rates slower than those implied by Levy processes. Out of sample performance is additionally reported. It is observed that risk neutral dynamics by and large reflect the presence of momentum in numerous probabilities. However, there is some reversion in the upper quantiles of risk neutral return distributions.

The Role of Hedging in Carbon Markets

In the European Emissions Trading System, power generators hold CO2 allowances to hedge for future power sales. First, we model their aggregate hedging demand in response to changes in expectations of future fuel, carbon and power prices from forward prices. This partial equilibrium analysis is then integrated into a two period model of the supply and demand of CO2 allowances considering also emissions impact and banking of allowances by speculative investors. We find that hedging flexibility can balance a CO2 allowance surplus in the range of 1.1-1.6 billion t CO2 at discount rates of future carbon allowances between 0-10%. If the surplus exceeds this level, then the rate at which today's carbon prices discount expected future prices increases. This points to the value of reducing the surplus estimated to be 2.6 billion t CO2 allowances in 2015 by about 1.3 billion t CO2, thus ensuring that hedging makes a significant contribution to stabilise carbon prices.

The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables

We have applied the Lie-Trotter operator splitting method to model the dynamics of both the sum and difference of two correlated constant elasticity of variance (CEV) stochastic variables. Within the Lie-Trotter splitting approximation, both the sum and difference are shown to follow a shifted CEV stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. These approximate probability distributions can be used to valuate two-asset options, e.g. spread options and basket options, where the CEV variables represent the forward prices of the underlying assets. Moreover, we believe that this new approach can be extended to study the algebraic sum of N CEV variables with potential applications in pricing multi-asset options.

Price Discovery in the Treasury‐Bill When‐Issued Market

AbstractWhen‐issued (i.e., forward) trading in T‐bills yet to be auctioned provides a unique environment for examining price discovery. Because T‐bills are auctioned in a sealed‐bid process, when‐issued traders cannot observe the spot market price. Yet the forward price must ultimately converge on the auction outcome price. Our results indicate that traders in the when‐issued market “discover” the ultimate auction price. Little evidence is found that standard order flow variables contribute to price discovery. Instead, the ability to observe a few trades with relatively small volume in the when‐issued market is sufficient to discover the auction price resulting from the sealed‐bid process.

A Comment on No-Arbitrage Pricing

In this short notice we present critical comments on no-arbitrage principle. We show that no-arbitrage pricing is complete in a pricing theory which ignores market risk and is dealing with the deterministic implied price of instruments. There is a unique price of a derivative in deterministic setting. The no-arbitrage pricing approach picks risk free bond which used as upfront funding instrument for financing deals. In such approach the underlying of the derivatives in deterministic setting becomes risk free bond. In stochastic setting no-arbitrage pricing replace real underlying on a virtual underlying that has risk free expected return and the original volatility. From our point of view this interpretation of the price of a derivative is incorrect. The derivatives pricing contains two steps. On the first step we define the ‘market price.’ This is the price for each admissible market scenario. On the second step we define a spot derivatives price. In some cases spot price can be implied price. In more complex situations for example such as options pricing construction of the spot price does not so simple. Given market and spot derivative prices we arrive at the market risk. The market risk by definition is the probability of scenarios that counterparty pays or loses more than it is implied by the spot price. Market and spot prices along with correspondent market risk is what we call derivatives price. We illustrate this approach by considering a forward contract pricing.

The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables

We have applied the Lie-Trotter operator splitting method to model the dynamics of both the sum and difference of two correlated constant elasticity of variance (CEV) stochastic variables. Within the Lie-Trotter splitting approximation, both the sum and difference are shown to follow a shifted CEV stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. These approximate probability distributions can be used to valuate two-asset options, e.g. spread options and basket options, where the CEV variables represent the forward prices of the underlying assets. Moreover, we believe that this new approach can be extended to study the algebraic sum of N CEV variables with potential applications in pricing multi-asset options.

Heterogeneous Beliefs, Regret, and Uncertainty: The Role of Speculation in Energy Price Dynamics

This paper proposes to investigate the impact of financialization on energy markets (oil, gas, coal and electricity European forward prices) during both normal times and extreme fluctuation periods through an original behavioral and emotional approach. To this aim, we propose a new theoretical and empirical framework based on a heterogeneous agents model in which fundamentalists and chartists co-exist and are subject to regret and uncertainty. We find significant evidence that energy markets are composed by heterogeneous traders which behave differently depending on the intensity of the price fluctuations and uncertainty context. In particular, energy prices are mainly governed by fundamental and chartist neutral agents during normal times whereas they face to irrational chartist averse investors during extreme fluctuations periods. In this context, the recent energy prices surge can be viewed as the consequence of irrational exhuberance. Our new theoretical model outperforms the random walk in out-of-sample predictive ability.

Electricity price modeling and asset valuation: a multi-fuel structural approach

We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity spot prices. The stack structure allows for a range of generator efficiencies per fuel type and for the possibility of future changes in the merit order of the fuels. The derived spot price process captures important stylized facts of historical electricity prices, including both spikes and the complex dependence upon its underlying supply and demand drivers. Furthermore, under mild and commonly used assumptions on the distributions of the input factors, we obtain closed-form formulae for electricity forward contracts and for spark and dark spread options. As merit order dynamics and fuel forward prices are embedded into the model, we capture a much richer and more realistic dependence structure than can be achieved by classical reduced-form models. We illustrate these advantages by comparing with Margrabe's formula and a simple cointegration model, and highlight important implications for the valuation of power plants.