Forward Prices Research Articles

Modeling the Dynamics of Implied Volatility Surfaces

The objective of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surface. The approach is similar to the Dumas, Fleming and Whaley (DFW) (1998) study; we use moneyness (e.g., in forward price) and out-of-the-money (OTM) put-call options on FTSE100 index. After these adjustments, the nonlinear parametric optimization technique is employed to estimate different models of DFW in order to characterize the implied volatility surfaces and produce smooth implied volatility surfaces. Next, principal component analysis (PCA) is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surface. Hence, we estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smile and time to maturity, and, therefore, the constant volatility model fails to explain the variations in the surfaces. Finally, we find that the first three principal components can explain about 69-82% of the variances in the implied volatility surfaces. The applications of our study are hedging of derivatives positions, trading, risk management, and policy making.

Spot and Forward Prices in the Brussels SE: Time Value v. Convenience Premiums

Until the mid-90s, the more active among the Brussels-listed stocks were traded in two parallel segments: spot'' (that is, with (t 3) settlement) and forward'' (periodic settlement at the end of a two- or three-week period). In this paper we study the opening prices from the angle of what drives the observed forward premiums. We test whether forward premiums are related to time to settlement and interest rates, and, if not, whether they seem to reflect extra costs (or shadow costs) of running out of either cash balances or long stock positions.The settlement effect is tested in each market separately and then on cross-market price differences. In spot markets there is very little evidence in favor or against a settlement effect, perhaps because the time value item has a very small variability. As expected, the time value signals are somewhat stronger in forward prices and noticeably so in forward premiums, but the estimates remain below our theoretical priors.Next, we show theoretically that a positive forward premium is more likely in a situation in which the order volume from cash-constrained buyers exceeds that of sellers without a long position. Likewise, a negative forward premium typically means that the order volume from sellers without long positions exceeds that of cash-constrained buyers. We find that abnormally high forward premiums are 2.5-3 times more frequent and larger than negative premiums, and that they persist in time, unlike negative premiums. Thus, contrary to what many academics may have expected, getting money loans seems to be a more frequent, more expensive, and more persistent problem than asset borrowing.

More Friction, Less Noise? Relative Efficiency in a Two-Tier Stock Exchange

If trading becomes easier and cheaper, does this attract more noise trades or more informed trades? We investigate this question in the Brussels market, where about 100 stocks were simultaneously traded in two parallel tiers, whereof one, the forward'' segment, was organizationally far superior than the tier. In an exploratory test based on Roll (1984), we write spot and forward prices as equal to a common true value, plus a market-specific settlement effect (a correction for time value until payment), plus an unpredictable noise term. We expect to find that in the forward markets the noise has lower variance, that is, the pricing is more efficient. Yet we find no such thing; in fact, by some measures the forward market may actually have been the more noisy one.Going on to the issue of price discovery, which is a more formal way of testing whether the forward market is less noisy, we extend the Margrabe-Silber price-discovery model to take into account the asynchronism in the opening forward and spot prices. Although the presence of the latent true morning return in our extended model precludes us from estimating explicitly the price adjustment coefficients, we can still identify the sign of the estimated difference of these coefficients and the lower and upper bounds of its t-statistic. This information enables us to conclude on the significance of the test. Also, our results reject the potential price discoverer status of the forward market: spot prices seem more informative than forward prices. Even more puzzlingly, the phenomenon is most pronounced for active stocks. For robustness, our Hasbrouck (1995) information-share analysis also supports this finding. This result raises the issue of how far the financial markets perform their central function of price discovery and how far the conventional wisdom can be trusted (e.g. the higher the trading volume or the lower the friction, the less noise the observed price contains).

Price formation in electricity forward markets and the relevance of systematic forecast errors

Since the liberalisation of the European electricity sector, forward and futures contracts have gained significant interest of market participants due to risk management reasons. For pricing of these contracts an important fact concerns the non-storability of electricity. In this case, according to economic theory, forward prices are related to the expected spot prices which are built on fundamental market expectations. In the following article the crucial impact parameters of forward electricity prices and the relationship between forward and future spot prices will be assessed by an empirical analysis of electricity prices at the European Energy Exchange and the Nord Pool Power Exchange. In fact, price formation in the considered markets is influenced by historic spot market prices yielding a biased forecasting power of long-term contracts. Although market and risk assessment measures of market participants and supply and demand shocks can partly explain the futures-spot bias inefficiencies in the analysed forward markets cannot be ruled out.

Table of Contents

Abstract Features Force Majeure to Apply Small Comfort to Some Crisis‐Affected Contracts A. Michael Sabino Anticipated Recession Effects—Natural Gas Recession Aside, Depending on NYMEX Forward Price Curve Is Mistake Dale M. Nesbitt and Thomas Y. Choi Anticipated Recession Effects—Gas Prices Natural Gas Prices in a Recession Christopher Gulick Anticipated Recession Effects—Storage Can Gas Storage Development Survive the Recent Financial Market Collapse? Kenneth L. Beckman Anticipated Recession Effects FERC Winter Outlook Shows Changing Economic Conditions, Falling Prices FERC Staff Columns Federal Regulation and Energy Issues Is the Era of Big Government Back? James J. Hoecker Energy and the Environment Measuring the Costs and the Benefits of Energy Development Jonathan A. Lesser

Optimization-Based Generation Asset Allocation for Forward and Spot Markets

One of the most important daily decisions that a Genco has to make is to allocate generation assets between the forward and spot markets. That is, how much capacity should be contracted in the forward market and how much should be kept to bid in spot market? This paper focuses on generation asset allocation between monthly forward contracts, such as bilateral contracts, futures contracts, options contracts, and daily spot markets, considering operating costs and constraints of generating units, as well as spot price risk. The problem is to find the optimal hedging position based on the known forward price and the forecasted hourly spot prices and is formulated based on the model of PJM market. The double dynamic programming method is applied to solve this optimal asset allocation problem with all the short-term operating constraints of the generating unit satisfied. Three types of forward contracts that are commonly used in practice are considered and their impact on generation asset allocation are analyzed and compared. The analytic relationship between the optimal contract quantity of a particular type and spot generation is established. Based on this relationship, the applicability and characteristics of a particular type of contract are discussed. Furthermore, with the solution to the generation asset allocation problem as a basis, the pricing strategy in the forward market is analyzed. A Nash game model is established and an iterative process is developed to determine the equilibrium pricing of futures contracts. Numerical testing shows that the method for the generation asset allocation is effective. Various factors influencing the decision of generation asset allocation and the relationship between futures contract price and spot price are tested and analyzed.

Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios

We derive in closed form distribution free lower bounds and optimal subreplicating strategies for spread options in a one-period static arbitrage setting. In the case of a continuum of strikes, we complement the optimal lower bound for spread options obtained in [Rapuch, G., Roncalli, T., 2002. Pricing multiasset options and credit derivatives with copula, Credit Lyonnais, Working Papers] by describing its corresponding subreplicating strategy. This result is explored numerically in a Black–Scholes and in a CEV setting. In the case of discrete strikes, we solve in closed form the optimization problem in which, for each asset S 1 and S 2 , forward prices and the price of one option are used as constraints on the marginal distributions of each asset. We provide a partial solution in the case where the marginal distributions are constrained by two strikes per asset. Numerical results on real NYMEX (New York Mercantile Exchange) crack spread option data show that the one discrete lower bound can be far and also very close to the traded price. In addition, the one strike closed form solution is very close to the two strike.

Can Companies Use Hedging Programs to Profit from the Market? Evidence from Gold Producers*

In this article, the authors summarize the findings of their recent study of the hedging activities of 92 North American gold mining companies during the period 1989‐1999. The aim of the study was to answer two questions: (1) Did such hedging activities increase corporate cash flows? (2) And if yes, were such increases the result of management's ability to anticipate price movements when adjusting their hedge ratios? Although the author's answer to the first question is “yes,” their answer to the second is “no.”More specifically, the authors concluded that: During the 1989‐1999 period, the gold derivatives market was characterized by a persistent positive risk premium— that is, a positive spread between the forward price and the realized future spot price—that caused short forward positions to generate positive cash flows. The gold mining companies that hedged their future gold production realized an average total cash flow gain of $11 million, or $24 per ounce of gold hedged, per year, as compared to average annual net income of only $3.5 million. Because of the positive risk premium, short derivatives positions did not generate significant losses even during those subperiods of the study when the gold price increased. There was considerable volatility in corporate hedge ratios during the period of the study, which is consistent with managers incorporating market views into their hedging programs and attempting to time the market by hedging selectively. But after attempting to distinguish between derivatives activities designed to hedge and those designed to profit from a view, the authors conclude that corporate efforts to time the market through selective hedging were largely if not completely futile. In fact, the companies' adjustments of hedge ratios appeared to consistently lag instead of leading the market.

Erratum: Ship funds as a new asset class: An empirical analysis of the relationship between spot and forward prices in freight markets

Erratum: Ship funds as a new asset class: An empirical analysis of the relationship between spot and forward prices in freight markets

Counterparty Risk Valuation for Energy-Commodities Swaps: Impact of Volatilities and Correlation

It is commonly accepted that Commodities futures and forward prices, in principle, agree under some simplifying assumptions. One of the most relevant assumptions is the absence of counterparty risk. Indeed, due to margining, futures have practically no counterparty risk. Forwards, instead, may bear the full risk of default for the counterparty when traded with brokers or outside clearing houses, or when embedded in other contracts such as swaps. In this paper we focus on energy commodities and on Oil in particular. We use a hybrid commodities-credit model to assess impact of counterparty risk in pricing formulas, both in the gross effect of default probabilities and on the subtler effects of credit spread volatility, commodities volatility and credit-commodities correlation. We illustrate our general approach with a case study based on an oil swap, showing that an accurate valuation of counterparty risk depends on volatilities and correlation and cannot be accounted for precisely through a pre-defined multiplier.

Ship funds as a new asset class: An empirical analysis of the relationship between spot and forward prices in freight markets

Over the last decade, various new asset classes have emerged as alternatives to the more traditional investments. Although they appear attractive at a first glance, there exists hardly any historical performance track record, and experience with the return generating variables is limited. For ship funds and the valuation of shipping projects, the prevailing freight rates are important price-determining factors. Therefore, knowledge about the time series properties of spot and forward freight rates is essential for a better understanding of the return generating process of ship funds. There are, however, several peculiarities. Because shipping is a nonstorable service, forward prices need not to be linked to spot prices by any direct arbitrage relationship. We test the implications of this notion by using data for Panamax size bulk carriers and find that even in informationally efficient markets spot freight rates are highly autocorrelated. In addition, spot and forward freight rates are cointegrated, and the equilibrium is established by spot rates converging to forward rates. An extension of the standard vector error correction model reveals time-variation in the adjustment speed. Overall, our empirical findings suggest that the time series properties of freight rates need to be well understood before investing in ship funds. Another important aspect is whether ship funds should hedge their freight rate exposure in the forward market to reduce the return volatility or whether investors can achieve the same outcome by holding ship funds in a portfolio context.

Market Power in Power Markets: Evidence from Forward Prices of Electricity

We examine the forward market for electricity for indications of misuse of market power, using a unique data set on OTC price indications posted by Elsam A/S, the dominant producer in Western Denmark, which is one of the price areas under the Nordic power exchange Nord Pool. The Danish Competition Council (the regulatory government agency) has ruled that Elsam has used its dominant position to obtain excessive spot prices over a period from July 2003 through December 2006. We show that significant forward premia exist, and that they are related both to spot market volatility and misuse of market power in the spot market, indicating that misuse of market power in the forward market accompanied that which took place in the spot market, according to this ruling. This is consistent with the hypothesis that Elsam used the forward market to disguise its spot market manipulation. The findings are consistent across forward premium regressions and structural forward pricing models.

Can Companies Use Hedging Programs to Profit from the Market? Evidence from Gold Producers

The literature on corporate risk management has traditionally assumed that derivative securities are fairly priced, and thus disregarded the possibility that non-financial firms might use derivatives to generate positive returns by exploiting market conditions. This premise has led researchers to rationalize corporate risk management by its beneficial effects on bankruptcy costs and taxes, debt capacity, cost of capital, underinvestment costs, and managerial risk aversion. Our study questions this fundamental premise and thereby makes two principal contributions. First, we show that the assumption that derivatives contracts are fairly priced on average can be violated for an extended period. By studying the hedging activities of a sample of North American gold mining companies over the 1989-1999 period, we find that these firms generated significant excess cash flows by selling gold forward. Our sample firms realized an average total cash flow gain of $11 million or $24 per ounce of gold per year, while their average annual net income was only $3.5 million. The source of these gains is a persistently positive spread between contracted forward prices and realized spot prices. This finding highlights a new motive for the corporate use of derivatives and a new potential source of value associated with risk management that the literature has previously ignored. Second, and in contrast to our first contribution, we show that firms do not realize economically significant cash flow gains by trying to time the market in their use of derivatives. Market-timing in the context of hedging programs is a form of speculation. We find considerable evidence in our sample that managers respond to changing market prices by varying the sizes of their hedge positions, and that this variation is far in excess of what can be explained by changes in a firm's fundamentals. However, these attempts to time the market do not yield positive cash flows on average. We conclude that managers in our study have no market-timing ability and speculating in this way creates no value (and probably destroys value) for shareholders. This finding is in stark contrast to a widely-held view among many corporate executives that market timing should be an integral part of any hedging program.

Risk Management and Optimal Pricing in Online Storage Grids

Online storage service providers such as Amazon S3 grant a way for companies, particularly startups, to avoid spending resources on maintaining their own in-house storage infrastructure and thereby allowing them to focus on their core business activities. These providers however follow a fixed, posted pricing strategy which charges the same price in each time period and thus bear all the risk arising out of demand uncertainties faced by their client companies. We examine the effects of providing a spot market with dynamic prices and forward contracts to hedge against future revenue uncertainty. We derive revenue-maximizing spot and forward prices for a single seller facing a known set of buyers. We perform a simulation study using publicly available traffic data regarding Amazon S3 clients from Alexa.com to validate our analytical results. Our field study supports our analysis and indicates that spot markets alone can enhance revenues to Amazon but this comes at the cost of increased risks, due to the increased market share in the spot markets. Furthermore, adding a forward contract feature to the spot markets can reduce risks while still providing the benefits of enhanced revenues. While the buyers incur an increase in costs in the spot market, adding a forward contract does not cause any additional cost increase while transferring the risk to the buyers. Thus storage grid providers can greatly benefit by applying a forward contract alongside the spot market.

Risk Management and Optimal Pricing in Online Storage Grids

Online storage service providers grant a way for companies to avoid spending resources on maintaining their own in-house storage infrastructure and thereby allowing them to focus on their core business activities. These providers, however, follow a fixed, posted pricing strategy that charges the same price in each time period and thus bear all the risk arising out of demand uncertainties faced by their client companies. We examine the effects of providing a spot market with dynamic prices and forward contracts to hedge against future revenue uncertainty. We derive revenue-maximizing spot and forward prices for a single seller facing a known set of buyers. We perform a simulation study using publicly available traffic data regarding Amazon S3 clients from Alexa.com to validate our analytical results. Our field study supports our analysis and indicates that spot markets alone can enhance revenues to Amazon, but this comes at the cost of increased risks due to the increased market share in the spot markets. Furthermore, adding a forward contract feature to the spot markets can reduce risks while still providing the benefits of enhanced revenues. Although the buyers incur an increase in costs in the spot market, adding a forward contract does not cause any additional cost increase while transferring the risk to the buyers. Thus, storage grid providers can greatly benefit by applying a forward contract alongside the spot market.

The price of power: The valuation of power and weather derivatives

Pricing contingent claims on power presents numerous challenges due to (1) the unique behavior of power prices, and (2) time-dependent variations in prices. We propose and implement a model in which the spot price of power is a function of two state variables: demand (load) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 1999–2001, the upward bias in the forward price was as large as $50/MWh for some days in July. By 2005, the largest estimated upward bias had fallen to $19/MWh. These large biases are plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This risk premium suggests that the power market is not fully integrated with the broader financial markets.

Short-Term Evolution of Forward Curves and Volatility in Illiquid Power Markets

We propose in this paper a model for the description of electricity spot prices, which we use to describe the dynamics of forward curves. The spot price model is based on a long-term/short-term decomposition, where the price is thought of as made up of two factors: A long-term equilibrium level and short-term movements around the equilibrium. We use a non-parametric approach to model the equilibrium level of power prices, and a mean-reverting process with GARCH volatility to describe the dynamics of the short-term component. Then, the model is used to derive the expression of the short-term dynamics of the forward curve implicit in spot prices. The rationale for the approach is that information concerning forward prices is not available in most of power markets, and the direct modeling of the forward curve is a difficult task. Moreover, power derivatives are typically written on forward contracts, and usually based on average prices of forward contracts. Then, it is difficult to obtain analytical expressions for the forward curves. The model of forward prices allows for the valuation of power derivatives, as well as the calculation of the volatilities and correlations required in risk management activities. Finally, the methodology is proven in the context of the Spanish wholesale market

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.

Empirical Investigation of the Size and the Nature of the Eurodollar Futures-Forward Differential

We investigate the magnitude of the forward-futures differential, also known as the convexity adjustment, for Eurodollar interest rate instruments and attempt to identify factors affecting its size using an extensive sample for the 1988-2007 period. The innovative feature of our analysis is that the construction of the differential is extended from using rates for maturities up to twelve months as in previous published research to rates for maturities up to three years through the use of swap rates that allows us to build the extended term structure of spot and forward rates. Opposite to the previous findings, we find that the magnitude of the forward-futures differential is much smaller than what was reported in earlier studies, and that its sign is negative on many occasions which contradicts theoretical implications. We further check for potential data skews and other imperfections that may be behind the obtained results and find that neither asynchronicity bias, nor the unconventional feature of the Eurodollar futures pricing can explain the observed phenomena. The term structure interpolation error and the two business day lag between the fixing (settlement) date and the transaction (value) date the implied forward rates and prices are applied to cannot be attributed to the observed abnormality either. We also find that the level of interest rates is a significant positive factor behind the differential and its explanatory power is magnified if the regression analysis is conducted for the price differential instead of that for the rate differential which also results in a better goodness-of-fit.

Factors affecting the use of forward pricing methods in price risk management with special reference to the influence of risk aversion

Risk aversion is the primary reason for farmers to use forward pricing methods to hedge against price risk. Previous international research on farmers' forward pricing behaviour found inconsistent results with respect to the relationship between risk aversion and the use of forward pricing methods. Ordinary Least Squares (OLS) regression is used in this research to investigate the relationship between the proportion of maize Vaalharts maize producers are willing to forward price and risk aversion. The quantity decision is modelled conditional on the adoption decision to ensure that the modelling procedure does not force the same variables to influence the two decisions in the same way. Regression results showed that more risk averse farmers are forward pricing a larger proportion of their crop produce. The main conclusion from this research is that the relationship between farmers' risk aversion and the quantity of maize forward priced is consistent with expected utility theory in spite of the fact that farmers needs to be less risk averse to adopt forward pricing. Future emphases should be placed on the factors affecting the adoption of forward pricing as risk management tool in order to promote risk management. Especially research that will change farmers' perception about forward pricing is necessary.