Pricing Of Forward Contracts Research Articles

The effects of skewness and kurtosis on production and hedging decisions: a Gram-Charlier expansion approach

In this study, we propose a Gram-Charlier expansion approach to investigate the impact of skewness and kurtosis on production and hedging decisions. Consistent with the existing literature, we find that skewness and kurtosis do not affect decisions regarding optimal production; however, they significantly influence optimal hedging decisions. We observe that positive skewness with platykurtic spot prices or negative skewness with leptokurtic spot prices often leads to over-hedging when the initial forward contract price exceeds its expected value. Conversely, under-hedging is expected when the initial forward contract price falls below its expected value. In other conditions, skewness can either promote or impede speculative future trading. Using the Gram-Charlier expansion of the spot price density function, we find that optimal future positions depend on forward prices, the hedgers’ risk preference, and the spot price distribution. Simulations validate our findings on the impact of skewness and kurtosis on future hedging. Finally, we analyze of a cotton storage and forward contracting dataset to illustrate the application of our methodology and support our theoretical results.

The heat modulated infinite dimensional Heston model and its numerical approximation

The HEat modulated Infinite DImensional Heston (HEIDIH) is introduced as a concrete case of the general framework of infinite dimensional Heston stochastic volatility models of (F.E. Benth, I.C. Simonsen '18) for the pricing of forward contracts. It is supported by a comprehensive numerical analysis. The model consists of a one-dimensional stochastic advection equation coupled with a stochastic volatility process. This process is a Cholesky-type decomposition of the tensor product of a Hilbert-space valued Ornstein-Uhlenbeck process, the solution to a stochastic heat equation on the real half-line. The advection and heat equations are driven by independent space-time Gaussian processes which are white in time and coloured in space, with the latter covariance structure expressed by two different kernels. First, a class of weight-stationary kernels are given, under which regularity results for the HEIDIH model in fractional Sobolev spaces are formulated. In particular, the class includes weighted Matérn kernels. Second, numerical approximation of the model is considered. An error decomposition formula, pointwise in space and time, for a finite-difference scheme is proven. For a special case, essentially sharp convergence rates are obtained when this is combined with a fully discrete finite element approximation of the stochastic heat equation. The analysis takes into account a localization error, a pointwise-in-space finite element discretization error and an error stemming from the noise being sampled pointwise in space. The rates obtained in the analysis are higher than what would be obtained using a standard Sobolev embedding technique. Numerical simulations illustrate the results.

Valuation of forward contract price in energy markets described by a fuzzy-stochastic model and mathematical algorithms: a case study of the PJM Western Hub Real-Time Peak market

Valuation of forward contract price in energy markets described by a fuzzy-stochastic model and mathematical algorithms: a case study of the PJM Western Hub Real-Time Peak market

Long- and short-term price behaviors in presale housing markets in Taiwan

In real estate transactions, buyers of presale houses incur greater risks than do buyers of pre-existing houses; consequently, presale housing prices should be discounted. However, in many areas, short-term presale housing markets often overheat. To illustrate this phenomenon, this paper adopts two theoretical models to analyze long-term equilibrium and short-term changes in the presale housing market. First, the cobweb model demonstrates that demand responds immediately to sudden shocks in the housing market. Because the supply of the spot housing market is lagging, the demand may be transferred to the forward market. Therefore, even though the price–volume relationship in the presale market is balanced in the long term, it may still be affected by sudden demand-side shocks and overheating in the short term. Second, the paper uses a forward contract pricing model to illustrate short-term fluctuations in the presale housing market and concludes that governments should raise interest rates and land holding costs to control the overheating of the presale housing market. City-level data from Taiwan are used to verify the long- and short-term price behaviors indicated by the two models.

On the Stability of Energy-Only Markets with Government-Initiated Contracts-for-Differences

Rising levels of variable renewable energy (VRE) in Australia’s National Electricity Market have been driven by a 20% renewable energy target by 2020. This certificated renewable portfolio standard has successfully driven new investment, allocated risk amongst buy- and sell-side market participants and met overall policy objectives. But a policy vacuum for achieving long-term CO2 emission targets post-2020 has led to sub-national and, potentially, national governments initiating contract-for-differences (CfDs) to drive further investment activity in new plant – with virtually no coordination between the jurisdictions. In a gross pool energy-only market setting, replacing on-market transactions between retailers and generators with off-market transactions between governments and generators may have unintended side-effects vis-à-vis market stability. In this article, an energy-only gross pool is modeled with rising levels of off-market government-initiated CfDs, with a specific focus on spot and forward contract market outcomes. Model results show that as VRE plant enters, coal plant exit, and on-market firm hedge contracts historically supplied by coal plant are progressively replaced by off-market CfDs. In the event, while a tractable equilibrium can be maintained in the spot market, shortages of “primary issuance” hedge contracts emerge in the forward market. Any shortage of hedge contract capacity is likely to raise forward contract price premiums above efficient levels, force price-elastic customers into accepting unwanted spot market exposures and may unintentionally foreclose non-integrated (2nd tier) energy retailers, all of which harms consumer welfare. A wide-ranging program of government CfDs may therefore not be compatible with an energy-only market design.

Data-Driven Stochastic Pricing and Application to Electricity Market

This paper develops a novel approach to computation of the probability integrals encountered in derivative pricing using stochastic models estimated from historical data. First, nonparametric probability distribution models are built directly from the data as a solution of a convex optimization problem scalable to very big datasets. Second, these models are used for numerical calculus of probability integrals, where the quadrature includes long tails of the probability distributions. The application example is the procurement contract in the day-ahead bulk market for electricity. The data for PJM utility loads and prices in the day-ahead and spot markets were used to estimate the risk and to price the contract. The data-driven forward contract pricing allows to optimize the contract cost and reduce it by 2% compared to the baseline; this corresponds to about $0.6B/year in potential utility savings.

A Hybrid SLV Model with Multifactor Stochastic Volatility

The need for more satisfactory pricing models has brought the attention of researchers and practitioners on Stochastic Local Volatility models. Despite the growing interest on the topic, however, it seems that no particular attention has been paid to the use of multifactor specifications for the stochastic volatility part. The additional flexibility given by this kind of approach in describing the skew dynamics becomes extremely important when we deal with the pricing of forward volatility sensitive contracts like forward start or cliquet options.This paper tries to fill the gap: we introduce the Wishart Stochastic Local Volatility model that describes the stochastic volatility by means of a Wishart process as proposed. The goal of the new framework is twofold: adding a realistic volatility dynamics to Local Volatility models without the limitations of standard 1-factor Stochastic Volatility approaches, and improving European claims pricing performance of pure Wishart Stochastic Volatility model. The latter is quite relevant since we need to introduce stringent parameters restrictions to satisfy existence and uniqueness conditions for the solution of Wishart SDE. These conditions are required when we want to properly simulate the variance process in order to price more exotic derivatives. However such conditions are not usually met when market calibration is performed and so the resulting constrained parameters set is not able to reproduce accurately the market implied volatility surface. The additional Local Volatility component acts then as compensator.We further present an innovative simulation scheme for the asset path in the pure stochastic volatility specification based on the approach. The simulation scheme is also used to tackle the calibration of the so-called leverage function and price derivatives in the new hybrid framework.

Volatility of Forward Price in Dry Shipping Market

The purpose of this paper is to investigate the volatility of forward contract price during different phases and holding periods in dry bulk shipping market, which could be helpful for the hedging and portfolio on the shipping market. This paper applies the Stochastic Volatility model to analyze the volatility, and the parameters of the model are estimated via the software package of Bayesian inference using Gibbbs sampling. The empirical results based on the daily price of Panamax forward freight agreement from 3 Jan 2006 to 13 Aus 2010 suggest that there are different stabilities, volatility persistence and trading active degrees in different conditions.

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.

Pricing and hedging of long-term futures and forward contracts by a three-factor model

This paper demonstrates the pricing and hedging efficiency of a three-factor stochastic mean reversion Gaussian model of commodity prices using oil and copper futures and forward contracts. The model is estimated using NYMEX WTI (light sweet crude oil) and LME Copper futures prices and is shown to fit the data well. Furthermore, it shows how to hedge based on a three-factor model and confirms that using three different futures contracts to hedge long-term contracts outperforms the traditional parallel hedge based on a single futures position by time series data and simulation. It also finds that the three-factor model outperforms the two-factor version with respect to the replication of actual term structures and that stochastic mean reversion models outperform constant mean reversion models in Out of Sample hedges.

Cross-hedging and forward-contract pricing of electricity in the Pacific Northwest

This paper develops a linear regression model for using actively traded NYMEX natural gas futures as a cross-hedge against electricity spot-price risk in the Pacific Northwest and for pricing the forward contracts in the presence of temperature and hydro risks. Our approach comports with reality and provides power purchasers with an effective instrument through which they can hedge their electricity bets through natural gas futures. It also demonstrates the sharp month-to-month variations in the natural gas futures' optimal hedge ratios and hedge effectiveness. Finally, it finds significant risk premiums in the Pacific Northwest forward prices, supporting the hypothesis that forward-contract buyers are relatively more risk-averse than sellers. Copyright © 2011 John Wiley & Sons, Ltd.

Forward Contract Pricing

Forward Contract Pricing

Risk Management and the Role of Spot Price Predictions in the Australian Retail Electricity Market

This study investigates the extent to which predicted electricity spot prices from a statistical model, along with consensus forecasts issued by the Australian Financial Market Association (AFMA), provide unbiased price estimates of a forward contract price over a specified time to expiration. The statistical model is a regime switching time series model which is based on the dynamics of the market mechanism. To evaluate a price estimate, two criteria are utilized in order to conclude appropriateness for use in the marking-to-market process. First is the requirement that the predicted prices converge to the spot price at expiration of a hedging contract. The second criterion refers to the mis-pricing due to the price estimates over the days leading up to the contract expiration. Over the data period under consideration, the ranking of alternatives for generating price predictions is clear. On both criteria the Stevenson (2001) model is preferred. Of significance is the lack of support for the consensus (market) prices. They do not converge to the spot price at equilibrium and, further, they generate a considerable overvaluation of the risk management portfolio.

Pricing of monthly forward contracts in the Nord Pool market

This paper investigates whether the pricing of forward contracts in the Nord Pool market is efficient. Monthly forward contracts were introduced in the Nord Pool market in 2003. Likewise, quarterly contracts that will replace seasonal contracts were introduced in 2004. For a transition period these contracts together with the pre-existing seasonal and yearly contracts constitute the forward market. In an efficient forward market the price of a seasonal forward contract should equal the time-weighted average of the underlying monthly forward contracts. In this paper we use historic forward price information to evaluate whether this relationship holds true and find that there are inefficiencies in the pricing.

Hedgers, speculators and forward markets: Evidence from currency markets

Since Keynes [Keynes, J.M., 1930. A Treatise on Money, vol. II. Macmillan, London.] and Hicks [Hicks, J.R., 1939. Value and Capital. Oxford University Press, Cambridge.] propounded their theory of normal backwardation, the issue of whether hedgers must pay speculators an insurance premium has remained controversial. Recent theoretical developments incorporating the existence of market imperfections have validated the existence of an insurance premium charged to hedgers by speculators. Owing to differences in data sets and econometric methods, a consensus has not yet been reached. Drawing inspiration from asset pricing theory a model of currency returns is used, similar to that in Mark [Mark, N.C., 1988. Time-varying beta and risk premia in the pricing of forward foreign exchange contracts. Journal of Financial Economics 22, 335–354.] and the importance of speculative influences is tested. The purpose of the paper is to highlight the theoretical and statistical deficiencies of the extant literature and to examine the robustness of previous empirical results to changes in specification. Applications to risk management and forecasting are immediate, as knowledge of any insurance premium is crucial in formulating an optimal hedging strategy and an optimal forecasting model.

Efficient frontiers for electricity procurement by an LDC with multiple purchase options

In meeting its retail sales obligations, management of a local distribution company (LDC) must determine the extent to which it should rely on spot markets, forward contracts, and the increasingly popular long-term tolling agreements under which it pays a fee to reserve generator capacity. We address these issues by solving a mathematical programming model to derive the efficient frontier that summarizes the optimal tradeoffs available to the LDC between procurement risk and expected cost. To illustrate the approach, we estimate the expected procurement costs and associated variances that proxy for risk through a spot-price regression for the spot-purchase alternative and a variable-cost regression for the tolling-agreement alternative. The estimated regressions yield the estimates required to determine the efficient frontier. We develop several such frontiers under alternative assumptions as to the forward-contract price and the tolling agreement's capacity payment, and discuss the implications of our results for LDC management.

A robust internet-based auction to procure electricity forwards

Securing forward contracts to manage procurement-cost risk is an intuitively appealing and economically reasonable strategy for a load-serving local distribution company (LDC) in today’s volatile electricity marketplace. However, knowing what to buy does not guarantee least-cost implementation. The forward-contract price quoted by a prospective seller may not be the ‘best deal’ that an LDC could have obtained, especially when the forward contract desired by the LDC is not actively traded. This paper reports the results from five internet-based auctions for electricity forward contracts with non-firm delivery and varying hourly quantities held monthly by a Florida municipal utility (MU) from September 2002 to January 2003. The results confirm that a multi-round auction design is robust in realizing competitive price offers made by credit-worthy sellers, time-efficient contracting, and consistent cost savings to the MU. Thus, the Anglo-Dutch auction described herein is a reasonable substitute for generation ownership by an LDC.

General equilibrium pricing of nonredundant forward contracts

AbstractWe derive the general equilibrium of a dynamic financial market in which the investors' opportunity set includes nonredundant forward contracts. We show that Breeden's (1979) consumption‐based CAPM equation for forward contracts contains an extra term relative to that for cash assets. We name this term a strategy risk premium. It compensates investors for the (systematic) risk that stems from their very portfolio strategies when the latter involve nonredundant forward contracts. We also show that Merton's (1973) multibeta intertemporal CAPM must be amended for forward contracts to exhibit adjusted risk premia for the market portfolio and all relevant state variables, as opposed to the usual risk premia for cash assets. Our results are shown not to depend on the usual cash‐and‐carry relationship, which, in general, does not hold. We, nevertheless, provide a well‐known special case where it does hold, albeit not grounded on the usual no‐arbitrage argument. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:817–840, 2003

Cross hedging and forward-contract pricing of electricity

Cross hedging and forward-contract pricing of electricity

Cross hedging and forward-contract pricing of electricity

We consider the problem of an electric-power marketer offering a fixed-price forward contract to provide electricity that it purchases from a potentially volatile and unpredictable fledgling spot energy market. One option for the risk-averse marketer who wants to hedge against the spot-price volatility is to engage in cross hedging to reduce the contract's profit variance, and to determine the forward-contract price as a risk-adjusted price — the sum of a baseline price and a risk premium. We show how the marketer can estimate the spot-price relationship between two wholesale energy markets for the purpose of cross hedging, as well as the optimal hedge and the forward contract's baseline price and risk premium.