Optimal Hedging Strategy Research Articles

Energy Commodities: A Review of Optimal Hedging Strategies

Energy is considered as a commodity nowadays and continuous access along with price stability is of vital importance for every economic agent worldwide. The aim of the current review paper is to present in detail the two dominant hedging strategies relative to energy portfolios, the Minimum-Variance hedge ratio and the expected utility maximization methodology. The Minimum-Variance hedge ratio approach is by far the most popular in literature as it is less time consuming and computationally demanding; nevertheless by applying the appropriate multivariate model Garch family volatility model, it can provide a very reliable estimation of the optimal hedge ratio. However, this becomes possible at the cost of a rather restrictive assumption for infinite hedger’s risk aversion. Within an uncertain worldwide economic climate and a highly volatile energy market, energy producers, retailers and consumers had to become more adaptive and develop the necessary energy risk management and optimal hedging strategies. The estimation gap of an optimal hedge ratio that would be subject to the investor’s risk preferences through time is filled by the relatively more complex and sophisticated expected utility maximization methodology. Nevertheless, if hedgers share infinite risk aversion or if alternatively the expected futures price is approximately zero the two methodologies become equivalent. The current review shows that when evidence from the energy market during periods of extremely volatile economic climate is considered, both hypotheses can be violated, hence it becomes reasonable that especially for extended hedging horizons it would be wise for potential hedgers to take into consideration both methodologies in order to build a successful and profitable hedging strategy.

Risk Structure and Optimal Hedging of Bitcoin Inverse Futures

In the Bitcoin futures markets, the dominating contracts are inverse contracts. Unlike standard futures, Bitcoin inverse futures have a non-linear payoff structure, are settled in Bitcoin instead of the fiat currency, and require Bitcoins to be deposited into the margin account during trading. We characterize the unique high-order risk factors, asymmetry effect and (de)leverage effect of Bitcoin inverse futures, and obtain optimal hedging strategies in closed forms for both short and long hedges under the minimum-variance framework. We use the market data of Bitcoin spot and futures to conduct empirical studies. Our findings show that the optimal hedging strategies of Bitcoin inverse futures achieve superior hedging performance across exchanges.

The optimal derivative-based corporate hedging strategies under equity-linked managerial compensation

The growing volume utilization of hedging instruments in emerging markets revives the debate regarding optimal hedging strategies–futures versus put options. Specifically, market perfection and the question of redundancy of the hedging instruments, i.e., commodity put options versus futures becomes extremely relevant. This study analyzes optimal hedging while crucially differentiating the principal-agent entities and preferences, and considering managerial equity-linked compensation. We demonstrate that, within the separation theorems frameworks, perfect substitution between commodity put options and exclusive futures hedging. Furthermore, the analysis validates multiple hedging instruments combinations, thereby rationalizing hedging devices diversity and volume for the sake of emerging markets stability.

Semi-static variance-optimal hedging in stochastic volatility models with Fourier representation

AbstractWe introduce variance-optimal semi-static hedging strategies for a given contingent claim. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy we use a Fourier approach in a multidimensional factor model. We apply the theory to set up a variance-optimal semi-static hedging strategy for a variance swap in the Heston model, which is affine, in the 3/2 model, which is not, and in a market model including jumps.

Conditional dependence structure between oil prices and international stock markets

PurposeThe purpose of this paper is to analyze the optimal hedging strategy of the oil-stock dependence structure.Design/methodology/approachThe methodology consists to model the data over the daily period spanning from January 02, 2002 to May 19, 2016 by a various copula functions to better modeling the dependence between crude oil market and stock markets, and to use dependence coefficients and conditional variance to calculate optimal portfolio weights and optimal hedge ratios, and to suggest the best hedging strategy for oil-stock portfolio.FindingsThe findings show that the Gumbel copula is the best model for modeling the conditional dependence structure of the oil and stock markets in most cases. They also indicate that the best hedging strategy for oil price by stock market varies considerably over time, but this variation depends on both the index introduced and the model used. However, the conditional copula method with skewed student more effective than the other models to minimize the risk of oil-stock portfolio.Originality/valueThis research implication can be valuable for portfolio managers and individual investors who seek to make earnings by diversifying their portfolios. The findings of this study provide evidence of the importance of stock assets for making an optimal portfolio consisting of oil in the case of investments in oil and stock markets. This paper attempts to fill the voids in the literature on volatility among oil prices and stock markets in two important areas. First, it uses copulas to investigate the conditional dependence structure of the oil crude and stock markets in the oil exporting and importing countries. Second, it uses the dependence coefficients and conditional variance to calculate dynamic hedge ratios and risk-minimizing optimal portfolio weights for oil–stock.

Potential benefits of optimal intra-day electricity hedging for the environment: The perspective of electricity retailers

Our article provides a better understanding of risk management strategies for all energy market stakeholders. A good knowledge of optimal risk hedging strategies is not only important for energy companies but also for regulators and policy makers in a context of climate emergency. Indeed, the electricity sector is key to achieve energy and ecological transition. Electricity companies should be on frontline of climate change struggle. Taking the perspective of electricity retailers, we analyze a range of portfolios made of forward contracts and/or power plants for specific hourly clusters based on electricity market data from the integrated German-Austrian spot market. We prove that intra-day hedging with forward contracts is sub-optimal compared to financial options and physical assets. By demonstrating the contribution of intra-day hedging with options and physical assets, we highlight the specificities of electricity markets as hourly markets with strong volatility during peak hours. By simulating optimal hedging strategies, our article proposes a range of new portfolios for electricity retailers to manage their risks and reduce their sourcing costs. A lower hedging cost enables to allocate more resources to digitalization and energy efficiency services to take into account customers’ expectations for more climate-friendly retailers. This is a virtuous circle. Retailers provide high value-added energy efficiency services so that consumers consume less. The latter contributes to reach electricity reduction targets to fight climate warming.

Hedging Strategies for Heat and Electricity Consumers in the Presence of Real-Time Demand Response Programs

Real-time pricing (RTP) is a component of some demand response programs (DRPs) in electricity markets. This paper proposes a real-time price-based demand response management model for heat and power consumers. In the proposed DRP, the responsive electrical load can vary in different time intervals. Real-time price risk can be shared among market participants sensibly by implementing several RTP hedge contracts. In this context, supply sources include energy from the real-time market, self-production facilities, as well as RTP hedge contract instruments. The model is introduced for electricity consumers equipped with combined heat and power systems, power-only unit, boiler unit, and heat buffer tank. Optimal hedging strategies, including hedge contract choices and hedged load percentages, can be acquired by solving the model. The proposed model makes it possible to achieve minimum energy cost while considering uncertainties in real-time electricity prices. The price uncertainty is addressed through robust optimization for minimizing the worst case electricity and heat demand procurement cost while flexibly adjusting the solution robustness. Numerical simulations are provided, which confirm the applicability and effectiveness of the proposed model.

Barndorff‐Nielsen and Shephard model for hedging energy with quantity risk

AbstractIn this paper, the Barndorff‐Nielsen and Shephard (BN‐S) model is implemented to find an optimal hedging strategy in the presence of quantity risk for oil produced in the Bakken, a new region of oil extraction that is benefiting from fracking technology. Hedging and price risk management become much more involved with the inclusion of quantity risk. Explorers and drillers have uncertainty on the quantity of oil that would be extracted, and governments have uncertainty of the quantity of oil that will be extracted, sold, and available for imposing tax regimes. One of the main assumptions typically made in a portfolio model of hedging is that the quantity of inventory or demand is known. This is inappropriate in many hedging situations. Quantity risk compounds the difficulty of determining the optimal size of the position under both price and production risk. In this paper, we provide a novel way of handling the quantity risk in connection with the BN‐S model. The model is analyzed as a quadratic hedging problem and related analytical results are developed. The results indicate that oil can be optimally hedged with a combination of variance swaps and options. For various quantity risks, the model is implemented to analyze hedging decisions numerically for managing price risk in the Bakken oil commodities.

HEDGING EFFECTIVENESS OF CROSS-LISTED NIFTY INDEX FUTURES

This paper investigates the hedging effectiveness of cross-listed Nifty Index futures and compares the performance of constant and dynamic optimal hedging strategies. We use daily data of Nifty index traded on the National Stock Exchange (NSE), India and cross-listed Nifty futures traded on the Singapore Stock Exchange (SGX) for a period of six years from July 15, 2010 to July 15, 2016. Various competing forms of Multivariate Generalised Autoregressive Conditional Heteroscedasticity (MGARCH) models, such as Constant Conditional Correlation (CCC) and Dynamic Conditional Correlation (DCC), have been employed to capture the time-varying volatility. The results clearly depict that dynamic hedge ratios outperform traditional constant hedge ratios with the DCC–GARCH model being the most efficient with maximum variance reduction from the unhedged portfolio.

Internal hedging of intermittent renewable power generation and optimal portfolio selection

This paper introduces a scheme for hedging and managing production costs of a risky generation portfolio, initially assumed to be dispatchable, to which intermittent electricity generation from non-dispatchable renewable sources like wind is further added. The proposed hedging mechanism is based on fixing the total production level in advance, then compensating any unpredictable non-dispatchable production with a matching reduction of the dispatchable fossil fuel production. This means making no recourse to short term techniques like financial hedging or storage, in a way fully internal to the portfolio itself. Optimization is obtained in the frame of the stochastic LCOE theory, in which fuel costs and $$\hbox {CO}_2$$ prices are included as uncertainty sources besides intermittency, and in which long term production cost risk, proxied either by LCOE standard deviation and LCOE CVaR Deviation, is minimized. Closed form solutions for optimal hedging strategies under both risk measures are provided. Main economic consequences are discussed. For example, this scheme can be seen as a method for optimally including intermittent renewable sources in an otherwise dispatchable generation portfolio under a long term capacity expansion perspective. Moreover, within this hedging scheme, (1) production cost risk is reduced and optimized as a consequence of the substitution of the dispatchable fossil fuel generation with non-dispatchable $$\hbox {CO}_2$$ free generation, and (2) generation costs can be reduced if the intermittent generation can be partially predicted.

Valuation of Guaranteed Unitized Participating Life Insurance under MEGB2 Distribution

Crisis events have significantly changed the view that extreme events in financial markets have negligible probability. Especially in the life insurance market, the price of guaranteed participating life insurance contract will be affected by a change in asset volatility which leads to the fluctuations in embedded option value. Considering the correlation of different asset prices, MEGB2 (multivariate exponential generalized beta of the second kind) distribution is proposed to price guaranteed participating life insurance contract which can effectively describe the dependence structure of assets under some extreme risks. Assuming the returns of two different assets follow the MEGB2 distribution, a multifactor fair valuation pricing model of insurance contract is split into four components: the basic contract, the annual dividend option, the terminal dividend option, and the surrender option. This paper studies the effect of death rate, minimum guaranteed yield rate, annual dividend ratio, terminal dividend ratio, and surrender on the embedded option values and calculates the single premium of the insurance contract under different influence factors. The Least-Squares Monte Carlo simulation method is used to simulate the pricing model. This article makes a comparison in the sensitivity of the pricing parameters under the MEGB2 distribution and Multivariate Normal distribution asset returns. Finally, an optimal hedging strategy is designed to cover the possible risks of the underlying assets, which can effectively hedge the risks of portfolio.

Bayesian Inference for Optimal Risk Hedging Strategy Using Put Options With Stock Liquidity

This paper considers the problem of hedging the risk exposure to imperfectly liquid stock by investing in put options. In an incomplete market, we firstly obtain a closed-form pricing formula of the European put option with liquidity-adjustment by measure transformation. Then, an optimal hedging strategy which minimizes the Value-at-Risk (VaR) of the hedged portfolio is deduced by determining an optimal strike price for the put option. Furthermore, we provide a new perspective to estimate parameters entering the minimal VaR, since the likelihood function is analytically intractable. A Bayesian statistical method is proposed to perform posterior inference on the minimal VaR and the optimal strike price. Empirical results show that the risk hedging strategy with liquidity-adjustment differs from the hedging strategy based on Black-Scholes model. The effect of the stock liquidity on risk hedging strategy is significant. These results can provide more decision information for institutions and investors with different risk preferences to avoid risk.

Multivariate Continuous-Time Modeling of Wind Indexes and Hedging of Wind Risk

With the introduction of the exchange-traded German wind power futures, opportunities for German wind power producers to hedge their volumetric risk are present. We propose two continuous-time multivariate models for the wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Employing the models to wind index data for wind sites in Germany and the underlying wind index of exchange-traded wind power futures contracts, the estimation results of both models suggest that they capture key statistical features of the data. We argue how these models can be used to find optimal hedging strategies using exchange-traded wind power futures for the owner of a portfolio of so-called tailor-made wind power futures. Both in-sample and out-of-sample hedging scenarios are considered, and, in both cases, significant variance reductions are achieved. Additionally, the risk premium of the German wind power futures is analysed, leading to an indication of the risk premium of tailor-made wind power futures.

Deep Hedging of Derivatives Using Reinforcement Learning

This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and optimal hedging for a short position in a call option when the objective is to minimize a function equal to the mean hedging cost plus a constant times the standard deviation of the hedging cost. Two situations are considered. In the first, the asset price follows geometric Brownian motion. In the second, the asset price follows a stochastic volatility process. The paper extends the basic reinforcement learning approach in a number of ways. First, it uses two different Q-functions so that both the expected value of the cost and the expected value of the square of the cost are tracked for different state/action combinations. This approach increases the range of objective functions that can be used. Second, it uses a learning algorithm that allows for continuous state and action space. Third, it compares the accounting P&L approach (where the hedged position is valued at each step) and the cash flow approach (where cash inflows and outflows are used). We find that a hybrid approach involving the use of an accounting P&L approach that incorporates a relatively simple valuation model works well. The valuation model does not have to correspond to the process assumed for the underlying asset price.

Hedging through index-based price contracts in commodity-based supply chains

This paper studies the optimal hedging strategy of risk-neutral firms in supply chain settings. We model a retailer procuring goods through index-based price contracts from two commodity processors. The processors’ input commodity prices are random and correlated. The retailer faces price-sensitive demand curves; therefore, it controls product demand through retail pricing in the final product market. We characterize the optimal contracting terms for the processors and show that they prefer to hedge part of their exposure to the commodity price risk. The optimal contract for processor comprises a processing margin independent of the commodity price volatility and a hedge ratio that is a function of the commodity price volatility and the products substitution factor. We uncover a new rationale for hedging in settings where downstream firms have pricing power; both processors and the retailer benefit from the retailer’s pricing power when their margins are linked to input prices; an index-based price contract is a means to link the processors’ and the retailer’s margins. We further investigate how different market parameters affect the optimal hedge ratios and extend our model to settings with random market sizes and asymmetric substitution for final products.

The optimal hedge strategy of crude oil spot and futures markets: Evidence from a novel method

AbstractHedging is an important measure for investors to resist extreme risks and improve their profits. This paper develops a FIGARCH–EVT–copula–VaR model to derive hedge ratio when hedging crude oil spot and futures markets, overcoming the limitations of static models and simple dynamic models in existing literature. The empirical results indicate that the FIGARCH–EVT–copula–VaR model is superior to the other three commonly used models based on four criteria: mean of returns, variance of returns, ratio of mean to variance of returns, and hedging effectiveness. Comparatively, the new model has superior performance to other three models during the sample period and can be used by investors to obtain excellent hedging effect.

Bitcoin returns and risk: A general GARCH and GAS analysis

This paper performs a general GARCH and GAS analysis for modelling and forecasting bitcoin returns and risk. Since Bitcoin trading exhibits excess volatility compared with other securities, it is important to model its risk and returns. We consider heavy-tailed GARCH models as well as GAS models based on the score function of the predictive conditional density of the bitcoin returns. We compare out-of-sample 1%-Value-at-Risk (VaR) forecasts under 45 different specifications using three backtesting procedures. We find that GAS models with heavy-tailed distributions provide the best out-of-sample forecast and goodness-of-fit properties to bitcoin returns and risk modelling. Normally-distributed GARCH models are always outperformed by heavy-tailed GARCH or GAS models. Besides, heavy-tailed GAS models provide the best conditional and unconditional coverage for 1%-VaR forecasts, illustrating the importance of modelling excess kurtosis for bitcoin returns. Hence, our findings have important implications for risk managers and investors for using bitcoin in optimal hedging or investment strategies.

Barndorff-Nielsen and Shephard model: oil hedging with variance swap and option

In this paper the Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for the oil commodity from the Bakken, a new region of oil extraction that is benefiting from fracking technology. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The results indicate that oil can be optimally hedged with the use of a combination of options and variance swaps. Theoretical results related to the variance process are established and implemented for the analysis of the variance swap. In this paper we also determined the optimal amount of the underlying oil commodity that has to be held for minimizing the hedging error. The model and analysis are used to numerically analyze hedging decisions for managing price risk in Bakken oil commodities. From the numerical results, a number of important features of the usefulness of the Barndorff-Nielsen and Shephard model are illustrated.

SHORTFALL RISK MINIMIZATION UNDER FIXED TRANSACTION COSTS

In this work, we deal with market frictions which are given by fixed transaction costs independent of the volume of the trade. The main question that we study is the minimization of shortfall risk in the Black–Scholes (BS) model under constraints on the initial capital. This problem does not have an analytical solution and so numerical schemes come into the picture. The Cox–Ross–Rubinstein (CRR) binomial models are an efficient tool for approximating the BS model. In this paper, we study in detail the CRR models with fixed transaction costs. In particular, we construct an augmented state-action space forming a Markov decision process (MDP) and provide a proof for the existence of optimal control/policy. We further suggest a dynamic programming algorithm for calculating the optimal hedging strategy and its corresponding shortfall risk. In the absence of transaction costs, there is an analytical solution in both CRR and BS models, and so we use them for testing our algorithm and its convergence. Moreover, we point out various insights provided by our numerical results, for example, regarding the change in the investor’s activity in the presence of friction.

Optimal hedging strategies in equity-linked products

Equity-linked insurance policies are one of the most widespread insurance products. In many cases such contracts have guarantees like a minimum return over the lifetime of the policy. Liabilities arising from such guarantees must be hedged by suitable investments. There are restrictions on hedging strategies in many jurisdictions but with the more flexible regulatory framework of Solvency 2 there are alternative ways to hedge certain guaranteed products using derivative securities. In this paper we investigate when it is optimal to switch to hedging liabilities with derivative securities in the framework of the Cox–Ross–Rubinstein model. This leads to optimal stopping problems that can be solved explicitly. Mortality is also incorporated in the model. The results may indicate the level of reserves necessary to meet obligations with the desired level of confidence. In particular the strategy may be applicable in adverse market conditions.