Optimal Hedging Policy Research Articles

Optimal hedging in the presence of internal flexibility

AbstractInternal flexibility aids in risk management and has a broader application than hedging instruments. This paper demonstrates how optimal hedging policies are affected by it. We develop a dynamic risk management model to capture financial and operational decisions. We first show that internal flexibility reduces the marginal value of hedging instruments. As a result, optimal financial hedging is selective and dependent on investment opportunities. These opportunities account for the majority of the difference between hedged and unhedged firms. By incorporating internal flexibility, the model becomes more realistic but also generates a complex interaction between financial hedging and marketing strategy. During the growth phase, hedging instruments are partially substitutive but have a synergistic effect on investment. In the mature or declining phase, the remedial effect of marketing strategy maintains investment, thereby increasing operating risk and the marginal value of financial hedging. These results are applicable to firms free of agency conflicts and provide a solid theoretical basis for future empirical tests. We advise that scholars thoroughly examine internal flexibility and development stages in the process.

Linear Versus Nonlinear (Convex and Concave) Hedging Rules for Reservoir Optimization Operation

AbstractHedging rules of reservoir operations decide the timing and magnitude of current water delivery reduction and consequent carryover water storage conservation based on the tradeoff between the utility of current and future water use. Different forms of hedging can be used for reservoir release decision. This study presents general optimality conditions for hedging with convex, concave, and linear relationships between reservoir water availability and release, using criteria based on the relative value of marginal value of risk tolerance (MVRT) with respect to current reservoir release versus carryover storage. MVRT is quantified to measure reservoir operators' risk tolerance change (sensitivity) to the change of reservoir release or carryover storage, reflecting their attitudes to the risk with current release and that with the carryover storage (i.e., future release), as well as their perception of future water availability uncertainty. Higher, equal, or lower MVRT with current release than that with carryover storage for future release corresponds to convex, linear or concave hedging. Various levels of risk tolerance toward hydrologic uncertainty underlie different hedging types for reservoir release decisions. Specifically, negative, positive, and null risk premiums (or risk seeking, risk aversion, and risk neutrality) result from convex, concave, and linear hedging rules, respectively. In general, high uncertainty will move the convex or concave curve closer to the linear curve. The MVRT‐based criteria for optimal hedging policies are illustrated through a real‐world case study.

Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures

Recently equal risk pricing, a framework for fair derivative pricing, was extended to consider dynamic risk measures. However, all current implementations either employ a static risk measure that violates time consistency, or are based on traditional dynamic programing solution schemes that are impracticable in problems with a large number of underlying assets (due to the curse of dimensionality) or with incomplete asset dynamics information. In this paper, we extend for the first time a famous off-policy deterministic actor-critic deep reinforcement learning (ACRL) algorithm to the problem of solving a risk averse Markov decision process that models risk using a time consistent recursive expectile risk measure. This new ACRL algorithm allows us to identify high quality time consistent hedging policies (and equal risk prices) for options, such as basket options, that cannot be handled using traditional methods, or in context where only historical trajectories of the underlying assets are available. Our numerical experiments, which involve both a simple vanilla option and a more exotic basket option, confirm that the new ACRL algorithm can produce (1) in simple environments, nearly optimal hedging policies, and highly accurate prices, simultaneously for a range of maturities (2) in complex environments, good quality policies and prices using reasonable amount of computing resources; and (3) overall, hedging strategies that actually outperform the strategies produced using static risk measures when the risk is evaluated at later points of time.

The Dual Nature of Foreign Currency Debt and Its Impact on Firm Performance: Evidence from French Non-Financial Firms

We investigate the impact of foreign currency debt on firm performance for a sample of non-financial French firms studied over the period 2002 to 2012. As foreign currency debt is both a financing and hedging instrument against foreign exchange risk, we examine whether its impact results from an optimal hedging policy or a capital structure policy. We find that foreign currency debt and domestic debt have the same positive effect before the crisis and negative impact after. The capital structure theory or the hedging theory can explain this result. During the crisis period, only corporate hedging theory explains the impact of foreign debt.

Comparison of Optimal Hedging Policies for Hydropower Reservoir System Operation

Reservoir operation rules play an important role in regions economic development. Meanwhile, hedging policies are mostly applied for municipal, industrial, and irrigation water supplies from reservoirs and it is less used for reservoir operation for hydropower generation. The concept of hedging and rationing factors can be used to maintain the water in a reservoir for the sake of increasing water storage and water head for future use. However, water storage and head are the key factors in operation of reservoir systems for hydropower generation. This study investigates the applicability of seven competing hedging policies including four customary forms of hedging (1PHP, 2PHP, 3PHP, DHP) and three new forms of hedging rules (SOPHP, BSOPHP, SHPHP) for reservoir operation for hydropower generation. The models were constructed in MATLAB R2011b based on the characteristics of the Batang Padang hydropower reservoir system, Malaysia. In order to maximize the output of power generation in operational periods (2003–2009), three optimization algorithms namely particle swarm optimization (PSO), genetic algorithm (GA), and hybrid PSO-GA were linked to one of the constructed model (1PHP as a test) to find the most effective algorithm. Since the results demonstrated the superiority of the hybrid PSO-GA algorithm compared to either PSO or GA, the hybrid PSO-GA were linked to each constructed model in order to find the optimal decision variables of each model. The proposed methodology was validated using monthly data from 2010–2012. The results showed that there are no significant difference between the output of monthly mean power generation during 2003–2009 and 2010–2012.The results declared that by applying the proposed policies, the output of power generation could increase by 13% with respect to the historical management. Moreover, the discrepancies between mean power generations from highest to lowest months were reduced from 49 MW to 26 MW, which is almost half. This means that hedging policies could efficiently distribute the water-supply and power-supply in the operational period and increase the stability of the system. Among the studied hedging policies, SHPHP is the most convenient policy for hydropower reservoir operation and gave the best result.

Integrated Commodity Inventory Management and Financial Hedging: A Dynamic Mean‐Variance Analysis

We consider a firm purchasing a storable raw material commodity from a spot market with volatile commodity prices and the access to an associated financial derivatives market. The purchased commodity is processed into an end product with uncertain demand and lost sales. The firm aims to integrate the inventory replenishment and financial hedging decisions to maximize the mean‐variance of terminal wealth over a finite horizon. Recognizing time‐inconsistency of mean‐variance criteria, we employ the dynamic programming approach to obtain a time‐consistent policy. Assuming no arbitrage in financial market, we show that the mean‐variance utility functions under the time‐consistent policy have a recursive representation which enables us to readily characterize the structure of the time‐consistent policy. We analyze two types of hedging instruments, vanilla hedges and exotic hedges, and show that inventory and financial hedging decisions can be separated in the presence of forward contracts and a myopic state‐dependent base stock policy is optimal. The optimal hedging policy can be obtained by minimizing the variance of the hedging portfolio, the value of excess inventory and the profit‐to‐go as a function of future price. In the presence of a continuum of option strikes, we show how to construct custom exotic derivatives using forwards and options of all strikes to replicate the profit‐to‐go function. We then show the optimality of the time‐consistent policy under exotic hedge for the initial mean‐variance objective. We further investigate the dynamic interplay of inventories and financial hedge and show that they can be substitutes in a dynamic environment. Finally, we compare the performances in different hedging environments to discuss how financial hedges add value and provide a numerical study.

Transporting Commodities: Hedging Against Price, Demand and Freight Rate Risk with Options

Like options on stocks, options on commodities provide firms with protection against adverse price movements. Many firms procure commodity at an offshore location and transport it via ocean freight. Increased globalization and increased demand for ocean-based transportation has resulted in ocean freight itself becoming a volatile commodity. We consider a commodity processor and develop models to determine the firm’s optimal hedging policy. The models allow for three sources of uncertainty; demand, commodity spot price and freight rate. The scenarios differ based on assumptions on independence between the uncertainties, and also assumptions on market competitiveness. The optimal hedging policies are variants of the classical newsvendor critical fractile. We show that partially procuring the commodity and its freight through option contracts, rather than entirely on the volatile spot market creates value, even for a risk-neutral firm. We then perform extensive numerical experiments to study the influence of the underlying parameters on the optimal hedging policies and value creation.

Genetic algorithms optimization of hedging rules for operation of the multi-purpose Ubonratana Reservoir in Thailand

Abstract. This study has developed optimal hedging policies for the multi-purpose Ubonratana Reservoir in northeastern Thailand based on its existing rule curves. The hedging policy was applied whenever the reservoir storage falls below a critical level for each month of the year. The decision variables, i.e. the set of monthly storages defining the critical rule curve that triggers rationing and the rationing ratio, were optimized by genetic algorithm (GA). Both single stage (i.e. with one critical rule curve and one rationing ratio) and two-stage (with two critical rule curves and ratios) of the hedging policy were considered in the optimization. To test the effect of the optimized hedging policies on reservoir performance, simulations were carried out, forced alternatively with the existing rule curves (i.e. without hedging) and the two optimized hedging policies. Performance was summarized in terms of reliability (time- and volume-based) and vulnerability. The results showed that the vulnerability was significantly reduced by using the optimized hedging rules. However, the number of water shortages increased with the optimized rules, causing the time-based reliability to worsen significantly. This should not be of concern since, although the number of shortages increased, the associated shortage quantities on most of these additional occasions were small, leaving the volumetric reliability largely unchanged.

Time-consistent mean–variance hedging of longevity risk: Effect of cointegration

This paper investigates the time-consistent dynamic mean–variance hedging of longevity risk with a longevity security contingent on a mortality index or the national mortality. Using an HJB framework, we solve the hedging problem in which insurance liabilities follow a doubly stochastic Poisson process with an intensity rate that is correlated and cointegrated to the index mortality rate. The derived closed-form optimal hedging policy articulates the important role of cointegration in longevity hedging. We show numerically that a time-consistent hedging policy is a smoother function in time when compared with its time-inconsistent counterpart.

Financial Hedging and Optimal Procurement Policies Under Correlated Price and Demand

We consider a firm that procures an input commodity to produce an output commodity to sell to the end retailer. Retailer’s demand for the output commodity is negatively correlated with the price of the output commodity. The firm can sell the output commodity to the retailer either through a spot or a forward contract. Input and output commodity prices are also correlated and follow a joint stochastic price process. The firm maximizes the value of its stakeholders by jointly determining the optimal procurement policy of the input commodity, and the financial hedging policy for the sales of the output commodity. We show that partial hedging dominates both perfect hedging and no-hedging when input price, output price, and demand are correlated, and we characterize this optimal hedging policy. We identify sufficient conditions under which myopic policy is optimal for the price taking firm. We also show that expected base-stock policy is optimal in the presence of yield uncertainty. Our analysis illustrates that hedging is most beneficial when output price volatility is high and input price volatility is low. Our model is tested on the futures price data between 4/1/2005 to 12/31/2011 from Chicago Board of Trade (CBOT) for corn and ethanol.

Managing Storable Commodity Risks: The Role of Inventory and Financial Hedge

We study how to manage commodity risks (price and consumption volume) via physical inventory and financial hedge in a multiperiod problem (with an interperiod utility function) for a risk-averse firm procuring a storable commodity from a spot market at a random price and a long-term supplier at a fixed price. The firm also has access to financial contracts written on the commodity price, such as futures contracts and call and put options. We examine different cases of financial hedging, for example, single-contract and multicontract hedges. For each case, we dynamically maximize the mean-variance utility of the firm's cash flow and characterize an optimal integrated policy of inventory and hedging, which is easy to compute and implement. We find that as long as futures are used in each period, alone or not, the optimal inventory policy is myopic. The optimal hedging policy, however, is never myopic, but depends on all the future optimal decisions. This is contrary to findings of the literature using intraperiod utility functions, which finds myopic hedging to be optimal. Moreover, we find that hedging may lead to inventory reduction in multiperiod problems. Thus the insights from the single-period studies in the literature—hedging leads to inventory increase—do not apply. Finally, insights are offered on the role and impact of inventory and financial hedge on profitability, variance control, and service level, using both analytical and numerical results.

Corporate Risk Management and Information Disclosure

Résumé Cet article se propose d’établir un lien entre la politique de gestion du risque, la politique informationnelle et le coût du capital d’une entreprise. Plus précisément, nous montrons que la gestion du risque peut être un outil au service de la politique informationnelle de la firme. Nous soulignons que la gestion du risque optimale ne consiste pas forcément à éliminer tous les risques : certains risques doivent être maintenus car ils ont un contenu informationnel alors que d’autres doivent être éliminés car ils sont source de bruit et nuisent à la lisibilité des signaux envoyés par la firme au marché financier. En éliminant le bruit, la firme réduit la variabilité de son coût du capital et créé ainsi de la valeur. Nous montrons, en outre, que la politique de gestion du risque optimale n’est pas la même selon qu’elle est observable ou non et nous discutons l’optimalité d’une réglementation visant à assurer l’observabilité des politiques de couverture des risques.

THE COST OF ILLIQUIDITY AND ITS EFFECTS ON HEDGING

Though liquidity is commonly believed to be a major effect in financial markets, there appears to be no consensus definition of what it is or how it is to be measured. In this paper, we understand liquidity as a nonlinear transaction cost incurred as a function of rate of change of portfolio. Using this definition, we obtain the optimal hedging policy for the hedging of a call option in a Black-Scholes model. This is a more challenging question than the more common studies of optimal strategy for liquidating an initial position, because our goal requires us to match a random final value. The solution we obtain reduces in the case of quadratic loss to the solution of three partial differential equations of Black-Scholes type, one of them nonlinear.

Reinsurance and corporate taxation in the United Kingdom life insurance industry

There are two main tax-related arguments regarding the use of reinsurance – the income volatility reduction and the income level enhancement arguments. The income volatility reduction argument contends that firms facing convex tax schedules have incentives to hedge in order to reduce the volatility of their annual taxable income and thereby lower expected tax liabilities [Smith, C.W., Stulz, R.M., 1985. Optimal hedging policies. Journal of Financial and Quantitative Analysis 19, 127–140]. The income level enhancement argument, advanced by Adiel [Adiel, R., 1996. Reinsurance and the management of regulatory ratios and taxes in the property–casualty insurance industry. Journal of Accounting and Economics 22, 207–240], is more specific to hedging via reinsurance. This perspective holds that reinsurance enhances current reported earnings via the receipt of reinsurance commissions and so increases tax liabilities. Consequently, insurance firms with high marginal tax rates should use less reinsurance than those with low marginal tax rates if tax matters. Prior studies using data on financial derivatives have produced mixed results on the validity of the first argument, while Adiel (1996) finds the second argument insignificant in his study of the use of reinsurance by a sample of United States (US) property–liability insurance firms. This study tests the two tax-related arguments using 1992–2001 data for a sample of United Kingdom (UK) life insurance firms. We find that UK life insurers with low before-planning marginal tax rates tend to use more reinsurance; in contrast, tax convexity is found to have no significant impact on the purchase of reinsurance and so the volatility-reduction argument is not supported.

Préférences par rapport au risque et marchés à terme : le cas d'une quantité incertaine

Cet article examine la decision optimale de couverture d’une firme faisant face a un double risque prix-quantite. Dans un cadre d’esperance d’utilite, nous montrons que la notion de prudence au sens de Kimball (1990) est essentielle dans la caracterisation de la position optimale de la firme sur le marche a terme. Plus surprenant, les notions d’aversion au risque et de prudence, peuvent donner lieu a des effets contraires, notamment lorsque la firme souhaite speculer.Classification JEL : D81, G10.

Optimal use of futures contracts for the competitive firm

Standard futures hedging policies are based on the so-called optimal hedge ratio which implicitly ignores the competitive environment in which the firm operates. The purpose of this study is to derive an optimal hedging policy for a firm facing random production costs and a downward sloping demand curve for its product. In this context, the study shows that the optimal number of futures contracts is positively related to the elasticity of the firm's demand function.

Optimal Dynamic Hedging Using Futures Under a Borrowing Constraint

Both financial and non-financial firms routinely implement hedging policies to mitigate their exposure to changes in asset prices. However, while these policies may perform satisfactorily in the limited sense of hedging the exposure under consideration, they might increase the overall likelihood of financial distress due to the liquidity risks that they create. This paper examines the case of hedging price risk using derivative contracts that are marked to market (such as futures contracts) and hence subject to margin calls. It is shown that liquidity risk, stemming from the need to meet margin calls on the futures position, can be a significant source of risk and can even lead to financial distress even though the firm remains hedged. Such risks should therefore be taken into account in the formulation of an optimal hedging policy. This paper derives the dynamic hedging strategy of a firm that uses futures contracts to hedge a spot market exposure. The risk emanating from the margin requirement on futures contracts is incorporated into the hedging decision by restricting the borrowing capacity of the firm. It is shown that this leads to a substantial reduction in the firm's optimal hedge, especially if the hedging horizon is long. The results provide theoretical support for the low level of hedging observed empirically.

Hedging the value of waiting

We analyze the optimal hedging policy of a firm that has flexibility in the timing of investment. Conventional wisdom suggests that hedging adds value by alleviating the under-investment problem associated with capital market frictions. However, our model shows that hedging also adds value by allowing investment to be delayed in circumstances where the same frictions would cause it to commence prematurely. Thus, hedging can have the paradoxical effect of reducing investment. We also show that greater timing flexibility increases the optimal quantity of hedging, but has a non-monotonic effect on the additional value created by hedging. These results may help explain the empirical findings that investment rates do not differ between hedgers and non-hedgers, and that hedging propensities do not depend on standard measures of growth opportunities.

Hedging the Value of Waiting

We analyze the optimal hedging policy of a firm that has flexibility in the timing of investment. Conventional wisdom suggests that hedging adds value by alleviating the under-investment problem associated with capital market frictions. However, our model shows that hedging also adds value by allowing investment to be delayed in circumstances where the same frictions would cause it to commence prematurely. Thus, hedging can have the perverse effect of reducing investment. We also show that greater timing flexibility increases the optimal quantity of hedging, but has a non-monotonic effect on the additional value created by hedging. These results may help explain the empirical findings that investment rates do not differ between hedgers and non-hedgers, and that hedging propensities do not depend on standard measures of growth opportunities.

Mean-Variance Hedging When There Are Jumps

In this paper, we consider the problem of mean-variance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem, and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and the theory of backward stochastic differential equations. The results we have obtained show how backward stochastic differential equations can be used to obtain solutions to optimal investment and hedging problems when discontinuities in the underlying price processes are modeled by the arrivals of Poisson processes with stochastic intensities. Applications to the problem of hedging default risk are also discussed.