Production and hedging under state‐dependent preferences

This study examines the behavior of the competitive firm under output price uncertainty and state‐dependent preferences. When there is a futures market for hedging purposes, the firm's optimal production decision is independent of the output price uncertainty and of the state‐dependent preferences. If the futures contracts are unbiased, the firm's optimal futures position is an over‐hedge or an under‐hedge, depending on whether the firm is correlation averse or correlation loving, and on whether the output price is positively or negatively expectation dependent on the state variable. When the firm has access not only to the unbiased futures but also to fairly priced options, sufficient conditions are derived under which the firm's optimal hedge position includes both hedging instruments. This study thus establishes a hedging role of options, which is over and above that of futures, in the case of state‐dependent preferences. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:945–963, 2012     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

RISK-AVERSION BEHAVIOR IN CONSUMPTION/INVESTMENT PROBLEMS1

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type function in the special case treated in the paper. Coefficients of absolute and relative risk aversion are defined to be the well-known curvature measures associated with the derived utility of wealth obtained as the value function of the agent's optimization problem. Through an analysis of these coefficients, we show how the change in agent's risk aversion as his wealth changes depends on his consumption utility and the other problem parameters, including the payment at bankruptcy. Moreover, in the HARA case, we can conclude that the agent's relative risk aversion is nondecreasing with wealth, while his absolute risk aversion is decreasing with wealth only if he is sufficiently wealthy. At lower wealth levels, however, the agent's absolute risk aversion may increase with wealth in some cases.     

Exports and hedging exchange rate risks: the multi‐country case

This article examines the optimal production, export allocation, and hedging decisions of a risk‐averse international firm that exports to several foreign markets with different currencies. The firm faces multiple exchange rate risks. Optimal decisions are analyzed under two scenarios. In the first, there is a forward market for one currency only. Then, the export allocation to different markets is separable from the firm's preferences and the joint distribution of the exchange rates. In contrast, total production is not separable except for a special case. In the second scenario, there is a forward market for each currency. Then, both production and export allocation are separable. Hedging with forward contracts depends on risk premia and on the joint distribution of the exchange rates. If tradable exchange rate risk is a linear function of untradable exchange rate risk plus noise, there is a conflict between cross hedging and taking a basis risk. If, alternatively, the untradable exchange rate risk is a linear function of the tradable exchange rate risk and noise, there is no such conflict. A speculative position in a biased forward market for one currency can be cross hedged using an unbiased forward market for another currency. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:843–864, 2000.     

Contingent Capital,Real Options,and Agency Costs

This paper aims to clarify how contingent convertible bond (CoCo) as a debt financing instrument affects a firm's investment policy, agency cost of debt, and capital structure. We consider endogenous and exogenous conversion thresholds, respectively. Under the exogenous case, there is an explicit optimal fraction of equity allocated to CoCo holders upon conversion, such that the agency cost reaches zero. Numerical analysis demonstrates that under an endogenous conversion threshold, CoCo induces overinvestment, a higher leverage, a possible bigger agency cost, and a stronger incentive to increase risk. But if the conversion threshold is exogenously determined, almost the opposite holds true.     

Hedging nontradable risks with transaction costs and price impact

A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the nontradable risk factor is nonlinear, we provide an approximation to the optimal strategy in closed‐form, and prove that the value function is correctly approximated by this strategy when cross‐impact and risk‐aversion are small. We further prove that when is nonlinear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's “Delta” under a particular probability measure.     

What to do if a dollar is not a dollar? The impact of inflation risk on production and risk management

An entrepreneur faces two types of risk: one from income generation, one from income spending. His income from firm profits is risky due to output price fluctuations and other risks. As a consumer, he is also exposed to inflation risk since he maximizes expected utility of real income. This article focuses on optimal production and risk management decisions of a risk‐averse entrepreneur jointly facing tradable output price risk and untradable inflation risk. Inflation risk applies multiplicatively to the entrepreneur's entire nominal income. Relative risk aversion and the risks' joint distribution determine the effect of introducing a futures market on production. For dependent risks, this effect may be negative if relative risk aversion is above one. Relative risk aversion and the joint distribution also determine optimal risk management with futures contracts where speculation on a real risk premium and cross hedging may be conflicting objectives. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:371–386, 2002     

A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements

This paper examines optimal consumption and investment choices and the cost of hedging contingent claims in the presence of margin requirements or, more generally, of nonlinear wealth dynamics and constraints on the portfolio policies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities' price process and the investor's preferences. As an illustration, explicit solutions are provided for an agent with ‘logarithmic’ utility. A PDE characterization of the cost of hedging a nonnegative path‐independent European contingent claim is also provided.     

Hedging under counterparty credit uncertainty

This study investigates optimal production and hedging decisions for firms facing price risk that can be hedged with vulnerable contracts, i.e., exposed to nonhedgeable endogenous counterparty credit risk. When vulnerable forward contracts are the only hedging instruments available, the firm's optimal level of production is lower than without credit risk. Under plausible conditions on the stochastic dependence between the commodity price and the counterparty's assets, the firm does not sell its entire production on the vulnerable forward market. When options on forward contracts are also available, the optimal hedging strategy requires a long put position. This provides a new rationale for the hedging role of options in the over‐the‐counter markets exposed to counterparty credit risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 248–263, 2008     

Pricing American options with stochastic volatility: Evidence from S&P 500 futures options

This article is the first attempt to test empirically a numerical solution to price American options under stochastic volatility. The model allows for a mean‐reverting stochastic‐volatility process with non‐zero risk premium for the volatility risk and correlation with the underlying process. A general solution of risk‐neutral probabilities and price movements is derived, which avoids the common negative‐probability problem in numerical‐option pricing with stochastic volatility. The empirical test shows clear evidence supporting the occurrence of stochastic volatility. The stochastic‐volatility model outperforms the constant‐volatility model by producing smaller bias and better goodness of fit in both the in‐sample and out‐of‐sample test. It not only eliminates systematic moneyness bias produced by the constant‐volatility model, but also has better prediction power. In addition, both models perform well in the dynamic intraday hedging test. However, the constant‐volatility model seems to have a slightly better hedging effectiveness. The profitability test shows that the stochastic volatility is able to capture statistically significant profits while the constant volatility model produces losses. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:625–659, 2000     

The use of foreign currency derivatives,corporate governance,and firm value around the world

This paper examines the impact of currency derivatives on firm value using a broad sample of firms from thirty-nine countries with significant exchange-rate exposure. Derivatives can be used for managers' self-interest, for hedging or for speculative purposes. We hypothesize that investors can appeal to a firm's internal (firm-level) and external (country-level) corporate governance to draw inferences on a firm's motive behind the use of derivatives, since well-governed firms are more likely to use derivatives to hedge rather than to speculate or pursue managers' self-interest. Consistent with this explanation, we find strong evidence that the use of currency derivatives for firms that have strong internal firm-level or external country-level governance is associated with a significant value premium.     

Effects of reduced government deficiency payments on post‐harvest wheat marketing strategies

Effects of reducing government deficiency payments on a wheat producer's post‐harvest marketing strategies are evaluated. The deficiency payment is predicted using an average option pricing model to properly value both intrinsic and time values of the deficiency payment. The biggest loss to producers from reducing deficiency payments is reduced revenue. The deficiency payment program was no better than hedging strategies in reducing post‐harvest risk, and when grain was sold at harvest, it even increased post‐harvest risk. Many producers will compensate for reduced deficiency payments by increasing use of futures or options contracts. For some producers, however, the optimal strategy is to sell wheat at harvest, because of high opportunity cost, storage cost, or risk aversion. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:243–263, 2000     

Hedging in Futures and Options Markets with Basis Risk

This paper analyzes the hedging decisions for firms facing price and basis risk. Two conditions assumed in most models on optimal hedging are relaxed. Hence, (i) the spot price is not necessarily linear in both the settlement price and the basis risk and (ii) futures contracts and options on futures at different strike prices are available. The design of the first‐best hedging instrument is first derived and then it is used to examine the optimal hedging strategy in futures and options markets. The role of options as useful hedging tools is highlighted from the shape of the first‐best solution. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:59–72, 2002     

Volatility and trading demands in stock index futures

In this study we examine how volatility and the futures risk premium affect trading demands for hedging and speculation in the S&P 500 Stock Index futures contracts. To ascertain if different volatility measures matter in affecting the result, we employ three volatility estimates. Our empirical results show a positive relation between volatility and open interest for both hedgers and speculators, suggesting that an increase in volatility motivates both hedgers and speculators to engage in more trading in futures markets. However, the influence of volatility on futures trading, especially for hedging, is statistically significant only when spot volatility is used. We also find that the demand to trade by speculators is more sensitive to changes in the futures risk premium than is the demand to trade by hedgers. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:399–414, 2003     

Trading under the proof-of-stake protocol – A continuous-time control approach

We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close-form solutions and show that the bang-bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk-adjusted valuation of the stakes. In particular, we show when a participant is risk-neutral or risk-seeking, corresponding to the risk-adjusted valuation being a martingale or a sub-martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk-control version of the consumption-investment problem; and for a special case, the “stake-parity” problem, we show a mean-reverting strategy is optimal.     

MISUSE AND OPTIMUM INSPECTING STRATEGY IN AGENCY PROBLEMS

Assets misuse by an agent and the optimal audit inspecting strategy are analyzed in this paper. The agent and the principal are acting to maximize their expected utility and both are characterized by risk aversion. The agent's decision about a theft takes into account the probability of benefiting from the stolen assets but also the probability of being penalized if caught. The principal's decision about the optimal number of audit teams, hence, the probability of uncovering the theft, takes into account the cost involved, the probability of one team of auditors uncovering the theft and the agent's decision about the theft. We get two response curves which describe the optimal behavior of both the agent and the principal and show that there may be a Nash solution to the problem. Since in real life there are often many principals (shareholders) with different utility functions, a set of efficient strategies is offered using the First and Second degree Stochastic Dominance rules. A numerical illustration which clarifies the methodology and displays the applicability of the model is also provided.     

Optimal partial hedging of options with small transaction costs

This study uses asymptotic analysis to derive optimal hedging strategies for option portfolios hedged using an imperfectly correlated hedging asset with small fixed and/or proportional transaction costs, obtaining explicit formulae in special cases. This is of use when it is impractical to hedge using the underlying asset itself. The hedging strategy holds a position in the hedging asset whose value lies between two bounds, which are independent of the hedging asset's current value. For low absolute correlation between hedging and hedged assets, highly risk‐averse investors and large portfolios, hedging strategies and option values differ significantly from their perfect market equivalents. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 31:855–897, 2011     

Hedging costs and joint determinants of premiums and spreads in structured financial products

Evaluating more than 317,000 discount certificates in the German secondary market, we find that premiums and spreads are endogenous and negatively related but depend on different key determinants. The fundamental determinants of the premiums are mainly profit-related, that is, dividends of the underlying, issuers’ credit risk, lifecycle effect, and competition, whereas hedging costs are less important. However, initial hedging costs (IHC) are priced into the premium in the case of large inventory changes. The spread is mostly determined by hedging costs and risk components, such as IHCs, rebalancing costs, volatility, scalper risk, and overnight gap risk—but also by dividends.     

Is volatility risk priced in the KOSPI 200 index options market?

The negative volatility risk premium is understood as a result for a hedging demand against market declines. Although this negative volatility risk premium is observed in most index options markets, there are some doubts about its presence in the KOSPI 200 index options market. The majority of KOSPI 200 index option holders do not possess any position in the underlying market; the composition of trading groups of the KOSPI 200 index options significantly differs from that of its underlying index; in this circumstance, the presence of a hedging demand is questionable. This study shows that volatility risk does not require a premium in the KOSPI 200 index options market. Rather, jump fears influence KOSPI 200 options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:797–825, 2009     

How firms should hedge: An extension

This note studies a firm's optimal hedging strategy with tailor‐made exotic derivatives under both price risk and quantity risk. It extends the analysis of Brown G. W. and Toft K.‐B. (2002) by relaxing the assumption of a bivariate normal distribution. The optimal payoff function of a derivative contract is characterized in terms of the expectation and variance of the quantity, conditional on the price. This main result is illustrated by different examples, stressing the importance of the dependence structure between price risk and quantity risk for the choice of appropriate hedging instruments. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:834–845, 2010