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.     

Hedging,liquidity, and the competitive firm under price uncertainty

In this paper, the behavior of the competitive firm under price uncertainty when the firm has access to an intertemporally unbiased futures market is examined. Futures contracts are marked‐to‐market and thus require interim cash settlement of gains and losses. The firm is subject to a liquidity constraint in that it is forced to prematurely close its futures position on which the interim loss incurred exceeds a threshold level. It is shown that the liquidity constrained firm optimally opts for an under‐hedge should it be prudent. Furthermore, the prudent firm cuts down its optimal level of output in response to the presence of the liquidity constraint. As such, the liquidity risk created by the interim funding requirement of a futures hedge adversely affects the hedging and production decisions of the competitive firm under price uncertainty. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:697–706, 2004     

On the ranking of price and quantity controls under uncertainty

It is shown that the equivalence of optimal price, optimal export quota and optimal import quota, known to hold under conditions of complete certainty, also holds if foreign demand is certain, however uncertain is the domestic production set. It is further shown that, even if foreign demand is uncertain, the three controls can be ranked in a special case.     

Multiple unit price promotions and their effects on quantity purchase intentions

Consumers often encounter multiple unit price promotions whereby a price reduction is presented as a reduced total price for multiple units of the same item (e.g., an item regularly priced at $1.25 each is promoted as “5 for $5”). In a series of experiments, we find that the positive effect of these promotions on quantity purchase intentions is contingent on the magnitude of the quantity specified in the offer and the rate of product consumption. However, offer effectiveness is not influenced by highlighting single unit prices, the unrestricted nature of these promotions, or aggregate savings. As predicted by the selective accessibility explanation, the effect of multiple unit price promotions on quantity purchase intentions is shown to be mediated by accessing anchor-consistent knowledge. An agenda for further research and the implications of our findings for retail practice are discussed.     

Hedging performance of shrimp futures contracts with multiple deliverable grades

The performance of the black tiger and white shrimp futures contracts traded in the Minneapolis Grain Exchange (MGE) is considered. These two futures contracts have suffered low trader participation[fn100] since their inception despite the underlying multibillion-dollar cash shrimp market. The article tries to find answers for such lack of interest in the context of the multiple deliverable category character of both contracts. In particular, the hedging effectiveness and the adequacy of the premiums/discounts are measured for the various shrimp size categories traded in each contract. The analyses indicate that the hedging effectiveness of both contracts is relatively modest. Part of the explanation for the performance of the contracts resides in high deliverable category exchange option values, which stem from volatility in the price differentials between size categories. The fixed premiums/discounts are not able to provide a remedy to the alternation in the cheapest to deliver category. There is also a liquidity problem that could result from the peculiarities of seafood trade. It is concluded that the lack of trader interest may be influenced by initial high deliverable category exchange option values. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 957–990, 1999     

Consumer price awareness in food shopping: the case of quantity surcharges

Quantity surcharges, higher unit prices on larger sizes than smaller sizes, are often found among grocery items. In this study we consider the question of why consumers buy surcharged goods. We hypothesize that it is the consequence of a failure to price search, and that some buyers purchase larger sizes in the belief they are cheaper, thus avoiding the need for price comparisons. In the analysis we examine canned tuna, using 1990 data from 54 grocery regions on sales, prices, and consumer demographics. Results support the hypothesis. We find evidence that buyers of surcharged items are mainly those with high time and information costs.     

Setting price or quantity: Depends on what the seller is more uncertain about

We consider a seller with uncertain demand for its product. If the demand curve were certain, then setting price and setting quantity would be equivalent ways to frame the seller’s problem of choosing a profit-maximizing point on its demand curve. With uncertain demand, these become distinct sales mechanisms. We distinguish between uncertainty about the market size and uncertainty about the consumers’ valuations. Our main results are that (i) for a given marginal cost, an increase in uncertainty about valuations favors setting quantity whereas an increase in uncertainty about market size favors setting price; (ii) keeping demand uncertainty fixed, there is a nonmonotonic relationship between marginal costs and the optimal selling mechanism (setting price or quantity); and (iii) in a bilateral monopoly channel setting, coordination occurs except for a conflict zone in which the retailer’s choice of a selling mechanism deviates from the coordinated channel selling mechanism.     

Hedging and value at risk

In this article, it is shown that although minimum‐variance hedging unambiguously reduces the standard deviation of portfolio returns, it can increase both left skewness and kurtosis; consequently the effectiveness of hedging in terms of value at risk (VaR) and conditional value at risk (CVaR) is uncertain. The reduction in daily standard deviation is compared with the reduction in 1‐day 99% VaR and CVaR for 20 cross‐hedged currency portfolios with the use of historical simulation. On average, minimum‐variance hedging reduces both VaR and CVaR by about 80% of the reduction in standard deviation. Also investigated, as an alternative to minimum‐variance hedging, are minimum‐VaR and minimum‐CVaR hedging strategies that minimize the historical‐simulation VaR and CVaR of the hedge portfolio, respectively. The in‐sample results suggest that in terms of VaR and CVaR reduction, minimum‐VaR and minimum‐CVaR hedging can potentially yield small but consistent improvements over minimum‐variance hedging. The out‐of‐sample results are more mixed, although there is a small improvement for minimum‐VaR hedging for the majority of the currencies considered. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:369–390, 2006     

Exponential Hedging and Entropic Penalties

We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X . We prove a duality relation between this problem and a dual problem for local martingale measures Q for X where we either minimize relative entropy minus a correction term involving B or maximize the Q -price of B subject to an entropic penalty term. Our result is robust in the sense that it holds for several choices of the space of hedging strategies. Applications include a new characterization of the minimal martingale measure and risk-averse asymptotics.     

论金融风险及其防范

目前，金融行业潜在的经营风险已日益引起人们的关注．金融风险及经营效益滑坡问题，不但严重影响着商业银行的经营成果，而且给其今后的生存发展也带来潜在的威胁，随时都可能诱发影响全社会的突发危机，从根本上动摇社会对银行体系乃至整个金融体系的信心，危及经济增长的融资来源．因此深入研究如何化解金融风险，已成为各商业银行的当务之急．     

Hedging with mismatched currencies

This article presents a model of a risk-averse multinational firm facing risk exposure to a foreign currency cash flow. Forward markets do not exist between the firm's own currency and the foreign currency, but do exist for a third currency. Because a triangular parity condition holds among these three currencies, the available forward markets, albeit incomplete, provide a useful avenue for the firm to indirectly hedge against its foreign exchange rate risk exposure. This article offers analytical insights into the optimal cross-hedging strategies of the firm. In particular, the results show that separate unbiasedness of the forward markets does not necessarily imply a perfect full hedge that eliminates the entire foreign exchange rate risk exposure of the firm. The optimal cross-hedging strategies depend largely on the firm's marginal utility function and on the correlation of the random spot exchange rates. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19:859–875, 1999     

Valuation and Hedging of Differential Swaps

This paper derives a general‐form formula for pricing and hedging differential swaps with the principal denominated either in a domestic, foreign, or third‐country currency. We first derive the formula for differential swaps with the principal in a domestic currency and identify an error in the formula of Wei (1994). We then show the pricing duality between differential swaps with the principal in a domestic currency and differential swaps with the principal in a foreign currency. Finally, we complete the pricing and hedging analysis on differential swaps by deriving a formula for differential swaps with the principal denominated in a third‐country currency. Simulation results indicate that constant margin rates are generally smaller than interest rate differentials and decline with the tenor of swaps. Correlation parameters associated with the exchange rate play a more important role than correlation parameters among interest rates in pricing differential swaps. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:73–94, 2002