Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market

This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk-free bank account, the underlying asset and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.Comment: 32 pages, 6 figure

Hedging Effectiveness under Conditions of Asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution

A note on the Fundamental Theorem of Asset Pricing under model uncertainty

We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of \emph{robust no-arbitrage} which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are \emph{non-redundant}. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.Comment: Final version. To appear in Risk

Hedging Barrier Options: Current Methods and Alternatives

This paper applies to the static hedge of barrier options a technique, mean-square hedging, designed to minimize the size of the hedging error when perfect replication is not possible. It introduces an extension of this technique which preserves the computational efficiency of mean-square hedging while being consistent with any prior pricing model or with any linear constraint on the hedging residual. This improves on current static hedging methods, which aim at exactly replicating barrier options and rely on strong assumptions on the availability of traded options with certain strikes or maturities, or on the distribution of the underlying asset.Barrier options, Static hedging, Mean-square hedging

HEDGING WHOLESALE BEEF CUTS

Live cattle futures markets do not offer much opportunity for effective hedging of wholesale beef cuts. If a Choice-to-Select price spread futures contract were introduced this would enhance hedging effectiveness although likely not enough to encourage cross hedging. If a Choice boxed beef futures contract were introduced, hedging Choice wholesale beef cuts would be less risky and the addition of a Choice-to-Select price spread would enhance hedging effectiveness especially for Select wholesale beef cuts.Livestock Production/Industries, Marketing,

Export production, hedging exchange rate risk: the duopoly case

This paper studies a Cournot duopoly in international trade so that the firms are exposed to exchange rate risk. A hedging opportunity is introduced by a forward market where the foreign currency can be traded on. We investigate two settings: First we assume that hedging and output decisions are taken simultaneously. We show that hedging is just done for risk managing reasons as it is not possible to use hedging strategically. In this setting the well-known separation result of the competitive firm holds if both firms have the hedging opportunity. In the second setting the hedging decisions are made before the output decisions. We show that hedging is used not only to manage the risk exposure but also as a strategic device. Furthermore we find that no separation result can be stated. --Exchange Rate risk,hedging,exports,duopoly