Abstract
Unlike delta-hedging or similar methods based on Greeks, global hedging is an approach that optimizes some terminal criterion that depends on the difference between the value of a derivative security and that of its hedging portfolio at maturity or exercise. Global hedging methods in discrete time can be implemented using dynamic programming. They provide optimal strategies at all rebalancing dates for all possible states of the world, and can easily accommodate transaction fees and other frictions. However, considering transaction fees in the dynamic programming model requires the inclusion of an additional state variable, which translates into a significant increase of the computational burden. In this short note, we show how a decomposition technique based on the concept of post-decision state variables can be used to reduce the complexity of the computations to the level of a problem without transaction fees. The latter complexity reduction allows for substantial gains in terms of computing time and should therefore contribute to increasing the applicability of global hedging schemes in practice where the timely execution of portfolio rebalancing trades is crucial.
Highlights
Hedging designates a variety of trading strategies designed to reduce the risk related to the price movements of certain assets
It is interesting to recall that one of the basic models for the evaluation of option contracts is based on a hedging argument: in a complete market, the value of an option is equal to the capital required to set up a portfolio providing a perfect hedge, meaning one that produces the same payoff for all possible realizations of the price of the underlying asset
Assuming that trading can be done in continuous time and that there are no transaction costs, under the delta-neutral hedging strategy, the value of the hedging portfolio is equal to the value of the option at all times
Summary
Hedging designates a variety of trading strategies designed to reduce the risk related to the price movements of certain assets. It is interesting to recall that one of the basic models for the evaluation of option contracts is based on a hedging argument: in a complete market, the value of an option is equal to the capital required to set up a portfolio providing a perfect hedge, meaning one that produces the same payoff for all possible realizations of the price of the underlying asset. This is the rationale behind the so-called delta-neutral option hedging strategy. The approach presented in the current paper should contribute to increase the applicability of global hedging algorithms in practice by alleviating the issue of high computing time and allowing for a faster and more precise execution of trades during portfolio rebalancing operations
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