# Super Hedging

The definition of a ‘super hedge’

Super hedging is a strategy that hedges positions with a self-financing trading strategy. It uses low price to pay for the portfolio such that its value is greater than or equal to a set time in the future.

Breaking down the super hedge’

Hedging transactions, limiting investment risks of the underlying asset by using options or futures. Options or futures are purchased in an opposite position in the underlying asset in order to lock in a certain amount of benefits. Super-the price of the hedging portfolio (a) is equivalent to the minimum amount you must pay for a valid portfolio (b) in the current time, so in a future time the value of B at least as big as A. in a perfect market, the super hedging price is equal to the price for hedging the original portfolio. In an incomplete market, such as options, the cost of such a strategy may be too high. The idea of super hedging has been studied by scientists, but this is a theoretical ideal and it is difficult to implement in the real world.

Super-hedging and Sub-hedging

The price of sub-hedge is the largest value that can be paid to any possible situation at some point in the future, you have a second portfolio in the amount of less than or equal to the initial. The upper and lower bounds created by the sub and super hedge prices on hedging, no-arbitrage boundaries, an example of a good Internet borders.

Super hedging and self-financing portfolios

The acceptance set (the set of acceptable future net worth) at a great price hedging is negative the set of values of the self-financing portfolio at the terminal time.

Self-financing portfolio is an important concept in financial mathematics. A portfolio is self-financing, if there is no external infusion or withdrawal of money. In other words, the purchase of a new asset must be financed by selling the old one.

Self-financing portfolio is the replicating portfolio. In mathematical Finance, a replicating portfolio for the asset or series of cash flows is a portfolio of assets with the same properties.

Given asset or liability, offsetting replication portfolio is called a hedge (it can be static or dynamic), and the construction of such a portfolio (through a sale or purchase) is called hedging (static or dynamic). In practice, replicating portfolios are rarely, if ever, just repetition. In addition, there is credit risk, dynamic replication is imperfect, since actual price changes are not infinitesimal, and transaction costs change in hedging not zero.