Hedging is to reduce risk such that we know the worst case of losses. Buying insurance is an example of hedging. For option pricing, hedging categorised into delta hedging, static hedging, partial hedging, superhedging, shortfall hedging

Delta hedging works for continuous time hedging, the idea is that we form a portfolio consisting a risky asset and bank account to replicate an option. We choose delta=V_{s} to eliminate random source. Static hedging is using options such as vanilla options, barrier options to replicate other option. (see Carr)Superhedging is used to incomplete market to obtain a heging portfolio which payoff is greater than or equal to the option at every state of word.Partial hedging is used for sv model.Shortfall hedging is just to hedge a confidence level (eg 95%) of risk.

- DominicConnor
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Hedging is to reduce risk such that we know the worst case of losses.Perhaps a more general definition is that it decreases the variance of outcomes.Few real world hedges offer an absolute floor, and in many cases it is far from optimal to even attempt this.

'Decrease the variance' - this is starting to look like the risk thread! But I hear you - it doesn't read like poetry, but 'adjusting the outcome DF to one that is more acceptable to the utility curve' is the mathematical definition, with the implicit idea that hedging is not done by risk-seekers with convex utilityIn my head I'm thinking about a kind of hedge where you change your exposure's position in the capital structure but increase the notional - i.e. you swap your bonds for a smaller amount of equity. This will make your worst case come out better relative to your equity delta, but the effect of the variance is not clear.

- DominicConnor
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Perhaps I need to refine it to "Hedging reduces the variance of the utility of outcomes", but as kr says, hardly poetry.A poetic definition might be "Hedging is the increase of the good, at the expense of the perfect".Reflecting the fact that hedging usually reduces returns,as well as their variance.

DCFC - I approve heartily of that one!I thought I was the only one in the world who used the term 'structured hedging' (maybe I really am). By this I mean that you take your P/L, add some reserve accounts, and slice some tranches. A waterfall or other set of rules is used to attribute the risk to the different tranches. Each may be marked on a different basis. The objective is to manage mismatches like liquidity differences between the long and the hedge, correlation problems, and other things that are not well-modelled in a liquid diffusion scenario. This idea may be used qualitatively in practice. The objective in any hedging is to identify and attribute risk factors... when the risk factors have mean-reverting behavior then structured hedging is a smart way to think. You are not losing sleep at night because of basis issues when you have modelled their mean-reversion at the outset.Another concept that lies under my idea of 'structured hedging' is that the trading strategy itself may be part of the structure. That is, the rules you use to adjust hedge positions are stated at the outset. Pricing is contingent upon the trading strategy. So, you don't agonize about complete markets because the strategy is a best-efforts approach, and you price the long deriv in the context of having the business break even or make enough money to pay the gang.

- spacemonkey
**Posts:**443**Joined:**

Hedging could be loosely defined as trading in assets in order to reduce the variability of the outcome in some financial transaction. Like backing every horse in a race so that you know you can't lose.This is very useful practically to reduce financial risk, and also theoretically because it is much easier to calculate the value of a sure thing than a gamble.

"Reflecting the fact that hedging usually reduces returns,as well as their variance." Do you know of an example when it doesn't?

When you take a position in a market, you want specific risk exposure. Hedging allows you to maintain this desired risk exposure through trading that keeps the partial of position value wrtunwanted risk = 0. For example, if you want only vega exposure, then the other greeks need to bemaintained near zero. This position is then only sensitive to volatility.

example of superhedging:buy the stock to hedge a call option. MJ

Now I am confused. I know this may sound silly (thats why it is in FAQ), I always thought that delta hedging is the rate of change of the option price with respect to the underlying asset. But MJ said this is called superhedging. When I look back through the thread Vincent said QuoteDelta hedging works for continuous time hedging, the idea is that we form a portfolio consisting a risky asset and bank account to replicate an option. We choose delta=V_{s} to eliminate random source. I think in Vincent's definition he is using the risk neutral approach. I always thought that delta hedging is the delta in the Black Scholes proof. Vincent said superhedging is done in incomplete market whereas in Black Scholes the market is complete. I think my confusion comes from my thinking that the market is complete and thus we can find a perfect hedge for all financial assets. Or it could be that I am totally confused and just talking gibberish. Any comments are welcome

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