Hello,I know how vanilla european options are hedged - using delta-neutral hedging.I also know that any derivative that provides at some future date a payoff, which is linked to the index value at that future date, can be hedged using the same approach. The only problem is the calculation of the delta of the non-standard derivative, but this can be done approximately using Monte Carlo vauation. That is, we can draw a graph of any dependence of the derivative payoff on the index value, and we can value and hedge such derivative without any problems.But I do not know how more complex derivatives are hedged. Does the same delta-neutral hedging approach work for them? For example, let's take the asian call. I can calculate its delta (for example, using Monte Carlo valuation). But if I perform delta-neutral hedging using this delta, will the option be perfectly hedged?Does delta-neutral hedging work with knock-in/out options, with forward-starting options, etc.? Or are they hedged using a completely different approach?So far I have mentioned only derivatives that depend on only one variable. What about those linked to several variables, for example, best-of options? What method is used to hedge them?I am interested in hedging not only theoretically, but also (and even primarily) practically: if I sell, for example, an Asian option, how should I hedge it in practice to get rid of the risks?By the way, the interesting thing is that all the options that I mentioned can be valued using Monte Carlo simulation. But knowing the fair vaue of an option, and knowing how to hedge it so that the hedging costs would be equal to the fair value - this is another big question.It would be great if someone could suggest some source of information on hedging (a website, article or book).Thank you.

QuoteI know how vanilla european options are hedged - using delta-neutral hedging.Really?What about vega?QuoteThe only problem is the calculation of the delta of the non-standard derivative, but this can be done approximately using Monte Carlo vauation.Again Really???????What about discontinuous payoffs like digitals....?QuoteBut I do not know how more complex derivatives are hedged. Does the same delta-neutral hedging approach work for them? For example, let's take the asian call. I can calculate its delta (for example, using Monte Carlo valuation). But if I perform delta-neutral hedging using this delta, will the option be perfectly hedged?I am getting the feeling that you don't understand the replication argument used to price products.Assuming that we/you only delta hedge and that the BS Model is correct, then the option will be perfectly hedged. However, as you need to vega hedge, gamma hedge etc.... as we are in the real world, then you will never capture the value of the trade as the model is ill posed.I suggest buying Mark Joshi's book on The Concepts and Practice of Mathematical Finance. You will definitely get a lot from this book.

Of course, I know that if volatility changes during the option life, delta-hedging will result in a loss or profit, so this is also a risk. By the way, taking this risk is called volatility trading.But anyway, the volatility risk, it seems to me, will not result in huge hedging errors.So let's suppose that the volatility is constant.Hedging binary options, in theory, is done in the same way as ordinary options, and, if hedged continuously and in a perfect world, all risk is taken away. Sure, discrete hedging in the real world will result in hedging errors - by the way, I am planning to perform some tests to assess these hedging errors (I asked in a topic for the binary option delta formula, but did not get any replies yet, unfortunately).Most of my knowledge of hedging options comes from the book "Buying and selling volatility" - the book and the explanations are very intuitive, and my understanding of hedging is based on intuition. I also know that delta-hedging works in practice (with some hedging error, sure). Unfortunately, I do not have a knowledge of mathematics deep enough to fully understand how that works - I cannot prove mathematically that the BS model is correct, and it is difficult for me to understand all the stochastic differential equations.What I wanted to know was whether all options, including knock-out, asian, etc., can be perfectly hedged in the BS world?The second this I wanted to know was how basket options that depend on several assets are hedged? Are there two deltas that are calculated or what?I'll have a look at the book you suggested - thank you for your advice.

QuoteI suggest buying Mark Joshi's book on The Concepts and Practice of Mathematical Finance. You will definitely get a lot from this book.always a good idea... you might also find taleb's "dynamic hedging" useful

"What I wanted to know was whether all options, including knock-out, asian, etc., can be perfectly hedged in the BS world?"You have already answered this question yourself. Using a Black Scholes Model in a Black Scholes World the hedge will be perfect - it follows necessarily from your assumptions. However, the important issue is what happens when you use the BS Model in the real world to hedge."The second this I wanted to know was how basket options that depend on several assets are hedged? Are there two deltas that are calculated or what?"This question is not one that is simple to answer as the methodology to hedge basket options is not solved easily. If we assume that we have risks on basket options where the option depends on 2 underlyings, then you will have "2 deltas" i.e. delta risks on the underlying assets, plus risks on combintations of the assets that captures the correlation risk from entering into the trade. The ability to hedge these complex greeks is restricted by the market's offerings.I agree with mj that the concept of hedging basket options is covered to some extent by Dynamic Hedging - although I have to say that it is not the clearest or greatest book on my shelf at home.

QuoteThis question is not one that is simple to answer as the methodology to hedge basket options is not solved easily.So it seems that there are big differences between hedging a derivative dependent on only 1 asset, and a derivative which depends on more than 1 asset.1) Derivative dependent on 1 asset.Such one can in theory be hedged perfectly using delta-neutral hedging, if the volatility is constant.2) Derivative dependent on many assets.Such cannot be hedged perfectly even in theory.Did I get you right?Hmm... An vanilla option dependent on a basket of stocks can be easily hedged, by buying and selling the basket of stocks. So it seems that the division between the two types (which can and which cannot be perfectly hedged in theory) is a bit different...

richbrad, mind if u recommend the books that u like?finished Taleb's "dynamic hedging", but frankly, i am still fudged quite a fair bit.thks a mil.

QuoteOriginally posted by: micha12Of course, I know that if volatility changes during the option life, delta-hedging will result in a loss or profit, so this is also a risk. By the way, taking this risk is called volatility trading. But anyway, the volatility risk, it seems to me, will not result in huge hedging errors. So let's suppose that the volatility is constant.Many people, including experienced traders, confuse hedging and strategy. In theory, there's a clear separation. You decide what bets you want to make (strategy) then refine your position to make those, and only those, bets (hedging). In practice things blur. If you are a vanilla option market maker, you buy and sell at customer convenience, trying to make a spread. You put on some portfolio hedges to minimize delta and vega risk at a minimum, and possibly some other risks. Whatever risk is left over is what you take. You could say you take that risk as a strategy, or as a defect in your hedging.Generally speaking, the hedging decision is driven more by costs than theory. If there are liquid instruments with high correlations to your positions, you either use them to hedge or choose to take a position. You then monitor the rest of your risk and hedge it only if it becomes unpleasant enough to justify the cost of using less-liquid instruments with lower correlations. If that doesn't solve the problem, you change your business.If you are a market maker in exotic options, you set your spreads high enough to cover your residual risk. You hedge what you can cheaply, then make a choice about the rest.If you buy or sell exotic options for profit, your hedge depends why you made the original trade. Most people buy Asian options to hedge a natural Asian exposure. If you think the Asian is expensive relative to the vanilla, you sell the Asian and hedge with the vanilla.

. (Edited after complaint).

seanster - What do you want to learn about??

hi richbrad, i am currently a new options traderlooking for more knowledge on the techniques of hedging, as well as a more detailed description of the further greeks i.e. vanna, volga, revga, bufga, vega hedging etcany recommended books will be very useful indeed.thks a mil brad.