<t>I think this might depend on what your purpose. A simple and practical approach is to introduce the market variables changes successively and figure out the risks. It works as follows, 1. value D(t1,s1,r1,vol1), where t: time, s: underlying, r: discount rate, vol: pricing volatility. 2. next D(t2...

<t> of course you are right that in case of long options, in the worst case you transfer the collaterals back to the seller and no more. but if you call it margin or not that is up to you, most people I know would call it so. Imagine you are running a book with thousands of long and short positions ...

<t>yes that's one story, there are others ... if you look at historical vix vs gamma swaption vols, you will find they move in tandem somewhat, it is not good enough for hedging as in bs, no way!! (like if you look at daily or weekly moves), but suggests a macro relationships (like, say quarterly fr...

good point, usually these hybrid products are percieved to make a difference in hedging demand, but then again, these are "hybrids", for pure equity vol, I think the view will be essentially macro. Great if you can share in case you find anything

<t>there are number of reasons why delta hedging dotm doesnt make sense -> your deltas will be tiny, it will have high 2nd order sensitivites (ddelta/dvol, ddelta/dspot etc) so your are never sure of your delta, and besides, for balancing tiny delta in the markets, probably you pay much more than it...

<t>this is interesting, though never heard of before, I would guess some real money players, with exposure to both equities and rates might want to put on a "macro" hedge using swaptions - probable reasons -> the equity rates correlations and longer date swaptions are relatively cheaper and more tra...

<t>well as far as i know1. you can get a margin call on a long option position -> for e.g. if you have a 2 way csa with your counterpart, you would pay the premium upfront to the seller, and at the end of the day the seller will post back the equivalent collateral with you -> and as days goes and yo...

<t>I think you would need a model ...an approach to replicate may be use the binomial expansion ... like on day 0, s = s0, so the "inverse" security value on n+1-th day is -> (1/s0) [1/{(1+r1)(1+r2)...(1+rn)}], => (1/s0)* (1 - r1 + ...)(1 - r2 + ..) etc, where r1, r2 are the returns. so to 1st order...

check out the "A Vega-Gamma Relationship for European-Style or Barrier Options in the Black-Scholes Model" by Mercurio (a simple google will get it), page 5, remark 1.2, thats the closest to your query I can remember right now

<t>simply follows from bs -> as the delta nears the atm delta, vega goes up, goes down otherwise. I dont see a need for formulizing this (we have too many of them already), but if you want you can -> given delta depends on Cum Norm and vega on Norm dist you can try and figure out a formula for vega ...

<t>you are right, sabr probably gives you a "better" hedge in the short end. but as gmike said, you simply can't just delta hedge and run an exotics book. You care more about skew dynamics than a "correct" delta, and I (and think most) am not comfortable with sabr dynamis on the longer terms trade, ...

<t>interesting ... am not an exotic guy (not anymore) and haven't been tracking latest sabr development, but curious anyway. What you mean by exotics? I think most people like sabr the way it fits the mkt smile, but few who actually believe in the model dynamics. So if you are pricing things that ar...

<t>have a feeling you are talking about FX here. I vaguely remember I was curious about this too a long while back ... and what dawned on me is this -> suppsed A = eur/usd, b = gbp/usd, so a/b is eur/gbp, so max(a-b,0) depends on eur/usd vol, gbp/usd vol and their correlations, and max(a/b - k,0) de...

<t>1. if you are hedging your 2y swap with a single swap, and computing risk w.r.t. your hedging instrument (which is a 2y swap), most of your risk will be in 2y bucket, just as in the case of 10y swap.2. if you are hedging your 10y position with futures (assuming you have futures till 10y) and comp...

<t>yes, z-spreads/swap spreads or similar. there are good reasons 1. as I said before, in normal mkt conditions, usually the relative spreads are more stable than the yield curves themselves, so it saves time to update your live curves, and maintaining a large book of various govvies less messy 2. s...