sgelb: This may not be true 100% but essentially assets have higher vol at very low levels because of what I call tick size.This is not really true. Something that trades at 0.03 with a minimum price increment (tick) of 0.01 will obviously display a much higher volatility. This however is more or less an artefact to be observed with penny stocks where there is no vol trading going on. If it was a very active instruments and the vol would be not high enough to to exceed the tick size, you would see huge bids at 0.02 and huge offers at 0.03, so you couldn't really trade your gamma as you would never get filled (yes, I'm aware that you could have pro-rata matching. How ever, you still couldn't get filled on your entire size then by definition)NeroTulip,Buy at market: Lift (or take) the offer - MineSell at market: Hit the Bid - YoursRegards

QuoteOriginally posted by: FDAXHunterGiven a lognormal distribution (i.e. no fat tails or centers), no transaction costs and frictionless markets, why should there still be a skew in plain vanilla options... and why should you definitely not use this skew for exotics?Assuming that is the question, FDAX asked it, and nobody has answered, I'll take a wild guess. Isn't there something with carry cost when an option is deep in-the-money?What, is an exotic like a barrier? I guess that either there is no underlying you can carry, or they never get "deep in-the-money" or something.MP

QuoteOriginally posted by: FDAXHuntersgelb: This may not be true 100% but essentially assets have higher vol at very low levels because of what I call tick size.This is not really true. Something that trades at 0.03 with a minimum price increment (tick) of 0.01 will obviously display a much higher volatility. This however is more or less an artefact to be observed with penny stocks where there is no vol trading going on. If it was a very active instruments and the vol would be not high enough to to exceed the tick size, you would see huge bids at 0.02 and huge offers at 0.03, so you couldn't really trade your gamma as you would never get filled (yes, I'm aware that you could have pro-rata matching. How ever, you still couldn't get filled on your entire size then by definition)NeroTulip,Buy at market: Lift (or take) the offer - MineSell at market: Hit the Bid - YoursRegardsI think that this question is very difficult and many different people will give you very different answers... its often something that people will have different views upon, hence you get a market for volaility skew.. The only other thing I would say would be that obviously in the real world, vol is not constant, maybe you will get a lognormal dist, but vols will change, and, my previous answer gives one case where this is probably true for financial assets. The Non-lognormality in the real world in my view has to do with market psychology and the position structure in the market (every one is long assets, most have to be, in a panic, obviously sellers outnumber buyers so asset prices get more volatile here. Now FDAX, are you going to share your answer to this question so we can all have wonderful insight to dealing options..? Im especially curious to hear your answer in exotics.

I'll give you a hint... think non-completeness of Black-Scholes with regard to volatility. Think convexity (not gamma!).

vega convexity?

explore that thought...

ATM dVega/dVol is essentially 0OTM dVega/dVol is positive (convexity)And convexity is good.

You're close NeroTulip.

Well, if the smile is flat I prefer the OTM option because its vega is convex. Hence I'm ready to pay a higher implied vol.You should not use this smile for exotics because it depends on the convexity of the vega of the option.Can I go get wasted now?

Yes, NeroTulip, you can get wasted now... nicely done.

A Frenchie beat you all... shame on you!

Thank you, Master.*bows*(^_^)

FDAX,If you are looking at Vega effects then I assume you are looking at a non-constant volatility. How does this non-constant volatility fit within your assumption of a lognormal distribution. I thought stochastic volatility led to fatter tails? Which you assumed away in the phrasing of your question. Cheers,Yurtle.

Just to chuck in my RMB 0.02:First, to answer Yurtle's point, you can use a MC with constant vol to investigate the P&Ls arising from different share price paths. You will quickly see that the P&L is path dependent. For example, if you are delta-hedging a long position in a call, you will make more if you experience your volatility when the call is ATM, having maximum gamma, than if the call is DITM having tiny gamma. Any options market maker will confirm this from experience.Second, on NeroTulip's point that "convexity is good". This is worth formalising a little. The point is that the market is incomplete in volatility, meaning that risk preferences have to be taken into account. The concavity of a risk-averse investor's utility function is *matched* by the convexity of the options. If investors were risk-neutral then they wouldn't care about the convexity.Third, on the point about not using the convexity to price exotics, there are two ways to proceed. Either (1) assume risk-neutrality: use the vanillas to calculate a bunch of vega-convexity adjustments and then use these adjustments to price the exotics or (2) assume risk-aversion and use the vanillas to back out a utility function and then use this function to price the exotics. I prefer (2) because I'm more used to it and because it's easy to see if the shape is ridiculous but (1) is equivalent.Finally, when FDAX says "A Frenchie beat you all... shame on you!" I'd just like to point out that I got this answer without the incompleteness hint when we discussed it a few days ago. So ..."The English, the English, the English are bestUp with the English and down with the rest!"

QuoteOriginally posted by: JohnnyJust to chuck in my RMB 0.02:First, to answer Yurtle's point, you can use a MC with constant vol to investigate the P&Ls arising from different share price paths. You will quickly see that the P&L is path dependent. For example, if you are delta-hedging a long position in a call, you will make more if you experience your volatility when the call is ATM, having maximum gamma, than if the call is DITM having tiny gamma. Any options market maker will confirm this from experience.But this is the essence of the vega convexity point. The operator prefers the OTM option because he has a view on the volatility of the underlying in a certain price "area". He doesn't have to pay a lot for a good position later. QuoteSecond, on NeroTulip's point that "convexity is good". This is worth formalising a little. The point is that the market is incomplete in volatility, meaning that risk preferences have to be taken into account. The concavity of a risk-averse investor's utility function is *matched* by the convexity of the options. If investors were risk-neutral then they wouldn't care about the convexity.I agree with johnny here.. a risk-neutral investor will take risk without compensation, In my view positive vega convexity is a sort compensation, thats why we (normally) have a healthy demand for wing options. QuoteThird, on the point about not using the convexity to price exotics, there are two ways to proceed. Either (1) assume risk-neutrality: use the vanillas to calculate a bunch of vega-convexity adjustments and then use these adjustments to price the exotics or (2) assume risk-aversion and use the vanillas to back out a utility function and then use this function to price the exotics. I prefer (2) because I'm more used to it and because it's easy to see if the shape is ridiculous but (1) is equivalent.sgelb is flapping his finger up and down on his lips like a retard.QuoteFinally, when FDAX says "A Frenchie beat you all... shame on you!" I'd just like to point out that I got this answer without the incompleteness hint when we discussed it a few days ago. So ..."The English, the English, the English are bestUp with the English and down with the rest!" yes, I would 'ave to agree on zis with you, zee froggies are 'orrible.. Anyone got any views on the convexity of brittney spears lovely bum? She's on 4 in ten minutes..!