Hi all,Hoping someone can help me out with this one....Lets say I have an ex-ante prediction of realized volatility on an underlying security (say an equity for example) which is different to that of the BS Imp Vol of some respective option (say a call option) on the equity.Lets assume my prediction "is correct". (E.g. say I predicted realized vol would be less than Imp Vol and so initially I bought the option and sold delta times the dollar value of my option position in the equity. Then proceeded to delta hedge daily untill expiry). Given my prediction is correct I should make a profit on my trade.Now, practically I am only going to be able to delta-hedge my position daily and not continuously - so lets ignore this aspect. Questions...1) Does this only work if I hold till expiry?2) Does this hold for any type of stochastic process dictating the price evolution if the underling?3) Does the length of the holding period matter?4) Assuming I hold to expiry am I able to ignore extreme changes in the options BS Imp Vol?5) Assuming I hold to expiry am I able to ignore the moneyness or tenor of the option I choose (given BS Imp Vol surface is not flat)?If so am I able to prove this mathematically, I.e. Especially in the instance where the underlying stochastic process has jumps and time-varying vol of vol???I know this is long winded question but I would very much appreciate people's expertise on the matter...Osiris.

Paul and Reza Ahmed's beautiful paper

Quote(E.g. say I predicted realized vol would be less than Imp Vol and so initially I bought the option and sold delta times the dollar value of my option position in the equity). my options knowledge is rusty but I don't think if your vol forecast is less than the option implied that you would be buying the option .......

QuoteOriginally posted by: osirisHi all,Hoping someone can help me out with this one....Lets say I have an ex-ante prediction of realized volatility on an underlying security (say an equity for example) which is different to that of the BS Imp Vol of some respective option (say a call option) on the equity.Lets assume my prediction "is correct". (E.g. say I predicted realized vol would be less than Imp Vol and so initially I bought the option and sold delta times the dollar value of my option position in the equity. Then proceeded to delta hedge daily untill expiry). Given my prediction is correct I should make a profit on my trade.Now, practically I am only going to be able to delta-hedge my position daily and not continuously - so lets ignore this aspect. Questions...1) Does this only work if I hold till expiry?2) Does this hold for any type of stochastic process dictating the price evolution if the underling?3) Does the length of the holding period matter?4) Assuming I hold to expiry am I able to ignore extreme changes in the options BS Imp Vol?5) Assuming I hold to expiry am I able to ignore the moneyness or tenor of the option I choose (given BS Imp Vol surface is not flat)?If so am I able to prove this mathematically, I.e. Especially in the instance where the underlying stochastic process has jumps and time-varying vol of vol???I know this is long winded question but I would very much appreciate people's expertise on the matter...Osiris.This has become a classic interview question: if you sell a call at e.g. 30% implied, delta-hedge until maturity (even continuously), and realised vol is e.g. 25%, you cannot predict the sign of your p/l because of p/l path-dependyI wrote a paper when I was still at JPMorgan in 2005 and also gave talks at the University of Chicago on that theme, showing that it is much better to use variance swaps to trade volatility than delta-hedge vanilla options...At about the same time, Dupire did some interesting work on 'Business Time' and claims that if a trader hedges the delta using a 'clock' based on quadratic variation, the P&L will only depend on QV and spot price... I don't know to which extent this approach is applicable in real life: I had an impression that the Business Time approach was somewhat akin to a different accounting treatment whereby the trader would keep the option premium collected at start in his pocket and release it progressively to pay for gamma losses, so that if at the end IV > QV there is something left in the pocket (what happens if IV < QV is not entirely clear to me). But I may well have formed a wrong interpretation.SB

QuoteOriginally posted by: osirisHi all,Hoping someone can help me out with this one....Lets say I have an ex-ante prediction of realized volatility on an underlying security (say an equity for example) which is different to that of the BS Imp Vol of some respective option (say a call option) on the equity.Lets assume my prediction "is correct". (E.g. say I predicted realized vol would be less than Imp Vol and so initially I bought the option and sold delta times the dollar value of my option position in the equity. Then proceeded to delta hedge daily untill expiry). Given my prediction is correct I should make a profit on my trade.Now, practically I am only going to be able to delta-hedge my position daily and not continuously - so lets ignore this aspect. Questions...1) Does this only work if I hold till expiry?2) Does this hold for any type of stochastic process dictating the price evolution if the underling?3) Does the length of the holding period matter?4) Assuming I hold to expiry am I able to ignore extreme changes in the options BS Imp Vol?5) Assuming I hold to expiry am I able to ignore the moneyness or tenor of the option I choose (given BS Imp Vol surface is not flat)?If so am I able to prove this mathematically, I.e. Especially in the instance where the underlying stochastic process has jumps and time-varying vol of vol???I know this is long winded question but I would very much appreciate people's expertise on the matter...Osiris.Giving up your intraday scalps on a long gamma position is basically throwing away free money.

QuoteOriginally posted by: StatTraderGiving up your intraday scalps on a long gamma position is basically throwing away free money.Could you please elaborate on this ?It seems to me that if you are long gamma, you will always earn the contribution due to gamma1/2 Gamma sigma^2 S^2 (dS/S)^2--- doesn't matter whether you delta hedge or not. I'm assuming that by intraday scalps, you meandelta hedging.I'd be interested in hearing your view on the matter.

It does matter if you delta hedge or not ...

QuoteOriginally posted by: MrMartingaleQuoteOriginally posted by: StatTraderGiving up your intraday scalps on a long gamma position is basically throwing away free money.Could you please elaborate on this ?It seems to me that if you are long gamma, you will always earn the contribution due to gamma1/2 Gamma sigma^2 S^2 (dS/S)^2--- doesn't matter whether you delta hedge or not. I'm assuming that by intraday scalps, you meandelta hedging.I'd be interested in hearing your view on the matter.If you're long gamma, regardless of the direction in which the underlying moves, your position will generate "good" deltas. By good, I mean if the underlying moves up you'll automatically get longer, if it goes down you'll automatically get shorter. Rebalancing thereby forces you to buy low, sell high so if you're rebalancing intraday you're effectively scalping the underlying with the safety net of your option position. Lets say at during the day your delta goes from 0 to 1 to -1 to 0. If you only delta hedge daily you're missing out on some pretty decent scalps. With each scalp you're crystalizing P&L which can help offset some of your time decay.

QuoteOriginally posted by: StatTraderQuoteOriginally posted by: MrMartingaleQuoteOriginally posted by: StatTraderGiving up your intraday scalps on a long gamma position is basically throwing away free money.Could you please elaborate on this ?It seems to me that if you are long gamma, you will always earn the contribution due to gamma1/2 Gamma sigma^2 S^2 (dS/S)^2--- doesn't matter whether you delta hedge or not. I'm assuming that by intraday scalps, you meandelta hedging.I'd be interested in hearing your view on the matter.If you're long gamma, regardless of the direction in which the underlying moves, your position will generate "good" deltas. By good, I mean if the underlying moves up you'll automatically get longer, if it goes down you'll automatically get shorter. Rebalancing thereby forces you to buy low, sell high so if you're rebalancing intraday you're effectively scalping the underlying with the safety net of your option position. Lets say at during the day your delta goes from 0 to 1 to -1 to 0. If you only delta hedge daily you're missing out on some pretty decent scalps. With each scalp you're crystalizing P&L which can help offset some of your time decay.Right. Presumably these "scalping" profits are basically the integral of 1/2 Gamma sigma^2 S^2 (dS/S)^2i.e. the contribution of (dS/S)^2 to your daily trading profits. Do you agree ?If so, it seems that you will earn these profits no matter whether you delta hedge or not. If you choose to not delta hedge you would earnDelta S (dS/S) + 1/2 Gamma sigma^2 S^2 (dS/S)^2 + Theta dtif you choose to delta hedge you would earn1/2 Gamma sigma^2 S^2 (dS/S)^2 + Theta dtAm I missing something ?

QuoteOriginally posted by: MrMartingaleQuoteOriginally posted by: StatTraderQuoteOriginally posted by: MrMartingaleQuoteOriginally posted by: StatTraderGiving up your intraday scalps on a long gamma position is basically throwing away free money.Could you please elaborate on this ?It seems to me that if you are long gamma, you will always earn the contribution due to gamma1/2 Gamma sigma^2 S^2 (dS/S)^2--- doesn't matter whether you delta hedge or not. I'm assuming that by intraday scalps, you meandelta hedging.I'd be interested in hearing your view on the matter.If you're long gamma, regardless of the direction in which the underlying moves, your position will generate "good" deltas. By good, I mean if the underlying moves up you'll automatically get longer, if it goes down you'll automatically get shorter. Rebalancing thereby forces you to buy low, sell high so if you're rebalancing intraday you're effectively scalping the underlying with the safety net of your option position. Lets say at during the day your delta goes from 0 to 1 to -1 to 0. If you only delta hedge daily you're missing out on some pretty decent scalps. With each scalp you're crystalizing P&L which can help offset some of your time decay.Right. Presumably these "scalping" profits are basically the integral of 1/2 Gamma sigma^2 S^2 (dS/S)^2i.e. the contribution of (dS/S)^2 to your daily trading profits. Do you agree ?If so, it seems that you will earn these profits no matter whether you delta hedge or not. If you choose to not delta hedge you would earnDelta S (dS/S) + 1/2 Gamma sigma^2 S^2 (dS/S)^2 + Theta dtif you choose to delta hedge you would earn1/2 Gamma sigma^2 S^2 (dS/S)^2 + Theta dtAm I missing something ?quite often dS may be zero (say day on day changes) but intraday (Smax-Smin) might be very large - hence the path dependency of the p+l.

Thanks for the feedback guys!I have done some further research and I have determined that delta hedging does not guarantee profit even if you correctly forecast realized vol relative to implied vol as a result of pathe dependency.However, one can trade variance/volatility swaps which do guarantee a profit given accurate volatility forecasts.Davevangel, I would be interested to hear your thoughts???Also does anyone know if daily realized vol can be traded analagously to a future? Thanks again!Osiris.

My 2 JPY for what its worth1. You might have the right call on vol but still lose money with an options trade even if you bought the option at implieds below forecast realised. For example, you buy a call with implied of 16%, the stock moves at 17% but has a strong trend. the option ends up in the money very quickly, your "gamma" is worth nothing.2. Variance swaps are a better way of taking a view on vol as you dont have the gamma problem. the disadvantage of var swaps is that the realised is on a close to close basis, the variance strike is typically higher than ATM if there is a pronounced skew and you dont benefit from the path dependency.

QuoteOriginally posted by: osirisThanks for the feedback guys!I have done some further research and I have determined that delta hedging does not guarantee profit even if you correctly forecast realized vol relative to implied vol as a result of pathe dependency.However, one can trade variance/volatility swaps which do guarantee a profit given accurate volatility forecasts.Davevangel, I would be interested to hear your thoughts???Also does anyone know if daily realized vol can be traded analagously to a future? The VIX ?

QuoteOriginally posted by: TraderJoeQuoteOriginally posted by: osirisThanks for the feedback guys!I have done some further research and I have determined that delta hedging does not guarantee profit even if you correctly forecast realized vol relative to implied vol as a result of pathe dependency.However, one can trade variance/volatility swaps which do guarantee a profit given accurate volatility forecasts.Davevangel, I would be interested to hear your thoughts???Also does anyone know if daily realized vol can be traded analagously to a future? The VIX ?The VIX itself isn't tradable and the VIX futures and options I've seen seem to have a large tracking error. I guess you could trade a basket of options to replicate the VIX but you're going to have huge negative edge due to the constant rebalancing required as strikes move around etc.

Why don't you trade variance swap ?