Well, the normal models apply e.g. Black Scholes, Cox Ross Rubinstein etc. However, most places, like OX won't output the probability value from these models. To be honest, the difference between calculated delta and probability is entirely dwarfed by the flaws and assumptions in said models as well as the garbage in, garbage out factors, so I wouldn't worry about it too much - it's more a piece of academic useless information. If you have access to the ToS platform, you can compare delta alongside probability to see the differences. If not already done so, I would recommend reading Natenburg's Option Volatility and Pricing. If anything, just reading chapter 3 and 4 in a book shop or library would be beneficial. To answer your question 1 sigma = 1 standard deviation = volatility (annualized). They are virtually interchangeable. e.g. if ATM IV is 10% that is telling you that 1 sigma/standard deviation is 10% and the market thinks (implied) that a year from now we will be trading at 1280 +/- 128 points 68%ish of the time (close to close). Ignoring interest rates/dividends etc. A one sigma move in this context is therefore 128 points. Knowing that standard deviation is proportional to the square root of time allows you to approximate volatility (standard deviation) values for different time periods. Back of envelope calculations: Daily volatility can be approximated by annualized volatility/16 Weekly volatility can be approximated by annualized volatility/7.2 Monthly volatility can be approximated by annualized volatility/3.5 (Implied) Volatility for just the period leading up to expiration can be approximated by pricing an ATM straddle. This will give you a $ amount rather than a % obviously. For all of the above, they are saying: during X time period, the underlying will trade +/- volatility value 68% of the time. OR for about 2 out of every 3 of X time periods the underlying will move by +/- volatility (close to close). Thus, you can think of implied volatility as implied sigma or implied standard deviation. I would recommend not entirely dismissing historical volatility as a tool to balance what you read from IV. Using the information I outlined above, you can decide whether this is reasonable or not! Good luck! MoMoney.
Ahem, not Coach but since I'm online... It might help if you just think of it as a split-strike combo/synthetic stock. long combo = long call + short put short combo = short call + long put A true synthetic would be same strikes put and calls and therefore the IV for both options at the same strike will be comparable. With the long split-strike synthetic you are potentially taking advantage of the skew: IV of the put is normally going to be a lot higher than IV of the call. So you are potentially selling something more "expensive" than that which you are buying relative to the moneyness of each option. The long split-strike synthetic is just like the long synthetic or long stock - a bullish position. The only difference is that with the split-strike, at expiration, PnL is flat in the middle between the strikes. Although it is extremely common to do so, perhaps throw out the notion of the sale of one option financing a purchase of another option - credits and debits, money in, money out....all sounds too much like accounting to me! Real money can be made on this trade by favorable skew activity before expiration which is a dimension of the position that simply isn't addressed in the whole credit/debit treatment. Doing the short split-strike combo to protect bull put credit spreads has less clear benefits from a dynamic/IV nature but they are: It's cheaper than a plain put hedge, It doesn't cap the payoff or gamma hedging capabilities that a put debit spread would do and lastly the long theta on the short call mitigates the decay on your long put. At expiration, you can end up flat if within the split-strike zone i.e. there is a degree of whipsaw forgiveness and the cost of this insurance if not used can be negligible. It might just be easier to go short ES albeit with greater risk of whipsaw. You may well have already executed the long split-strike combo synthetically in the past without even realizing it! A not uncommon variation of the infamous covered call (synthetic short put) is to sell a call vertical (multiple) on your long stock - this allows you to participate in upside movement which would not occur in a covered call scenario. long stock + bear call vertical = split-strike combo. If the ratio is 1:1 you get the split-strike combo. However if you ratio more bear call verticals you end up with Cottle's slingshot hedge which we've discussed before - round and round we go, where will it stop, nobody knows. HTH. MoMoney.
Yeah, I guess you'll have to do. So a bear risk reversal would be the selling of the call and the buying of a put. Let's talk about the SPX. Selling a naked call would have a very high margin, so one would need to sell a bear call. Any thoughts on strike selection for the R/R. If it helps to use a hypothetical position. Let's use Coach's position. June bull put SPX 1160/1140 at $0.75.
momoney, as always a great post outlining strategy details. In this case - risk-reversals. I would like to add one more thing if you don't mind. When people consider using the r/r vs a straight up long premium/debit spread hedge they must be mindfull of the unbound risk beyond the short strike.(many traders will stop/get limited right here due to various reasons like margin, trading permission, etc.) The r/r could be a great/inexpensive hedge for the FOTM spread because of the benefits you outlined. However, a swift market move towards your short strike will cause some serious damage due to the gearing of the position as riskarb likes to say. (The combo moves quickly in each direction)
Ahh, you've spotted the minor fly in the ointment - what, no free lunch?! Yes, margin requirements for short calls on SPX are not insignificant LOL. A more digestible alternative is to use ES options for this play. If not, you have proposed, bear calls to get around Reg-T. However by using bear calls you are offsetting many benefits of the naked calls. More specifically, you are muting the theta, delta and cost advantages that the naked call position provides. To gain back some of these you would have to sell multiple bear calls for each long put. Chances are, you already have bear calls in place as part of an iron condor! So as for strike selection on the call side it would be anywhere that you thought wouldn't be at risk of whipsaw which is probably where you already had bear call spreads. Doing a U-turn, and bringing in back the calls financing the puts perspective: in this instance you would be using the credit from your bear calls to finance a put hedge to protect your bull put credit spread i.e. the problem becomes reduced to simply buying puts Strike selection for the puts is dependent on whether you want to be proactive or reactive in the hedge. You would need to choose the right ratio of puts at the right strikes in order to provide you with enough cover for any loss on the bull put credit spread. This is of course Cottle's Slingshot hedge. Choose the wrong ratio or strike and you decimate the credit from your spread OR alternatively, you don't provide enough protection for the hedge. It depends on each person's personal goals which is subjective. I am in no way advocating the following but a ratio of 1:5 sounds reasonable meaning one put for every 5 spreads. You really need to have a bearish bias in order to put on a short split-strike combo Long PUT 1225 Short CALL 1305 That's a "risk-reversal" for net credit of .80c which you get to keep if SPX finishes between 1225 and 1305 but not really the point of the position. One of those for every 5 bull put credit spreads should provide a decent amount of black swan insurance in addition to very nice convergence gains (positive PnL as SPX moves towards the short strike of your credit spread) should you be right on direction. Doing the above with bear calls instead of naked calls e.g. 1305/1310 would obviously be a lot less margin intesive but require a ratio of about 5 bear call spreads to each 1 long put e.g. you would have 1 long put for each 5 iron condors! To summarize: Iron condor: 5 * 1160/1140/1305/1310 Long PUT hedge: 1 * 1225 Probably best to play around with strikes and numbers to get a feel for what is appropriate to your own risk appetite and directional bias etc. Cottle's discussion on the slingshot hedge is a good place to start. MoMoney.
Yes, unbounded risk just like long/short stock. Margin call implications are similar if over leveraged. Swift adverse moves against naked leg are mitigated somewhat by movement in IV. Not so with long/short stock. Overall, depending on leverage being used can be somewhat tamer than a corresponding long/short stock or futures position. At any rate, I wouldn't advocate this strategy in general. MoMoney.
For anyone having trouble visualizing the expiration risk profile for the short (bear) split-strike combo a.k.a "risk-reversal" Tiny bit of info here Another quick reference to the strategy if you like bright colors and big pictures. Page 22
Correction: swift adverse moves against naked legs are obviously made worse by movement in IV LOL. ET overload. Apologies.
Thanks, Mo. I remember now that riskarb did mention to use futures on this. I think I'll start paper trading these to get a feel for how this works. Again, appreciate the detailed, clear explanation and references. BTW: Do you ever post any of your positions anywhere where we might get a look. EDIT: Also, didn't someone post earlier that, I think it was Dan Sheridan, recommends adding two long puts to 10 bull put contracts. I'd try to find it myself, but we all know who the master is at web search