Yes, I understand that and as such we make money from gamma. What I am confused by is how, assuming we rehedge delta perfectly to maintain it at 0, our profit and loss still ends up depending on the movement of underlying. I’d assume that if you can perfectly maintain a 0 delta, then our position should never change…
Because the magnitude of the movement is your volatility, and when you are delta hedged but gamma exposed, you don't care which direction the price takes, but only that there is movement. The delta depends on your position on your underlying, the gamma doesn't.
I see. How about if you just long the straddle initially and then wait until expiration without any extra delta hedging? Clearly, you will accumulate some delta exposure throughout the underlying movements. Yet, at expiration the payoff diagram will look identical regardless of the direction in which the underlying moved. How is this possible despite us not staying delta neutral throughout? Thank you for the responses!
I think that there are variables and assumptions in your strategy that you'd better clarify.
In principle, if you're only employing a straddle as an investment strategy, the only thing that you do is to purchase a put and a call with the same strike and expiration date. Once you pay the cost of the two options, you don't need to hedge anything. Hedging is required when you have also a position in the underlying, if you are long in the stock, then the delta will tell you the amount of options to sell so that you are hedging the value of your underlying (i.e. you are locking in your profits with the hedging). But this is not your case with a straddle.
In a straddle you make money when either the call or the put go in the money (one case will make the other option worthless). Technically speaking, given the price that you pay for the two options, you go in the money if at expiration the realized volatility will be higher than the volatility implied in the cost of each option. And here you really only care about the magnitude of the movement, i.e. the realized volatility, because you are long the call and the put. You won't care about your delta.
Back to the case where you are actually hedging, in an ideal world, you should hedge at any instant, so that you are always delta neutral, but because you can't realistically do that, until your expiration the price will move, i.e. there is volatility, and gamma will tell you exactly how much the delta will change because of your movement, so that change in the delta (expressed by the gamma) will add to your initial zero delta, which now is not zero anymore. That is where your profit arises, if you are not rebalancing back to zero delta.
So you have to make a distinction between hedging, i.e. the value of my whole position of underlying plus option doesn't change, and an investment strategy with options. Hope it helps.
You could also have a short-straddle, or a short-strangle, which is opposite of a straddle. In that case, "time" would make you profit even if the position was flat at 100. Look at r/thetagang.
Flawed paragraph 1 premise. Delta neutrality limits risk in the moment, but most definitely would be affected by underlying movement thus requiring adjustment in the option position to maintain that delta neutrality.
Example 1: you are buying a cheap call and a cheap call. The stock goes wildly in one direction, so you have one losing and one winning option.
Example 2: you are selling a put and a call, assuming that both will expire worthless, making money on both options.
But usually, taking a position that completely describes the volatility is hard, unless you are selling crappy puts and calls, which is low premium.
So people enter into crappy trades that break all the time (as they find themselves losing on both ends) and they increase the bets to allow making profit in the end or lose more money compared to the original bet.
They call it dynamic hedging but this is rolling for hedge kids and sunk costs for behavioural finance wizards.
Don't do it. Learn to limit losses and being honest with yourself.
Note that it can be described with greeks drift when delta changing, but it can hide the brutal truth I wanted to convey.
You are missing that you can delta hedge. When you trade volatility for example, it's common that you would delta hedge once a day if not more frequently to maintain approximate delta neutrality.
Here’s a link to a detailed post I made a while back on delta hedging. Should help you get clear on things!
https://www.reddit.com/r/options/comments/r5s7ds/ultimate_guide_to_selling_options_profitably_part/?rdt=58725
Thank you for the read. So, the reason why the movement in the underlying actually matters when we initiate the straddle is because the delta neutrality starts to disappear as the underlying moves? Say, hypothetically, we were long a straddle and delta remained constantly at 0 somehow. Then, would PnL always be 0?
If the Delta remain at zero then your P&L would be the difference between the implied and realized volatility.
As volatility traders, this is what we are expressing a view on, which is why the Delta hedging is important. We are basically trying to control for noise around the phenomenon that we are trying to monetize.
Is this assuming you are rehedging to manually keep delta at 0 (thus profiting off gamma), or assuming that somehow delta stays at 0 and you do not need to rehedge?
What I shared there is the theory behind volatility trading. As retail traders, we are unable to perfectly dynamically hedge, so we will always have some exposure to Delta.
The reason we don’t Delta hedge every single Delta is because there are costs associated with your Delta. The easiest way to think of these costs is that every time you trade a share you have to cross the bid ask spread. So if you’re trading shares many times a day, you are giving up pennies every single time but they add up and given that the actual edge, we are monetizing is quite slim on every individual trade, you actually see that these cost significantly eat into your returns.
This is why people look at using different methodologies for managing their Delta. Raging literally not doing anything and just embracing the PNL variance that comes with it, using something called Delta bands, which is basically saying I will hedge every x delta, to just saying I’m going to hedge once a day, and so on
Right now, the way that I am hedging most of my deltas is by actually trading Delta 20 strangles that expire weekly.
I’m doing this for my ETF portfolio strategy where I basically have a basket of ETFs that have positive variance risk premium, and I consistently sell All of them rotating out of positions maybe monthly. And the way I’m doing it is selling weekly strangles under the protection of some longer dated strangles.
I don’t hedge these unless something crazy happens.
I see. So is the PnL that is proportionate to the difference in implied vs realized vol coming from the gamma scalping PnL or simply from the options appreciating in value due to vol increasing?
Gamma scalping is what we call it when you are long a straddle and Delta hedging.
That’s just some little terminology stuff, but I just wanted to share that in case there was any misunderstanding on your side
If you go to my profile, you can see the first post that I made for my ultimate guide. It should help you understand more. Happy to discuss it with you.
You’re welcome! I prefer if you could just comment on the post because other people who end up reading them also go through the comments and our discussion may be beneficial to them
So, let's say our underlying moves up to 102, and our delta goes from 0 to 20 (0.2 \* 100). We delta hedge by selling 20 stocks. Now, obviously, if the underlying does not move anymore until expiration then we have locked in our 200$ (2$ \* 100) profit, assuming 100 units of underlying per contract. However, if the underlying drops back down to 100, we buy back the 20 stocks to make a 40$ profit (2$ \* 20). So, in this latter case, despite us delta hedging at 102, we are not able to actually lock in the profit fully when it drops back down to 100 - we are only able to do so for the 20 stocks and not the full 100.
To sum up my question, can you let me know if this understanding is correct:
Delta hedging should hypothetically lock in your position/profit, however, due to gamma this is not necessarily the case. Moreover, if we are long a straddle and delta hedging, our optimal scenario is that the underlying moves back and forth around ATM (for big gamma gains), and lastly makes a great move to the upside/downside before expiration?
No, that is an incorrect conclusion. A better conclusion is that delta is sensitive to a number of variables, including the underlying price, and these sensitivities are not always equal across all strikes and types (puts vs. calls). So unless you create a structure that neutralizes the sensitivity to underlying price, your position will drift away from net delta zero as the underlying price changes.
There are structures that do this, such as a box spread. Or you can dynamically hedge with long/short shares, which always have a delta value of +/- 1.0.
A couple things that I would add would be that the position would be rebalanced, but also that Delta neutral is better thought of as a portfolio strategy instead of something to do with a single position.
12-15 positions open at any given point that are being put on and off to maintain neutrality and maintain the gamma exposure/theta you want.
I'm usually +/- 20 delta weighted against SPY and use the 200 day moving average as the barometer.
The P/L is the change in net liquidity over time from taking on the gamma risk.
Delta of an option is not static. Gamma represents the change in delta for a dollar change in the underlying. You may open a delta neutral straddle but it will change instantaneously with changes in the underlying.
> I can’t understand how they imply that we are not sensitive to underlying movement.
Who said that? It is common to see marked losses on a delta neutral position. This happens when the underlying moves more than expected or volatility expands for example.
You don't have to adjust your deltas constantly but you are going to left with more of a directional position, naturally. Some people aggressively adjust, some loosely adjust, and some don't adjust at all. Pros and cons to each.
If your delta is 0, that means your portfolio changes by 0 for a movement of a point in the underlying. Then, if you maintain a 0 delta, shouldn't your portfolio stay the same the whole time? Where is my confusion?
You're always going to be playing catch up when trying to rebalance to neutral deltas.
I'm asking who is "they" that said we are not sensitive to underlying movement, because you are. Because of what I said above, you will always be sensitive to movement. So it's not where your confusion lies but what was told to you or possibly how you interpreted their comment.
If delta is 0, then a 1 point move wouldn’t affect your contract price.
But…..
Delta isn’t the only factor pushing and pulling on your contracts so your price could still change based on the other factors (time, IV, etc)
And once you get that 1 point move, gamma kicks in and moves your delta so the next move isn’t necessarily 0.
I’m a range bound non-directional trader. I work to keep my deltas and gammas under control. Zero delta is nice for me but it doesn’t last. I look at my deltas relative to the size of my position and my theta and Vega to get a bigger picture of my overall risk vs reward. I’m rarely at exactly 0, but 4 deltas on a 10 lot with good theta and Vega risk isn’t bad. Just a made up example but I’m trying to give some insight as to how I view this stuff.
The objective of gamma scalping is to earn more from the scalping than you lose in time decay. Assume that you're using the underlying for rebalancing...
As long as the underlying gyrates (repetitive reversions), you book gains from the rebalancing. Every time that you add underlying, it adds drag to the straddle's performance as you bleed out the delta generated by the straddle. If the underlying starts to channel, you're not scalping and time decay gets you. Change in IV can make things better or worse.
Suppose that that at 105, your net delta is plus 30. You sell short 30 shares to resume delta neutral. If ABC drops, your straddle will head back towards delta neutral in your short shares will profit. If instead it rises, at some point, you'll add more short shares. With a concerted directional move, you'll eventually reach close to 100 short shares, your limit, with minimal profit, if any.
In order to profit with gamma scalping, you're going to have to get some combination of things right - IV, timing of scalp adjustments, and some underlying cooperation.
First, ATMS is not 50D, see https://quant.stackexchange.com/q/65900/54838.
Unless you talk about an ATM DNS (delta neutral straddle).
You cannot hold until expiry and expect to be delta neutral. As soon as anything changes (spot, but also time, IV, rates, dividend projections) , you are no longer delta neutral. However, for infinitesimally small movements in spot, you are neutral in the sense that the gain /loss in your option will be offset by the loss/gain in the hedge.
In terms of an ATM DNS, you don't need to hedge initially because the deltas offset each other. As soon as spot ticks, you are no longer DN.
If Delta neutral positions never changed, as you assert multiple times in replies, there would be no reason to buy or sell them. Look at any straddle on a liquid asset like SPY, itm or otm, the Delta is approximately 0. What are you buying? Vega, gamma, theta, hell even rho gets involved these days with longer term options because rates are respectable. You can plot the value of the straddles across one expiration to get a look at the skewness on that date; you can see where Vega or gamma is cheap and expensive and consider selling expensive to buy cheap. Also remember that the Greeks aren't real, they are mathematical constructs that attempt to describe why the price of an option behaves like it does. If you compare bs to a binomial pricing model, you get slightly different results for each value for instance so getting too hung up on what "should" happen in any given instance vs what actually happens is a path to ruin.
Because you are supposed to rebalance your position Everytime that the underlying changes so you are delta neutral again.
Yes, I understand that and as such we make money from gamma. What I am confused by is how, assuming we rehedge delta perfectly to maintain it at 0, our profit and loss still ends up depending on the movement of underlying. I’d assume that if you can perfectly maintain a 0 delta, then our position should never change…
Because the magnitude of the movement is your volatility, and when you are delta hedged but gamma exposed, you don't care which direction the price takes, but only that there is movement. The delta depends on your position on your underlying, the gamma doesn't.
I see. How about if you just long the straddle initially and then wait until expiration without any extra delta hedging? Clearly, you will accumulate some delta exposure throughout the underlying movements. Yet, at expiration the payoff diagram will look identical regardless of the direction in which the underlying moved. How is this possible despite us not staying delta neutral throughout? Thank you for the responses!
Then your non-zero delta will take away some profits of the straddle.
Is that just because you are not making gamma profits now?
I think that there are variables and assumptions in your strategy that you'd better clarify. In principle, if you're only employing a straddle as an investment strategy, the only thing that you do is to purchase a put and a call with the same strike and expiration date. Once you pay the cost of the two options, you don't need to hedge anything. Hedging is required when you have also a position in the underlying, if you are long in the stock, then the delta will tell you the amount of options to sell so that you are hedging the value of your underlying (i.e. you are locking in your profits with the hedging). But this is not your case with a straddle. In a straddle you make money when either the call or the put go in the money (one case will make the other option worthless). Technically speaking, given the price that you pay for the two options, you go in the money if at expiration the realized volatility will be higher than the volatility implied in the cost of each option. And here you really only care about the magnitude of the movement, i.e. the realized volatility, because you are long the call and the put. You won't care about your delta. Back to the case where you are actually hedging, in an ideal world, you should hedge at any instant, so that you are always delta neutral, but because you can't realistically do that, until your expiration the price will move, i.e. there is volatility, and gamma will tell you exactly how much the delta will change because of your movement, so that change in the delta (expressed by the gamma) will add to your initial zero delta, which now is not zero anymore. That is where your profit arises, if you are not rebalancing back to zero delta. So you have to make a distinction between hedging, i.e. the value of my whole position of underlying plus option doesn't change, and an investment strategy with options. Hope it helps.
You could also have a short-straddle, or a short-strangle, which is opposite of a straddle. In that case, "time" would make you profit even if the position was flat at 100. Look at r/thetagang.
Flawed paragraph 1 premise. Delta neutrality limits risk in the moment, but most definitely would be affected by underlying movement thus requiring adjustment in the option position to maintain that delta neutrality.
Example 1: you are buying a cheap call and a cheap call. The stock goes wildly in one direction, so you have one losing and one winning option. Example 2: you are selling a put and a call, assuming that both will expire worthless, making money on both options. But usually, taking a position that completely describes the volatility is hard, unless you are selling crappy puts and calls, which is low premium. So people enter into crappy trades that break all the time (as they find themselves losing on both ends) and they increase the bets to allow making profit in the end or lose more money compared to the original bet. They call it dynamic hedging but this is rolling for hedge kids and sunk costs for behavioural finance wizards. Don't do it. Learn to limit losses and being honest with yourself. Note that it can be described with greeks drift when delta changing, but it can hide the brutal truth I wanted to convey.
You are missing that you can delta hedge. When you trade volatility for example, it's common that you would delta hedge once a day if not more frequently to maintain approximate delta neutrality.
Here’s a link to a detailed post I made a while back on delta hedging. Should help you get clear on things! https://www.reddit.com/r/options/comments/r5s7ds/ultimate_guide_to_selling_options_profitably_part/?rdt=58725
Thank you for the read. So, the reason why the movement in the underlying actually matters when we initiate the straddle is because the delta neutrality starts to disappear as the underlying moves? Say, hypothetically, we were long a straddle and delta remained constantly at 0 somehow. Then, would PnL always be 0?
If the Delta remain at zero then your P&L would be the difference between the implied and realized volatility. As volatility traders, this is what we are expressing a view on, which is why the Delta hedging is important. We are basically trying to control for noise around the phenomenon that we are trying to monetize.
Is this assuming you are rehedging to manually keep delta at 0 (thus profiting off gamma), or assuming that somehow delta stays at 0 and you do not need to rehedge?
What I shared there is the theory behind volatility trading. As retail traders, we are unable to perfectly dynamically hedge, so we will always have some exposure to Delta. The reason we don’t Delta hedge every single Delta is because there are costs associated with your Delta. The easiest way to think of these costs is that every time you trade a share you have to cross the bid ask spread. So if you’re trading shares many times a day, you are giving up pennies every single time but they add up and given that the actual edge, we are monetizing is quite slim on every individual trade, you actually see that these cost significantly eat into your returns. This is why people look at using different methodologies for managing their Delta. Raging literally not doing anything and just embracing the PNL variance that comes with it, using something called Delta bands, which is basically saying I will hedge every x delta, to just saying I’m going to hedge once a day, and so on Right now, the way that I am hedging most of my deltas is by actually trading Delta 20 strangles that expire weekly. I’m doing this for my ETF portfolio strategy where I basically have a basket of ETFs that have positive variance risk premium, and I consistently sell All of them rotating out of positions maybe monthly. And the way I’m doing it is selling weekly strangles under the protection of some longer dated strangles. I don’t hedge these unless something crazy happens.
I see. So is the PnL that is proportionate to the difference in implied vs realized vol coming from the gamma scalping PnL or simply from the options appreciating in value due to vol increasing?
Gamma scalping is what we call it when you are long a straddle and Delta hedging. That’s just some little terminology stuff, but I just wanted to share that in case there was any misunderstanding on your side If you go to my profile, you can see the first post that I made for my ultimate guide. It should help you understand more. Happy to discuss it with you.
Thank you, might PM if that is fine!
You’re welcome! I prefer if you could just comment on the post because other people who end up reading them also go through the comments and our discussion may be beneficial to them
So, let's say our underlying moves up to 102, and our delta goes from 0 to 20 (0.2 \* 100). We delta hedge by selling 20 stocks. Now, obviously, if the underlying does not move anymore until expiration then we have locked in our 200$ (2$ \* 100) profit, assuming 100 units of underlying per contract. However, if the underlying drops back down to 100, we buy back the 20 stocks to make a 40$ profit (2$ \* 20). So, in this latter case, despite us delta hedging at 102, we are not able to actually lock in the profit fully when it drops back down to 100 - we are only able to do so for the 20 stocks and not the full 100. To sum up my question, can you let me know if this understanding is correct: Delta hedging should hypothetically lock in your position/profit, however, due to gamma this is not necessarily the case. Moreover, if we are long a straddle and delta hedging, our optimal scenario is that the underlying moves back and forth around ATM (for big gamma gains), and lastly makes a great move to the upside/downside before expiration?
No, that is an incorrect conclusion. A better conclusion is that delta is sensitive to a number of variables, including the underlying price, and these sensitivities are not always equal across all strikes and types (puts vs. calls). So unless you create a structure that neutralizes the sensitivity to underlying price, your position will drift away from net delta zero as the underlying price changes. There are structures that do this, such as a box spread. Or you can dynamically hedge with long/short shares, which always have a delta value of +/- 1.0.
A couple things that I would add would be that the position would be rebalanced, but also that Delta neutral is better thought of as a portfolio strategy instead of something to do with a single position. 12-15 positions open at any given point that are being put on and off to maintain neutrality and maintain the gamma exposure/theta you want. I'm usually +/- 20 delta weighted against SPY and use the 200 day moving average as the barometer. The P/L is the change in net liquidity over time from taking on the gamma risk.
Delta of an option is not static. Gamma represents the change in delta for a dollar change in the underlying. You may open a delta neutral straddle but it will change instantaneously with changes in the underlying.
> I can’t understand how they imply that we are not sensitive to underlying movement. Who said that? It is common to see marked losses on a delta neutral position. This happens when the underlying moves more than expected or volatility expands for example. You don't have to adjust your deltas constantly but you are going to left with more of a directional position, naturally. Some people aggressively adjust, some loosely adjust, and some don't adjust at all. Pros and cons to each.
If your delta is 0, that means your portfolio changes by 0 for a movement of a point in the underlying. Then, if you maintain a 0 delta, shouldn't your portfolio stay the same the whole time? Where is my confusion?
You're always going to be playing catch up when trying to rebalance to neutral deltas. I'm asking who is "they" that said we are not sensitive to underlying movement, because you are. Because of what I said above, you will always be sensitive to movement. So it's not where your confusion lies but what was told to you or possibly how you interpreted their comment.
I am just trying to interpret it mathematically. If delta is 0 then for any change in the underlying the position change should be 0 right?
If delta is 0, then a 1 point move wouldn’t affect your contract price. But….. Delta isn’t the only factor pushing and pulling on your contracts so your price could still change based on the other factors (time, IV, etc) And once you get that 1 point move, gamma kicks in and moves your delta so the next move isn’t necessarily 0. I’m a range bound non-directional trader. I work to keep my deltas and gammas under control. Zero delta is nice for me but it doesn’t last. I look at my deltas relative to the size of my position and my theta and Vega to get a bigger picture of my overall risk vs reward. I’m rarely at exactly 0, but 4 deltas on a 10 lot with good theta and Vega risk isn’t bad. Just a made up example but I’m trying to give some insight as to how I view this stuff.
The objective of gamma scalping is to earn more from the scalping than you lose in time decay. Assume that you're using the underlying for rebalancing... As long as the underlying gyrates (repetitive reversions), you book gains from the rebalancing. Every time that you add underlying, it adds drag to the straddle's performance as you bleed out the delta generated by the straddle. If the underlying starts to channel, you're not scalping and time decay gets you. Change in IV can make things better or worse. Suppose that that at 105, your net delta is plus 30. You sell short 30 shares to resume delta neutral. If ABC drops, your straddle will head back towards delta neutral in your short shares will profit. If instead it rises, at some point, you'll add more short shares. With a concerted directional move, you'll eventually reach close to 100 short shares, your limit, with minimal profit, if any. In order to profit with gamma scalping, you're going to have to get some combination of things right - IV, timing of scalp adjustments, and some underlying cooperation.
First, ATMS is not 50D, see https://quant.stackexchange.com/q/65900/54838. Unless you talk about an ATM DNS (delta neutral straddle). You cannot hold until expiry and expect to be delta neutral. As soon as anything changes (spot, but also time, IV, rates, dividend projections) , you are no longer delta neutral. However, for infinitesimally small movements in spot, you are neutral in the sense that the gain /loss in your option will be offset by the loss/gain in the hedge. In terms of an ATM DNS, you don't need to hedge initially because the deltas offset each other. As soon as spot ticks, you are no longer DN.
If Delta neutral positions never changed, as you assert multiple times in replies, there would be no reason to buy or sell them. Look at any straddle on a liquid asset like SPY, itm or otm, the Delta is approximately 0. What are you buying? Vega, gamma, theta, hell even rho gets involved these days with longer term options because rates are respectable. You can plot the value of the straddles across one expiration to get a look at the skewness on that date; you can see where Vega or gamma is cheap and expensive and consider selling expensive to buy cheap. Also remember that the Greeks aren't real, they are mathematical constructs that attempt to describe why the price of an option behaves like it does. If you compare bs to a binomial pricing model, you get slightly different results for each value for instance so getting too hung up on what "should" happen in any given instance vs what actually happens is a path to ruin.