1/ Vega is sensitivity of option price to change in level of implied volatility. Appraised is an unusual word choice.
You'll have more gamma if the asset price is near the strike price of the option. But gamma can actually be lower near expiration for the same strike if its fairly out of the money - gamma will only be higher for at/near the money options.
6/ Market makers buy and sell volatility and outside of retail, prices are usually quoted in vol terms. That's not to say that professionals can't do some crazy things trying to hedge risk, including theta (time) and rho (interest rates) but the original trade is a vol trade first and foremost.
My slightly different explanation: Delta is the 1st deriv change in price of the option wrt the value of the underlying asset. Gamma is the 2nd deriv, ie the rate of change of delta. As expiration approaches, gamma gets very like a dirac delta function, centered at the strike price. Easy to understand - moments before expiration a call option value is either worthless or exactly (Underlying - Strike price) Thus a delta of either 0 or 1 (-1 if you are short) with gamma equal to delta.
As the original poster explained, traders hedge by buying or selling the delta amount of the underlying (if delta is 0.5, you do 50% of your notional contract size). As the underlying moves, the short trader needs to buy when the underlying rises (his negative delta is increasing) or sell when it falls (his delta is decreasing so less hedge needed) to maintain a 'neutral' position wrt to small changes in the price of the underlying.
Recall, gamma is the rate of change of the delta and so determines how much the hedge needs to change. On day of expiration at the money strikes have very high gamma and thus subject the short option trader to large whipsaw risk - the need to add or remove a hedge aproaching 100% while chasing the underlying. The art is really in deciding when to hedge on/hedge off and how much, regardless of the formulaic delta and gamma values at the current underlying price.
As for "appraised" that's an invention of mine to explain the difference between actual movement and guessed movement. When the market is moving up and down you will realize some amount of PnL regardless of what you paid for it. But you have to pay something for it, and that's the appraisal of the market for whatever period in the future your option covers. It's like pricing a swap, that floating leg will be some number that you'll receive, but you pay some guess about what it's going to be over the period. The thing about that is you probably have more certainty in the near term than the long term, and there's a term structure coming out of that.
About quoting in vol terms, I found people mostly do that in FX and fixed income. In equities it seemed to be prices. There's calculators for everything anyway, so you can easily swap between them.
1) Are options market makers mostly long or short gamma, and does this tendency differ if we're talking about puts versus calls? I know this can all vary over time, but I'm wondering if there's any systematic tendencies here, especially pertaining to index options.
2) Do you think gamma hedging drives a significant percent of volume in index futures (say 5% or more), or is it just a trivial %?
3) What would be a good way to estimate/approximate the gamma exposure of options market makers if we wanted to predict gamma squeezes, and we've only got public market data (e.g. trades and open interest)? SqueezeMetrics advocates using open interest but I'm wondering if there's a better way to do this.
4) Compared to delta & gamma hedging, do any of the other greeks (e.g. vanna) drive a significant percentage of volume in in the underlying in certain contexts, or are they mostly a side show?
2) I think so, firms I worked for threw around a fair few index futures to hedge. quantifying it isn't too easy though. A lot depends on how close you are to the strike and the expiry.
3) You can't avoid looking at open interest, but I guess you can weight it by the gamma.
4) Vanna is a cross greek of vol and price. The other missing piece is interest rates, and from that you can imagine a zoo of greeks. But mainly it's the connection between vol and price that matters, there's a slidey thing you use to move the volatility surface when the price moves.
I guess if I were you I'd scrape all the open interest info and see about the relative size of presumed gamma to liquidity in the market. It's a bit of an exercise.
(1) and (3): If we're to use open interest (along with the gamma of such open interest), it seems that we have to make specific assumptions about whether options' market makers are going to be net short/long, and by how much, in each specific contract, in order to perform the calculations. What such assumptions do you think that we should use for that, and I wonder if there's a way to make it more accurate than simply assuming "100% of this open interest in this specific put is held short by options market makers"? That seems to be the assumption made in [1], which is definitely very incorrect but maybe it's the best we can do?
(4) So I guess flow that results from vanna hedging (and the other greeks aside from delta/gamma) is pretty small then. A number of people on Twitter make a big deal out of vanna hedging - they seem to think it can predict moves in the underlying, but they must be mistaken if not much flow comes from it as a result.
The squeezemetrics people seem to have quantified it, it's actually quite impressive. The GEX and VEX thing seems to be what you are alluding to, and they seem to have crunched the numbers.
Browsing the papers it seems they assume that the customers are selling the calls and buying the puts? I think it makes sense, it's more sensible than saying all the open interest is one way on the market makers.
Puts are where it is likely to be just market makers on the short side - lots of insurance buying but few nakeds or covered shorts.
I know you referenced "good feel for the underlying and market participants" in order to answer that question, but I'm wondering if there's a specific idea you could suggest regarding that to help narrow my focus?
> It is not just market makers that sell calls
Would you guess that market makers are, on average, net flat, net short, or net long calls?
I've been wondering if Elon's TSLA comp package was designed with this in mind. It really would be perfect SEC like move.
As you're in the know, would love to see how you would contextualise your examples on GameStop (GME) this week which is all over r/wallstreetbets.
As a lurker it has been quite the case study to observe - the OI for calls and puts are absolutely insane. Is this normal? What would the option writer be thinking/doing? What would the option owners be thinking?
Allegedly one fund took out a single 50k deep ITM position in a put that could possibly even expire OTM. The tinfoilers believe this was an attempt to deliberately induce selling pressure via these gamma squeeze mechanics you've mentioned.
This world is deep, never would have realised so many layers were going on under just a stock price...
The share is super volatile and can swing 15% in a day - how do option writers hedge in these situations?
If you're a whale, sure you can make brokers squirm by throwing your money around to buy a ton of options, forcing said brokers to bid up the underlying price hedging their short calls.
But then (as the whale), while the price is high you'd want to close some part of your position and realize gains. This means you sell the underlying at the inflated price, and then re-buy it at the lower price by exercising your call options? Is that the strategy?
Can you explain this? Maybe I just need an example to understand how this works
You did nothing in the meantime, so you collected the premium on the expired option.
Note this system isn't closed, we have not accounted for where the money came from. The market makers in the underlying are out the amount of the hedge gains.
Is there a guide to all this sort of stuff? What do tell the newbies? It's really hard to find good information about trading of the enormous amount of spam out there.
As for a guide yes it's hard due to all the get rich quick adverts. Perhaps read Wilmott to get an overview of how things are priced.
Thread of other resources on derivs: https://twitter.com/bennpeifert/status/1238823808946954241
The code is here: https://github.com/FinancialMarkets/5MinuteFinance/tree/mast...
1. Options have asymmetric payoff. One way you win, the other way you don't lose, assuming you are the buyer. The opposite is true for the seller.
2. Because of the asymmetry, movement is positive for the owner. So the option is priced based on how much movement is expected. There's a distinction here between vega and gamma, which are both movement related. Vega is sensitivity to the appraised future volatility, which means the option has more of that if it's long dated. Gamma is (2nd deriv) sensitivity to movement in the current price, so you'll have more of that if you're near the expiry.
3. As an options market maker, you are not in it to guess which way the underlying stock goes, you are in it to gain an edge in pricing that movement risk. So you hedge it when you trade an option with someone. If you buy a call, you sell some underlying so that your delta is flat. (Delta is just the 1st order price sensitivity)
4. If you flattened your delta, you can imagine the gamma making your local PnL vs price a parabola. If you are long the option you'll make money when the price moves either way, and you'll be needing to buy low and sell high to get back to flat delta. (Incidentally this is also why we don't really care whether it was literally a put or a call, as in the right to buy or sell. The 2nd order is the same, so has the same effect on your PnL when the price moves.)
5. The opposite is a less nice position to be in. The more the price moves, the more wrong your position is. In fact, the more it runs away, the more you have to push it the wrong way, because you'll be selling into a falling market or buying a rising one.
6. Natural question is, why would anyone ever be short gamma then? Well, you're going to charge people for their gamma, and if things turn out right you'll have charged them more than it's worth in terms of potential movement that they can buy low and sell high on.
7. So what happens with squeezes? Well sometimes that gamma gets so out of hand, there's some player with a huge wrong position squirming to flatten his position, but he is pushing it further and further away with each trade. Note that near expiry, a lot of things get hairy. You can imagine the gamma gets really spiky near the strike, because the time value is coming out of the price, and so you have a discontinuity at that corner. Also with binaries, knock-outs, and other simple non-vanilla options, you get some weirdness that can momentarily cause some large sensitivities. I've seen more than a few days where someone is defending some level and the price action looks odd.
8. Isn't the pressure the opposite for someone else somewhere? Technically yes, but often incentives are not the same for different agents. Different players have different risk tolerances, and they have different business models. For instance if someone has taken a load of options and shoved them into a structured product, maybe they're not quite as worried about hedging it as someone who doesn't have that customer flow. Or someone just has some cash to take a punt on the option, and they don't care if it expires worthles. Remember it's not just the two people who traded the option, there's the market in the underlying as well. Interestingly that means you can trade an option with me and we can both make money.