1/ Welcome to Options 201! You might remember me from such threads as Options 101:
Or What’s The Deal With Having Edge?
https://twitter.com/AgustinLebron3/status/1346141073488314371
Or What’s The Deal With Having Edge?
https://twitter.com/AgustinLebron3/status/1355324308470415362
2/ I wasn’t sure if I should keep going. We’re getting closer to “how to make money in options,” and I think public sources of such claims are always and invariably scams.
But I’ve decided this is still more “useful information to know” than trading edge, so it should be ok.
But I’ve decided this is still more “useful information to know” than trading edge, so it should be ok.
3/ Let’s start by talking about time. Time is surprisingly hard to think about. But why do we care?
Well, as we said in Options 101, we want to convert our options prices into vols because of #reasons. And to do so, you need to know t_exp.
Well, as we said in Options 101, we want to convert our options prices into vols because of #reasons. And to do so, you need to know t_exp.
4/ Ok, no big deal. my_option.exp_date – datetime.now(), done. Not so fast.
In the real world, time flows at a constant rate.
In the financial world it doesn’t.
In the real world, time flows at a constant rate.
In the financial world it doesn’t.
5/ When you’re talking about vol and time-to-exp, different periods are more or less vol-y.
Time flows more slowly on the weekend.
Faster on Mondays and Fridays.
Time flows very fast on earnings day.
Time flows more slowly on the weekend.
Faster on Mondays and Fridays.
Time flows very fast on earnings day.
6/ Remember, BS assumes vol is constant in time. Every timeslice is the same as every other.
So if we want to calc sensible vols, we need to calc a sensible clock for the stock. A way to “divide time” so that the clock ticks off constant chunks of volatility. In theory at least.
So if we want to calc sensible vols, we need to calc a sensible clock for the stock. A way to “divide time” so that the clock ticks off constant chunks of volatility. In theory at least.
7/ This is impossible to do perfectly. If you knew what vol was going to be in the future, just trade it!
What we’re really after is a decent approximation. So here’s a thing we can do:
What we’re really after is a decent approximation. So here’s a thing we can do:
8/
A. Take 5min returns of the stock intraday (or whenever options trade) and overnights/weekends.
B. Calculate variances for every block for a few years.
C. Aggregate by days in the monthly exp cycle.
This variance-time is now our measuring stick.
A. Take 5min returns of the stock intraday (or whenever options trade) and overnights/weekends.
B. Calculate variances for every block for a few years.
C. Aggregate by days in the monthly exp cycle.
This variance-time is now our measuring stick.
9/ Lots of variance on a Monday morning from 9:35am to 9:40am? Time flows fast in that 5min block.
Of course we should probably renormalize variances so that the units are still roughly days or years or something intelligible. Hopefully you get the idea.
Of course we should probably renormalize variances so that the units are still roughly days or years or something intelligible. Hopefully you get the idea.
10/ Yes there are problems with this approach.
Q: What if the stock had earnings on some day?
A: Probably we need to throw that out for our var-time calculation.
Q: What if the stock had earnings on some day?
A: Probably we need to throw that out for our var-time calculation.
11/ What else?
Q: Does it make sense to have a different var-time for different stocks?
A: Technically probably yes, but they should be fairly similar to each other in the same country, or size, or sector or whatever. Probably some aggregation is in order.
Q: Does it make sense to have a different var-time for different stocks?
A: Technically probably yes, but they should be fairly similar to each other in the same country, or size, or sector or whatever. Probably some aggregation is in order.
12/ More questions:
Q: How far back should we sample data for?
A: Bias vs variance tradeoff. Again.
Q: What about if you had a market crash in your dataset?
A: I dunno, maybe throw it out? Depends.
Q: How far back should we sample data for?
A: Bias vs variance tradeoff. Again.
Q: What about if you had a market crash in your dataset?
A: I dunno, maybe throw it out? Depends.
13/ Yet more:
Q: Why aggregate monthly? Why not weekly?
A: Weekly could be sensible...
Q: Why aggregate monthly? Why not weekly?
A: Weekly could be sensible...
14/ Closing thoughts.
There’s no right answer here. All there are are tradeoffs. But if you want to get vols even vaguely right, you do need to think about this stuff.
Comments?
There’s no right answer here. All there are are tradeoffs. But if you want to get vols even vaguely right, you do need to think about this stuff.
Comments?
15/ Ok, today we’re continuing with Options 201 by talking about THE GREEKS!
But before we do, let’s take stock (ha!) of where we are. Because some of you will say “Bah, Greeks, that’s 101 stuff”. I don’t agree.
But before we do, let’s take stock (ha!) of where we are. Because some of you will say “Bah, Greeks, that’s 101 stuff”. I don’t agree.
16/ Options are weird and wonderful, and it takes some time until your intuitions line up with reality.
Thinking in terms of partial derivatives helps build intuitions, but only after you really “get” the more basic stuff.
Thinking in terms of partial derivatives helps build intuitions, but only after you really “get” the more basic stuff.
17/ Thinking in terms of Greeks, IMO, is not the right place to *start building options intuitions.
Ok, enough soapbox, off we go.
Ok, enough soapbox, off we go.
18/ As I said, all we’re talking about are partial derivatives of some options things with respect to other options things.
But what’s important is that for most of these, there are many ways of thinking about the same thing.
And those connections matter a lot.
But what’s important is that for most of these, there are many ways of thinking about the same thing.
And those connections matter a lot.
19/ DELTA.
“The change in option price as a f’n of a change in und price.” BORING!
Delta is how happy/sad you are if stock goes with/against you. But only for small quick changes.
“The change in option price as a f’n of a change in und price.” BORING!
Delta is how happy/sad you are if stock goes with/against you. But only for small quick changes.
20/ Like if you’re long an ATM call (say 100 strike) and stock goes up 10c in the next minute. You probably made 5c. On paper. Yay.
But if stock goes up $1000, you definitely made more than $500!
But if stock goes up $1000, you definitely made more than $500!
21/ Same on the down side. If stock went down 10c, you probably lost 5c on paper.
But if stock drops to zero, you didn’t lose $50. You lost much less (the premium of the option before the move).
But if stock drops to zero, you didn’t lose $50. You lost much less (the premium of the option before the move).
22/ That’s the deal with the being long options.
When und moves in your favor, you “make more than you should” and when it goes against you, you “lose less than you should”.
When und moves in your favor, you “make more than you should” and when it goes against you, you “lose less than you should”.
23/ The “should” here is relative to owning (or getting short) the underlying. Of course, you’re paying for that wonderful behavior. The amount you’re paying we call “premium”. Right?
But delta isn’t only this. It’s much much more!
But delta isn’t only this. It’s much much more!
24/ Delta is also (somewhat obviously, if you’re paying attention) how much you should hedge your position in order to be indifferent to those small moves.
25/ And being indifferent is a good thing.
If you’re trading options, you should almost never do it because of an opinion in the und. If you do, just trade the und.
Remember Options 101?
If you’re trading options, you should almost never do it because of an opinion in the und. If you do, just trade the und.
Remember Options 101?
26/ So “delta-hedging” in this way lets us get rid of a risk we’re not being paid to take, and lets us isolate the ones we do want to take.
But wait, there’s more!
But wait, there’s more!
27/ Delta is also (roughly) the chances you’re going to want to exercise your option at expiration. In other words, the chances the stock will end up above/below the strike price of your call/put.
Not exactly, but usually close enough.
That’s kinda cool, I think.
Not exactly, but usually close enough.
That’s kinda cool, I think.
28/ GAMMA.
“The change in delta as a f’n of change in the underlying price.” Again, BORING!
Remember small moves? When the und moves small, the delta of an option stays basically the same. But now let’s make the move “a bit” larger.
“The change in delta as a f’n of change in the underlying price.” Again, BORING!
Remember small moves? When the und moves small, the delta of an option stays basically the same. But now let’s make the move “a bit” larger.
29/ Now the delta itself changes. If und moved in your favor and you were long, the delta went up. Against, delta went down.
Flip these if you’re short options.
Flip these if you’re short options.
30/ Gamma is the way that the “more than you should” and “less than you should” bits above express themselves. So it’s a measure of option-y-ness.
31/ A waaay OTM option doesn’t have any gamma because the optionality is all gone.
The stock is way far away from the strike price so change in stock don’t affect that option’s value. It’s near zero.
The stock is way far away from the strike price so change in stock don’t affect that option’s value. It’s near zero.
32/ But a waay ITM option ALSO doesn’t have any gamma because it basically behaves just like stock.
It’s getting exercised, almost definitely, so you’re getting (or selling) stock almost definitely, so it’s not really an option anymore.
It’s getting exercised, almost definitely, so you’re getting (or selling) stock almost definitely, so it’s not really an option anymore.
33/ Gamma, or optionality, concentrates near-the-money. There’s where the action is, which is why that’s where the liquidity and volume are in options markets.
34/ THETA.
“The change in price of an option due to the passage of time.” Hmm, sounds complicated.
Why “theta”? Because theta starts with t, and so does the word time. Genius right?
“The change in price of an option due to the passage of time.” Hmm, sounds complicated.
Why “theta”? Because theta starts with t, and so does the word time. Genius right?
35/ So what does this mean? Let’s go back to our way OTM option. It doesn’t have much theta because its value is already basically zero. That’s easy.
36/ But our deep ITM option ALSO has zero theta.
Because remember, it’s going to turn into stock for sure, so its value basically only tracks stock. If stock doesn’t move, our deep ITM option price doesn’t move.
Because remember, it’s going to turn into stock for sure, so its value basically only tracks stock. If stock doesn’t move, our deep ITM option price doesn’t move.
37/ All the theta concentrates in the near-the-money parts. Sound familiar? It should.
Gamma, our old (4 tweets ago) friend!
In fact, ignoring some scaling bits, gamma and theta are the same thing! Which they should be.
Gamma, our old (4 tweets ago) friend!
In fact, ignoring some scaling bits, gamma and theta are the same thing! Which they should be.
38/ If gamma expresses how much optionality a option has, then surely that optionality disappears over time.
And the amount of optionality you’re losing over time is exactly what theta expresses. The system works!
And the amount of optionality you’re losing over time is exactly what theta expresses. The system works!
39/ VEGA.
“The change in price of an option due to change in volatility.” Ok, I’m going to level with you.
Vega isn’t real like the other greeks are. But what do I mean by “real”?
“The change in price of an option due to change in volatility.” Ok, I’m going to level with you.
Vega isn’t real like the other greeks are. But what do I mean by “real”?
40/ Well up to now, the sensitivity of options prices were to observable things. Und chg, und chg chg, time. These are real things.
Even if you had no idea about options pricing models, you could come up with delta, gamma and theta estimates just by looking at historical prices.
Even if you had no idea about options pricing models, you could come up with delta, gamma and theta estimates just by looking at historical prices.
41/ But “change in vol” isn’t a real thing because vol isn’t a real thing. It’s only real in the context of some model: some way of transforming prices into vols and back again.
And there are LOTS of ways of making that transformation. Just ask Espen Haug! It’s model-dependent.
And there are LOTS of ways of making that transformation. Just ask Espen Haug! It’s model-dependent.
42/ And yet vega is among the most important sensitivities options traders track. Usually #2 next to delta, in fact. (Don’t yell at me if you’re a short-term gamma scalper!)
43/ Because remember, when you’re trading options you’re trading vol. That second-order moment.
So vega is really the equivalent of plain old delta in stock-land. If you’re long stock and it goes up, you win. And vice versa.
So vega is really the equivalent of plain old delta in stock-land. If you’re long stock and it goes up, you win. And vice versa.
44/ Well vega plays the same role in options land. If you buy some options, keep them nicely hedged, and aren’t close to expiration, your Pnl is defined by your vega.
If you’re long options and vol goes up, you win $. It’s pretty much that simple.
If you’re long options and vol goes up, you win $. It’s pretty much that simple.
45/ But because vega is model-dependent, it gets more complicated to even be sure what your exposure is sometimes.
Just ask those VIX traders last March, right?
Just ask those VIX traders last March, right?
46/ Ok, that’s good for today. We covered the big ones. If there’s interest, we can get to the crazy ones next.
(No, rho isn’t a big one. Interest rates will be zero until the end of time, remember?)
(No, rho isn’t a big one. Interest rates will be zero until the end of time, remember?)
47/ Aaaand we’re back, talking about second-order greeks.
Honestly, I don’t really get why so many people care. I was an options market-maker for a long time, and I almost never thought about second-order greeks.
Like a few times a month, tops.
Honestly, I don’t really get why so many people care. I was an options market-maker for a long time, and I almost never thought about second-order greeks.
Like a few times a month, tops.
48/ If you’re an exotics trader then fine. But I doubt there are more than a dozen of you reading this.
And if you’re exo trader or options MM, you should have better sources of info than some rando Twitter handle. :)
And if you’re exo trader or options MM, you should have better sources of info than some rando Twitter handle. :)
49/ So why does #fintwit care? Some of it is curiosity, learning for the sake of learning. That’s great.
But I bet some of it is trying to feel and sound smart. However, feeling and sounding smart doesn’t pay the bills. So be careful.
Ok, no more soapbox. Let’s go.
But I bet some of it is trying to feel and sound smart. However, feeling and sounding smart doesn’t pay the bills. So be careful.
Ok, no more soapbox. Let’s go.
50/ SPEED: d gamma / d spot.
Ok, I’m cheating already since this is a *third* order greek. Booo! But it’s the most important “weird one” for a market maker IMO.
Ok, I’m cheating already since this is a *third* order greek. Booo! But it’s the most important “weird one” for a market maker IMO.
51/ Gamma is basically “How much am I going to need to hedge to stay delta neutral?”
The delta of low-gamma positions stays pretty constant, high-gamma positions have deltas that move around a lot.
Why should I care?
The delta of low-gamma positions stays pretty constant, high-gamma positions have deltas that move around a lot.
Why should I care?
52/ Expiration, usually. Say I have a pos with high gamma. I’m probably trading a lot (more than I’d like) trying to stay flat.
If I have a high speed on top of it, then I’m exposed to the risk that if stock moves, I’ll have so much gamma I won’t be able to hedge well anymore.
If I have a high speed on top of it, then I’m exposed to the risk that if stock moves, I’ll have so much gamma I won’t be able to hedge well anymore.
53/ Near expiration, I could easily get stuck with a large delta I can’t hedge.
No market maker likes to sweat a big delta over the weekend. That’s not what you’re paid to do.
No market maker likes to sweat a big delta over the weekend. That’s not what you’re paid to do.
54/ CHARM: d delta / d time.
Another one that matters mostly near expiration, for much the same reasons as above. Near expiration, the mere passage of time can change your delta a lot.
ITM options get ITMier, OTM options get OTMier.
Another one that matters mostly near expiration, for much the same reasons as above. Near expiration, the mere passage of time can change your delta a lot.
ITM options get ITMier, OTM options get OTMier.
55/ Of course, ATM options kind of stay around 50 delta as long as spot doesn’t move.
So the charmiest options are the ones on the shoulders of the Gaussian. The 25/75 delta options, basically.
So the charmiest options are the ones on the shoulders of the Gaussian. The 25/75 delta options, basically.
56/ VOMMA: d vega / d vol.
I didn’t worry much about this one, because I didn’t really trade long-dated options and this is a thing that matters more as t_exp gets bigger.
Usually, the way you think about this is “If vol explodes, does my book get bigger or smaller?”
I didn’t worry much about this one, because I didn’t really trade long-dated options and this is a thing that matters more as t_exp gets bigger.
Usually, the way you think about this is “If vol explodes, does my book get bigger or smaller?”
57/ Since we’re good boys and girls and we’re delta hedging, options trading is about trading vol. And vega is the size of your vol bet.
58/ And since IV only really moves fast in one direction (up), vomma tells you the answer to the question “If the world goes crazy, do I now have a massive book on my hands?”
Which is something worth knowing, for sure.
Which is something worth knowing, for sure.
59/ D VEGA / D SPOT:
I don’t know what this one’s called. But it’s another specific case of d vega / d whatever.
And as before, what we care about is “How big/small does my book get if X happens?”
I don’t know what this one’s called. But it’s another specific case of d vega / d whatever.
And as before, what we care about is “How big/small does my book get if X happens?”
60/ In fact, as you can tell, this is how I think about all of these 2nd order greeks.
I’ve never put on a trade thinking “Ooh, I see a vomma mispricing”.
I’m sure that’s someone’s job but it never was mine. Thinking about this stuff was always about risk management for me.
I’ve never put on a trade thinking “Ooh, I see a vomma mispricing”.
I’m sure that’s someone’s job but it never was mine. Thinking about this stuff was always about risk management for me.
61/ But again, usually if you take care of the first-order stuff, you don’t really need to think about the second-order stuff except in weird situations.
I think that’s it for second order greeks. Yes I skipped a big one. That’s cuz I have nothing interesting to say about it.
I think that’s it for second order greeks. Yes I skipped a big one. That’s cuz I have nothing interesting to say about it.
62/ Please don’t think of this as definitive on the subject. It’s just one person’s perspective, given the experiences I’ve had.
I’m sure @bennpeifert @Ksidiii and others have different (and possibly more informed) views. That’s ok too.
I’m sure @bennpeifert @Ksidiii and others have different (and possibly more informed) views. That’s ok too.
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