Vega of calendars

[guru]

Did you increase vol 40 percent across the board or did you nuke short dated and do you have wide duration calenders?

It doesn't matter because each of my position groups/combos is self-balancing and hedging for a single/specific expiry. When I have positions for multiple expirys then each expiry is managed separately. They'are also tested historically since 2007, while if I'm wrong then I'll lose an amount I'm ok with losing because I'd lose less than everyone else while I'd love to buy shitload of SPY at 40% discount.

the question is: which term is your vega located at? And how does your position delta move with volatility?

It also doesn't matter because I don't even use the greeks, but I use logic and historical analysis. I look at the greeks because other people tell me to, and then I see that I have negative Vomma which everyone is so afraid of
Though on individual stocks I have so much Vega and Vomma that they could offset any losses on SPX anyway.

 

[taowave]

I find the risk graphs of calendars particularly deceiving. It's good to have an intuitive understanding of the positions behaviour before one falls in love with break even points and max payout scenarios

Well said

 

[guru]

I find the risk graphs of calendars particularly deceiving. It's good to have an intuitive understanding of the positions behaviour before one falls in love with break even points and max payout scenarios

Yes, my point was only that the OP doesn’t have intuitive understanding, it may come from experience but not from trying to use one software or another, or trying to make assumptions. The issue is the input, so if you can test various inputs/scenarios then you will see the same outcomes regardless whether using the risk graph or the greeks, or one software or another. Basically I don’t know what any other software can do that ToS wouldn’t, but I’d be interested in such software as well.
While even experienced people get caught with their pants down, but calendars are not that bad. At least the OP is not selling naked stuff, while understanding he can lose the whole bet.

 

[LM3886]

Thank you for so many great thoughts. I really appreciate them.

My confusion is that, when calculating vega, there has to be a single vol as the variable to take derivative with. For a single option, it's clear that it's the vol of the option. For a calendar spread, it's not clear to me which vol to take derivative with. The way I see it is that, after reading the comments, there is a hidden vol (hidden because it's not the vol of any leg), and the vols of each leg are (stocastic) functions of the hidden vol. So one has to use the chain rule to take the derivative w.r.t. the vols of each leg first and then the derivative of leg vol w.r.t. the hidden vol. If the leg vol and hidden vol obey simple squared root time scaling, then it boils down to root time weighting of leg vegas.

On the other hand, I like your discussion about higher-order greeks. But I lack the intuition because I don't really have them in ToS or TWS. I know this might lead to the question of high-end option software again

 

[emulimu]

then I see that I have negative Vomma which everyone is so afraid of

Where can you see Vomma in TOS? Or is it some other software? Can you tell which one?

 

[MrMuppet]

Thank you for so many great thoughts. I really appreciate them.

My confusion is that, when calculating vega, there has to be a single vol as the variable to take derivative with. For a single option, it's clear that it's the vol of the option. For a calendar spread, it's not clear to me which vol to take derivative with. The way I see it is that, after reading the comments, there is a hidden vol (hidden because it's not the vol of any leg), and the vols of each leg are (stocastic) functions of the hidden vol. So one has to use the chain rule to take the derivative w.r.t. the vols of each leg first and then the derivative of leg vol w.r.t. the hidden vol. If the leg vol and hidden vol obey simple squared root time scaling, then it boils down to root time weighting of leg vegas.

On the other hand, I like your discussion about higher-order greeks. But I lack the intuition because I don't really have them in ToS or TWS. I know this might lead to the question of high-end option software again

OK, look. I think we should attack this topic from another angle: Let's talk about implied volatility and greeks.

Actually options were traded before the Black Scholes Model was invented: http://web.archive.org/web/20120326213505/http://www.thederivativesbook.com/Chapters/05Chap.pdf

Thing is, all trading has it's roots in some kind of relative value. Fundamental value vs. market cap, one instrument vs the other (pairs trading), actual queue position vs. orderbook price, etc, etc.
But in order to come up with a value of something, you need another thing that is similar or equal that you can compare it to. And in finance you look to replicate the cash flow of one instrument by trading another one.

So when you look at an option of a stock that trades at 100$ with a strike of 120$ that is 2$ and compare it to another option with a strike of 150$ which is 50cts, how do you compare the prices of the two? Which one is expeinsive and which one is cheap?

Right, you can't because you miss a common denominator.

Then some geeks came up with the idea, that you can replicate the cashflow of an option by trading the underlying: If you fade every move of the underlying (sell on upmoves, buy on downmoves), you basically replicate the cashflow of a short option. If the stock moves a lot, your P/L will move a lot, too and if you don't like that, you will have to trade in smaller increments.

So the idea was born that the value of an option is linked to how much a stock moves. By quantifying that, you could exactly replicate the cashflow of an option, thus you could for example buy the synthetic option (buy the underlying on every upmove and sell it on every downmove) and sell the real option against it. The model told you how much of the underlying you'd have to buy or sell.

This model is the Black/Scholes we all know and love. It's parameters quantify the options sensitivity to stock movements and to time and most important, it delivered a common denominator which can be used to compare two different options.

What do we learn from this wall of text?

1. Its totally possible to trade options without ever using the greeks at all
2. It's NOT the implied volatility that drives the options price. Options are priced based on supply and demand and implied volatility serves as a common mathematical denominator. Just like you would convert a 5$ dividend of a 100$ stock into percentages to be able to compare it to a 3$ dividend of a 30$ stock, you would convert the options price to something that lets you compare two options.
3. Greeks make it a lot easier to know a complex portfolios sensitivities at a glance
4. There is not one single implied volatility that is somehow given through the stock price. Implied volatility is called that way because the price of the option IMPLIES that the underlying will move with a certain magnitude...wether that's true or not. Each option has it's own implied volatility.


Therefore:
1. These options analyzers are forcing bad habits onto retail traders, since they bucket all the options implieds into one single vol.
2. Because you know now that each option has it's individual volatility, how much sense does it make now to slap on a calendar spread between a 1m and a 6m option while looking at the average 3m implied volatility?
3. You can bucket the implied volatility several ways: vertical (all IVs of the same maturity), horizontal (all IVs of the same strike) and deltas (all IVs of the same deltas) but you have to be aware that you are averaging them, which isn't 100% precise.



In conclusion, learn to be more exact with how you specify your bets. A long calendar spread is NOT a theta bet that is long vol. That's 100% incorrect. It is a bet on short term vols being too high and long term vols are too low.
A butterfly is also not a theta bet. It is a bet that the wing bucket (25-30 deltas) is too low compared to the ATM vols.

 

[guru]

Where can you see Vomma in TOS? Or is it some other software? Can you tell which one?

My own internal software/calculations. I use Interactive Brokers and had to create my own tools, but sometimes also export my positions to ToS just to see more stuff visually, like playing with adjusting volatility. But I also didn’t see higher order greeks there.

 

[guru]

Because you know now that each option has it's individual volatility, how much sense does it make now to slap on a calendar spread between a 1m and a 6m option while looking at the average 3m implied volatility?

I don't think that ToS (or anyone for that matter) uses the average volatility of the options in a combo or portfolio, but they use the volatility of each individual option and calculate the Vega of each individual option. The final/displayed Vega of a combo like calendar is the sum of all Vegas across the legs.
Would the result be the same as if using avg IV (not sure)?
At least adding the Vegas of individual legs seems correct, because your profit is also the sum of smaller gains & losses, whether from stock/shares or individual options/legs. The greeks usually translate to dollar amounts of gain/loss per delta/time/volatility unit, so adding up the dollar gains/losses from each leg, whether directly or by translating them to/from greeks seems logical.

The only thing I'm confused about is the proposed multiplication of Vega x square root of time, especially as I do not use the greeks all the time, though starting to utilize them to either confirm some of my assumptions or to discover potential issues. The thing I don't understand is that if you'd need to multiply Vega by anything, then you're no longer using Vega but some other derivative of Vega, similar to higher order Greeks.
Basically a calendar is a set of 2 legs, but you could just as well look at those legs or any number of legs individually, and each one would be associated with some risk & gain/loss and its own greeks. So when one leg loses $120 due to its own Vega and the other one makes $100 due to its own Vega, then as result you have $20 loss, whether it comes from the sum of dollar gain/loss of each leg, or the sum of the two Vegas. If you need to multiply Vega by something else then you're no longer using the Vega but something else. So the Vega of your portfolio should be the sum of Vegas, while the "Vega x SQRT(time) (aka root time vega)" of your portfolio may be the sum of "root time vegas" of each leg. And this may be something else to look at besides other greeks, but may not be the Vega. At least from my understanding.
And yes, the Vegas can change differently for each expiry, but that's related to things like Vanna, so if you add up the Vannas of both legs then you should also see the Vanna of your portfolio and therefore you'd know where you stand.

But I'm not sure if/where I may be wrong, so would appreciate some pointers/rebuke.

 

[taowave]

Keeping it simple,if you have a time spread with greatly different durations,bare minimum you should know how the vols/ delta's "could" react in an adverse move...

It's no different than being short skew delta,or at least being aware of the possibility...

 

[LM3886]

I don't think that ToS (or anyone for that matter) uses the average volatility of the options in a combo or portfolio, but they use the volatility of each individual option and calculate the Vega of each individual option. The final/displayed Vega of a combo like calendar is the sum of all Vegas across the legs.
Would the result be the same as if using avg IV (not sure)?
At least adding the Vegas of individual legs seems correct, because your profit is also the sum of smaller gains & losses, whether from stock/shares or individual options/legs. The greeks usually translate to dollar amounts of gain/loss per delta/time/volatility unit, so adding up the dollar gains/losses from each leg, whether directly or by translating them to/from greeks seems logical.

I think summing the deltas or thetas of individual options is correct because each option is dependent on the same underlying price and same time. Summing the vegas of individually options isn't mathematically accurate because each option is dependent on different vols. But these vols are still correlated, either in the form of skew or term structure.

1. Its totally possible to trade options without ever using the greeks at all
2. It's NOT the implied volatility that drives the options price. Options are priced based on supply and demand and implied volatility serves as a common mathematical denominator. Just like you would convert a 5$ dividend of a 100$ stock into percentages to be able to compare it to a 3$ dividend of a 30$ stock, you would convert the options price to something that lets you compare two options.
3. Greeks make it a lot easier to know a complex portfolios sensitivities at a glance
4. There is not one single implied volatility that is somehow given through the stock price. Implied volatility is called that way because the price of the option IMPLIES that the underlying will move with a certain magnitude...wether that's true or not. Each option has it's own implied volatility.

I agree that greeks are not required to evaluate a trade/position. In fact, greeks are local metrics which may not show the entire picture. A pricing model or a PnL curve should contain all the necessary information to stress test a position. I understand that implied vol is derived from option prices, not the other way around. But in order to stress a position, I shock the vol to see how prices would change. Due to the term structure, it is not accurate to shock vols for each leg uniformly. I think my conclusion from this discussion is that one can shock the vol using root time scaling for a quick and dirty approach, or rely on some complex correlation models.