Vega of calendars

[LM3886]

In a calendar spread, the vols of front month and back month change differently. Tools like TOS show a Vega figure for a calendar spread. Does anyone know what it is with respect to? Front month vol, back month vol, or something else?

 

[guru]

Vega is the current Vega based on current vols, as they currently are for each month. When any of the vols will change then the Vega may change.
You can test this by adjusting each vol for each expiry individually.

 

[MrMuppet]

In a calendar spread, the vols of front month and back month change differently. Tools like TOS show a Vega figure for a calendar spread. Does anyone know what it is with respect to? Front month vol, back month vol, or something else?

TOS calendar vols are just additive for both terms without root time weighting. Not very useful, but as @guru mentioned, you can adjust each individual term to shock your book

 

[LM3886]

root time weighting

Does it mean if I change the 30-day vol by x%, then I should change the 60-day vol by x% / sqrt(2)? Of course given that there is no foreseeable event between the two terms.

 

[MrMuppet]

Does it mean if I change the 30-day vol by x%, then I should change the 60-day vol by x% / sqrt(2)? Of course given that there is no foreseeable event between the two terms.

You usually select a reference month to weight your vegas with. Let's say you're long the 60 day and short the 30 day while the 30 day is the most liquid one.

Then you use SQRT(referrence/day to expiration) x raw vega. It's a very dirty calc but it helps a lot when dealing with multiple expirations. This is also explained in Talebs first book.

I think IB also has added something similar: https://www.elitetrader.com/et/threads/time-weighted-vega-vs-inverse-square-root-vega.320991/

The basic idea is the fact that short term vega moves more than long term vega. While on a net basis you're long vega with a calendar, you're actually almost flat

 

[guru]

You usually select a reference month to weight your vegas with. Let's say you're long the 60 day and short the 30 day while the 30 day is the most liquid one.

Then you use SQRT(referrence/day to expiration) x raw vega. It's a very dirty calc but it helps a lot when dealing with multiple expirations. This is also explained in Talebs first book.

I think IB also has added something similar: https://www.elitetrader.com/et/threads/time-weighted-vega-vs-inverse-square-root-vega.320991/

The basic idea is the fact that short term vega moves more than long term vega. While on a net basis you're long vega with a calendar, you're actually almost flat

Would this affect option P&L graphs in programs like ToS, as they calculate option prices using B/S and the Vega is the result of calculations (output), while they assume the current/static vol (which may be reasonable as we don’t know future vol) ?

 

[LM3886]

You usually select a reference month to weight your vegas with. Let's say you're long the 60 day and short the 30 day while the 30 day is the most liquid one.

Then you use SQRT(referrence/day to expiration) x raw vega. It's a very dirty calc but it helps a lot when dealing with multiple expirations. This is also explained in Talebs first book.

I think IB also has added something similar: https://www.elitetrader.com/et/threads/time-weighted-vega-vs-inverse-square-root-vega.320991/

The basic idea is the fact that short term vega moves more than long term vega. While on a net basis you're long vega with a calendar, you're actually almost flat

Thanks, I will check that book for details. I'm also curious what would be a not-so-dirty calc?

 

[MrMuppet]

Would this affect option P&L graphs in programs like ToS, as they calculate option prices using B/S and the Vega is the result of calculations (output), while they assume the current/static vol (which may be reasonable as we don’t know future vol) ?

yes it would. ToS and other analyzers asume constant vol over all terms which is why everyone thinks of calendars being long vol (since the longer term has more vega).

However, if you watched vol of vol over various terms, you'd realize that 1m vol probably goes from 20vols to 30vols and back while 9m vol goes from 25vols to 26vols and back.

The vol of vol difference is not accounted for and it would be really difficult to implement this since vol of vol correlations over various terms are not static

 

[MrMuppet]

Thanks, I will check that book for details. I'm also curious what would be a not-so-dirty calc?

the not so dirty way would be a correlation study. This way you could figure out how many front vols it takes to imply a 1vol move in a longer term. Like when the 6m jumps from 30 to 31vols how many vols is the jump in the 1m.

This differs a lot from underlying to underlying and is not static. Remember that the only thing that ties different vol terms together is calendar arbitrage, which is a very lose no arb criterium (short term with the same strike can never be the same or higher price than long term).

Usually when you don't have a specific setup in the term structure of vol, you better think in vega buckets across terms to hedge yourself. The calendar as a theta/gamma play isn't really a thing IMO, especially when vol of vol is high

 

[LM3886]

the not so dirty way would be a correlation study. This way you could figure out how many front vols it takes to imply a 1vol move in a longer term. Like when the 6m jumps from 30 to 31vols how many vols is the jump in the 1m.

This differs a lot from underlying to underlying and is not static. Remember that the only thing that ties different vol terms together is calendar arbitrage, which is a very lose no arb criterium (short term with the same strike can never be the same or higher price than long term).

Usually when you don't have a specific setup in the term structure of vol, you better think in vega buckets across terms to hedge yourself. The calendar as a theta/gamma play isn't really a thing IMO, especially when vol of vol is high

Sounds like a lot pieces to put together. I assume this is not freely available. Do you know if there is any reasonably priced platform that provides such study results (or, even better, applies to PnL)?