Calculating Expected move using different models

[TheBigShort]

hey everyone I was wandering if some of you could help me out with a problem I am facing. In this example I will use MBUU as I put on a short straddle last night as a way to express an opinion solely on the jump.

There are 2 models I use to calculate the jump. The first (and most frequent one I use) is the the term structure model. So to calculate the expected jump I use this formula:

event_var = (V_front^2 - V_back^2)/(1/Dte_front - 1/Dte_back)

From this I can find the expected move by the formula:

sqrt(1/252)*sqrt(event_var)*sqrt(2/pi)

On MBUU last night at 15:45 before market close MBUU Sep ATM vol was 60.06% and Oct ATM vol was 42.4%. The Bus days to expiration were 12 and 32. Plugging this into the equation we got an expected jump of 9.4%. To price the front month straddle I also need to see what the diffuse vol will be after the event, I use the forward vol formula to figure this out. To do this I plug in the same numbers into the standard forward vol calc:

forward_vol = sqrt(V_front^2 *Dte_front - V_back^2*Dte_back)/(Dte_Back - Dte_front)
Plugging in the same numbers we get a forward vol of 26.5%.

MBUU opens and here is what happened to the vol.

The vol hangs around the 50% mark! This screwed my position. I know there is generally some residual vol left over. BUT with 12 bus days to go you would think the vol level would be much closer to the forward vol level (dilution of the event follow through). This has happened to me before but not at this magnitude. If I used a time series model and plugged in 50% as my residual vol, then the implied jump would have only been 5% instead of 9.4%!!!!! ( a much worse deal)

So my question is, does anyone have a better method to capture what the residual/diffuse vol will be in the morning for a given maturity?

 

[newwurldmn]

The vol reset is the tricky part. The algebra is an approximation.

Often the implied move is greater because the term structure goes upward sloping.

 

[TheBigShort]

The vol reset is the tricky part. The algebra is an approximation.

Often the implied move is greater because the term structure goes upward sloping.

Hi Newwurldmn,

I am just looking to get close to what the reset will be +/- 5 vol points. With less than 15 bus days to go, the jump will dominate so if I can just get a close approximation to the reset figure that would be great. As you can see in the MBUU i was 25 vol points off!! Horrendous. Any tricks/better equations you have learned over the years?

 

[tommcginnis]

There was a good-sized price climb in there, taking the price from ~45¢ to ~$1.00 -- which would cut the IV observed -- just as it did for the remainder of the day. (If I'm reading that lower graph/labels correctly...)

FWIW, I worked overnight (6.5hr) volatility change into the BSM PDE with an approximation of 1pt. IV per %change Underlying -- so, a 0.50% drop in the underlying would equate to a .5pt increase in IV, a 0.25% climb in underlying ==> 0.25 decrease in IV. Is it perfect? No. But it lends more credence to a calculation that gives me the willies. In practice, it works like a charm. As well, it works as an end-of-day calc. too -- very nice for inventory.

 

[guru]

I mostly trade vol expansions and contractions, so I wish I could sell vol one minute and buy it back the next, or even the next morning. Formulas don't matter if you simply use BS and/or assume that vol should be close to the forward vol level, as you did. Why do you need this to happen in the morning? Wouldn't 2 mornings be sufficient? IV expansions very often last for several days, but one day may be sufficient if market makers see the price stabilized, as well as there isn't someone who may know more than them.

 

[oldmonk]

I've been looking for a good solution to this problem myself. The approach I use is similar to the "term structure" method you've mentioned, but looks at the first few expirations past the earnings date, as opposed to just 2 expirations. This is just so we can use more data for estimation. I posted this on another thread a few days back, pasting it here (the data is now outdated, but the method is the same):

Consider MU, which has earnings on Sep 21. Looking through the option chain, we see that the aggregate IVs for the Sep 21, Sep 28, Oct 5, Oct 19, Nov 16 options are 0.56, 0.51, 0.48, 0.47 and 0.44, respectively. I want to use this data to compute the implied earnings and ambient vol. Since the earnings weight is always 1/DTE, we have the following equation to solve for the total IV given the ambient (AV) and earnings vol (EV):

IV^2 = 1/DTE * EV^2 + (1 - 1/DTE)*AV^2

Since we're given the IVs, we can solve for the EV and AV using a system of linear equations, one for each expiration (so I just used a generic solver). This gives me an ambient vol of around 0.39, and an earnings vol of around 1.88.

I can send you the R code for this if you need. The problem I've found with the "forward vol" approach is that the values vary massively depending on the expirations used.

 

[TheBigShort]

I mostly trade vol expansions and contractions, so I wish I could sell vol one minute and buy it back the next, or even the next morning. Formulas don't matter if you simply use BS and/or assume that vol should be close to the forward vol level, as you did. Why do you need this to happen in the morning? Wouldn't 2 mornings be sufficient? IV expansions very often last for several days, but one day may be sufficient if market makers see the price stabilized, as well as there isn't someone who may know more than them.

I am trading the implied jump vs my prediction on the day of the event. I am having a hard time understanding what you are talking about here. I think we are talking about two different things.

I've been looking for a good solution to this problem myself. The approach I use is similar to the "term structure" method you've mentioned, but looks at the first few expirations past the earnings date, as opposed to just 2 expirations. This is just so we can use more data for estimation. I posted this on another thread a few days back, pasting it here (the data is now outdated, but the method is the same):

Oldmonk this looks like an interesting approach to calculating the ambient vol. I usually just use what is implied for the expiration before the event and add/subtract depending what the SPX term structure looks like. I will have to take a look at this tanks for posting. However what I am looking for is what the diffuse vol will be in the morning after the jump with a decent degree of certainty.

 

[oldmonk]

Oldmonk this looks like an interesting approach to calculating the ambient vol. I usually just use what is implied for the expiration before the event and add/subtract depending what the SPX term structure looks like. I will have to take a look at this tanks for posting. However what I am looking for is what the diffuse vol will be in the morning after the jump with a decent degree of certainty.

Since we can't actually predict what the post-jump implied vol will be, wouldn't our best estimate be the current ambient vol i.e. the portion of the IV not attributable to the event?

 

[TheBigShort]

Since we can't actually predict what the post-jump implied vol will be, wouldn't our best estimate be the current ambient vol i.e. the portion of the IV not attributable to the event?

No, because the day after earnings we usually see a move 30%-50% larger than usual days(this will be very significant if there are only say 5 days to expiration). But this is giving me an idea... Since vol is additive, calculate the ambient vol (potentially the way you are suggesting), break it down into individual days and change one of the days to a 30-50% larger move. That should give me a pretty close approximation. I'll post an example in a few minutes.

 

[TheBigShort]

Your formula is a bit off, to calculate the Event vol, you are using the term structure method which is incorporating forward vol. The ambient vol you are solving for would be the exact same if you just used forward vol calculation between each maturity