jlakes85


Total Posts: 3 
Joined: Oct 2020 


Hi Everyone,
I working through some of the ideas in Sinclair's Volatility Trading and want to make sure I'm running the calculation properly. On p. 79 he illustrates a method to calculate the implied jump in the underlying between front and second month options, where sig1  front month implied vol, sig2  is second month implied vol and T1 and T2 are times to first and second expiries, respectively. Expected Jump is sqrt((2/pi))*sqrt(((sig1^2sig2^2)((T1*T2)/(T2T1))).
I'm looking at the ATM straddle of a stock, where sig1 is 78.27% and sig2 is 71.47%. T1 is 29 days and T2 is 57 days. This seems to provide an implied movement of 1.96% in the underlying. Does this seem correct? I would would greatly appreciate any help.
John 



kloc


Total Posts: 40 
Joined: May 2017 


Haven't done the calc, but 2% looks a a bit off.
The value should be approximately equal to the difference in variance over that time period. I'm assuming the IVs are provided are annualized so the implied difference in the variance should be close to the square root of (warning: *very* approximate numbers):
~ 1.5 * 0.1 * 0.1
(the three factors are approximately: vol1+vol2, vol1vol2, and time in years). So, I would expect the final number to be close to:
sqrt(0.015) ~ 0.12 = 12%
For this estimate, you can ignore the sqrt(2/Pi) factor (roughly one) so the final value should be around 10%, not 1%.
Are you properly taking into account that the input values should be annualized (including time intervals)?
Just noticed that a quick rough estimate became a long writeup...



jlakes85


Total Posts: 3 
Joined: Oct 2020 


Kloc,
Thanks for taking a look at this. The IV values are pulled from the TOS option chain, so I'm pretty sure that they are annualized. The 'T' values are given in days, and should have been annualized, as you mentioned. I should've seen this before. 



Casey


Total Posts: 4 
Joined: Apr 2020 


John, can you put an email in your profile I'd like to connect with you, looks like we're working on similar stuff 


ronin


Total Posts: 610 
Joined: May 2006 


Without doing the numbers.
The first vol is 78 (variance just under 9), the average of the first and the forward is 71 (variance around 8). So the forward variance would be around 7, for forward vol a bit under 50.
Something that moves by 50% in a month would move by 50 / sqrt(12) in a month. Which is around 14%. So not far off @kloc's 12%, but miles from your 2%. 
"There is a SIX am?"  Arthur 


Mistro


Total Posts: 32 
Joined: Aug 2018 


In Filthys book he is solving for forward vol between the tenors and using that as the non event vol.
Note* it is easier to work with variance but since you are quoting in vols ill do the examples in vols.
In your example, the forward volatility between month 1 (lets say 20 bus days) and month 2 (lets say 40 bus day) would be calculated as follows
fv = sqrt((V2^2 * Dte2  V1^2 * Dte1)/(Dte2  Dte1)) fv = sqrt((.7147^2 * 40  .7827^2*20)/4020) fv = 64%
64% is considered the non event vol in the book. Non event vol meaning the average of the vol leading up into the earnings event (ambient) and the vol post earnings event (diffuse).
Once we have the nonevent vol we can solve for the event vol eventvol = sqrt(v2^2*Dte  fv1^2*(Dte1)) eventvol = sqrt(.7827^2*20  .64^2*(201)) eventvol = 215% We are subtracting 1 because the option has 19 days of non event vol and 1 day of the event.
Now that we have the event vol we need to convert this to a 1 day implied move number.
1dayMove = sqrt(1/252)*eventvol*sqrt(2/pi) 1dayMove = sqrt(1/252)*2.15*sqrt(2/pi) 1dayMove = 11%
A few very important things to keep in mind when creating implied move numbers. 1) The model above and in Filthys book assumes the non event vol term structure is flat. This is rarely the case. You can use an index or etf to adjust the term structure. 2) The implied move is mostly expressed in the wings. In order to get a better estimate you want to look at all strikes and get the implied variance for the full expiration. You can reference the VIX calculation from CBOE. MS also wrote a paper on this but I can't seem to find it.
If you code in R I can send you some code to do the calcs.

men lie, women lie, numbers don't 
