Forums > Basics > Convert Event Vol into an Implied Distrobution

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Display using: Mistro Total Posts: 22 Joined: Aug 2018
 Posted: 2019-07-23 17:58 Hi I was wondering if we could discuss the event vol/implied move as a distribution. I am looking for some clarification.CAT Today is trading @ 137 the company has earnings tomorrow. The 137 Aug16 Call is 4.15 and the 137 Aug16 Put is 4.00. The straddle price is 8.15.I calculate the atm iv to be 28.5% (I am using Business Days tte = 21/260 and the derivmkts package in R).Next I use a predicted ExEvent IV. This is the implied vol the day after the event. In my case the ExEvent IV is 22%Next I calculate the event volatility using the iv today and the expected Iv after the event.EventVol = sqrt(tte * v2^2 - v1^2 * (tte-1))Where: tte2 = total time to expirationv2 = total vol (iv)v1 = ExEvent IvImplied Standard Deviation = sqrt(1/260)*EventVolImplied Move = Implied Standard Deviation * sqrt(2/pi)Implied Median Move = .69 * Implied MoveIn our example if we fill in the blanksEventVol = sqrt(18 * .285 ^2 - .22^2 * 17)EventVol = .80Implied Standard Deviation = sqrt(1/260) * .80Implied SD = .05Implied Move = .04Implied Median Move = .0275Was the math here correct? This concludes my first part of the question.The second part has to do with the break evens of the Straddle the day after the event and why this number is different than the implied Move.The Straddle Price today costs 8.15Following the event (assume no move) using our ExEvent Iv and 17 busdays the 137 Straddle will be priced @ 6.15.This means our max profit on a short straddle is \$2 and the break evens are:Spot+(-delta/gamma) for Down Side Break EvenSpot+(delta/gamma) for Up Side Break Even. (This May be wrong)Our Break evens 143.8x and 130.5xOur Break evens are roughly \$6.50 on either side of the straddle.That is equal to 6.5/137 = 4.75%So what is our break evens telling us in regards to the distribution? It seems our break evens are much closer to the Standard deviation than our implied move.The whole point of this is I want to compare the empirical earnings distributions with the implied distro using ATM options only.Thank you men lie, women lie, numbers don't  TakeItAndRun Total Posts: 100 Joined: Apr 2010
 Posted: 2019-07-23 20:39 Last time I checked the number of US business days in a year is around 252.The implied move formula depends on the definition and the definition is not given.For the second part, Taylor series expansions for the call and put are needed:Assuming instant move (dt=0), opposite deltas of around 50%, identical gammasC1 = C0 + dx delta + dx² gamma / 2 + peanuts (1)P1 = P0 - dx delta + dx² gamma / 2 + crumbs (2)(1) + (2) gives:S1 = S0 + dx² gammaS1 - S0 = \$2 hence dx² = 2 / gamma dx is the break even and dx = +/- sqrt(2 / gamma).What do you get with this formula?  Mistro Total Posts: 22 Joined: Aug 2018
 Posted: 2019-07-23 21:41 Hi TakeItAndRun, thanks for the response.I might need some help with the definition. To me the event vol is the the total volatility from the close before the event to the close after the event. This makes the implied move the expected value of the straddle at the close the day after the event. This could also be seen as the average move the underlying will experience from closeT1 to closeT0. This is super helpful! With the formula you provided I get sqrt(2/.076) = 5.12. What does the break even tell us about the distribution of the event? In percentage the +/- 5.12 break even is about 5.12/137 = 3.7%Another way I am thinking about it is, if we plot CAT's past earnings moves. It has a mean absolute move of 4.6% and a SD of 5.4%. How can I transform a 30 day straddle to help me compare what the market is implying vs the empirical distribution stated above. Ps.Just to clarify, the gamma I am using for sqrt(2/gamma) is the gamma of today's straddle not tomorrows straddle. men lie, women lie, numbers don't  TakeItAndRun Total Posts: 100 Joined: Apr 2010
 Posted: 2019-07-24 06:59 In my formula, gamma means the gamma of today's call or today's put i.e. half the gamma of today's straddle.sqrt(4/.076) = 7.25 and the break even is 7.25/137 = 5.3%.With the empirical distribution of the event (mean 4.6%, stdev 5.4%) by using Monte Carlo simulations, one can compute the expected P&L of the straddle position at the end of the day and deduce the Value at Risk. Hence, you get useful indicators as the max loss for 95% or 99% of the distribution under your assumptions (ExEvent IV = 22%, no delta adjustment). Page 1 of 1