Hey Folks, Suppose you buy an ITM call (lasts 30 days) to profit from breakout from a flat base. I'd like to predict the change in extrinsic value if an X% move occurs within 25 days given an option's delta, gamma, theta, vega, and vomma. Doesn't need to be perfect, just need a good approximation. Need this to help determine reward/risk ratio of this trade. Is there a simple way to use the greeks listed above to do this? I thought another way was to use B-S twice, one for the initial condition, and one for the final condition. However I don't know how the implied volatility will change from initial to final. Does anyone know how to figure that out? And if we figure that out, will my method of comparing 2 points from the B-S model work? I'm skeptical, since B-S is supposed to assume a constant volatility of the underlying between initial and final points.
Its intrinsic value will. But the extrinsic value includes the implied volatility, which changes during the period you hold the option.
Assuming sticky-strike, read your expected extrinsic price from option at strike = strike * (1 - (x/(1+x)) and DTE = DTE - 25. If there is no tenor at exactly DTE - 25, linearly interpolate between the two spanning tenors. Yes, but not necessary, read extrinsic price directly. Calcs for sticky-delta assumption are a bit more complex and require an additional assumption of time-constant atm vol, which your question seems to exclude. Edit: this gets a bit easier to visualize if you start to think in log changes instead of percent. Not a big difference at very small percentages, but significant at 25%. N.B. above is a back of the envelope approximation, it won't be exact, even if sticky-strike holds.
So to simulate the X% move to the final state, you just lower the strike for the original option by a factor involving X% correct? If so, why don't you lower the strike this way: Strike = Strike(1-x)? Does this have to do with log math? Sorry if newbie question, read many options books and many ignored this stuff. 2 questions: What do you mean by N.B. above? (I assume it is the approximation you gave me). Also, how do I know whether I should assume sticky strike or sticky delta?
Yes, or you can think of it as a change in base. Suppose you wanted to analyze a 200% jump. Subtracting 200% instead of the correct 67% would get your strike below zero. "N.B. above" just means "Note that [the] above [method]..." Neither sticky strike nor sticky delta work all that well. Derman has a good write-up on it. Google "Emanual Derman Sticky Strike vs. Sticky Delta" and you'll certainly find his paper on it. The method I outlined in my previous post just assumes that, for example, after a 25% up move, a call that was atm will now trade at the same vol as a 20% otm put did before the move -- in other words the call strike will move left (towards the put side) on the vol curve and (due to put-side skew) trade at a higher vol.
2 questions: 1) Doesn't this assume that implied volatility is only a function of strike price? I don't think this applied to stock breakouts. IV spikes before the catalyst (typically earnings) then falls quickly after the breakout, even when the stock moves. But the assumption you (and most options books) seem to assume would have IV increase. 2) Do you know how to consider directionality when predicting the change in extrinsic value? The current pricing models assume completely random stock price behavior, which is not applicable to this use of options because we are playing a breakout from a chart pattern for a stock passing certain fundamentals. We are only buying this call because we believe there is a decent chance the stock movement after the breakout from the base will NOT be random. To find this chance, we consult the known average failure rate (see work by Thomas Bulkowski) of the particular chart pattern in question.
About a year ago, I decided that I was weak on portfolio/inventory management -- not on multiple underlyings [I was 99.87% SPX], but on expiries and layers within them. So I went 'back to school' and re-tooled some BSM equations much like you're discussing now. My goal was, rather than multiple decision inputs and 'professional judgment', I wanted a single graph/set-of-numbers, that I could hand off to anyone and say, "address this." What I came up with was a re-work of the BSM PDE, described (pretty well) in some posts here: https://www.elitetrader.com/et/threads/greeks-and-price-question.312919/page-2#post-4512530 It's been in daily use for over a year now, and seriously, I don't know what I'd do without it, and don't know why it's not on every platform. (It's not. ) I've been doing this a long time, and ..... the more I write down and take OUT OF my poor, over-cooked brain, the happier I am. To fast-forward to your immediate question, I'd encourage you to think about what happens to IV with an "X%" move up, and what happens with an "X%" move down... My thoughts in these posts (re SPX in 2017) may not be your thoughts for your target underlying in 2018... but the idea will hold, and if not, it's a snap to build a vega impact variable into things.
According to your post, the equation is "Port = delta + 0.5gamma^2 + 0.25theta + [arith.inverse]vega" What changes do I need to make to apply it to this instance? What is the arithmetic inverse of vega? Simply 1/vega? And in this instance, port would just be the change in initial investment in the particular contract, correct? This is my problem. Do you know how to do this assuming there is some bullish bias in directionality (NOT Brownian motion)?
Need4Greed Don't sweat the small stuff. All you have to know is that ITM options will change in value almost dollar for dollar to the underlying. All other variables will have a negligible impact on the R:R.