Tony: Thomas, we're back my friend with The Skinny On Options Math and we got Jacob in the house.

Tom: Burning Man.

Jacob: Yes.

Tom: It's a concert.

Jacob: No.

Tony: It's a gathering.

Jacob: It's a art and music festival.

Tom: Art and music festival. It's called Burning Man?

Jacob: It's called Burning Man.

Tom: Where is it?

Tony: The Nevada desert, all the way in the middle, where I'd like to send you, but I'd put you in a hole.

Tom: Say it slowly. Burning Man.

Jacob: Yes.

Tony: Yeah. They burn a big …

Jacob: Yeah. There's a big wooden effigy.

Tony: If you went there you'd be the biggest man there so they would burn you.

Tom: Where in the desert?

Jacob: It's in the Black Rock Desert, so it's …

Tony: I don't know, but can I send you?

Tom: Shut up for a second. Where is it?

Jacob: In Black Rock Desert, so it's a couple hours south of Reno.

Tom: A couple hours south of Reno. You've got a giant trip planned.

Jacob: It's long.

Tom: Tell everybody where you're going. You're going to New York?

Jacob: I'm going to New York to see the family.

Tom: They need to see you every once in a while.

Jacob: Then Oregon to talk to professors and stuff. Then back to New York because the rest of the family is coming in. This was not ideal planning, but it's what happened.

Tom: You mean back and forth across the country.

Jacob: Yes. Then I'm going to Reno.

Tom: Then back the other way?

Jacob: Yeah.

Tom: Yes. This is not good planning. Well, two trips across country, you'll get some miles for that.

Jacob: I don't know, I paid for them with miles so I don't get any so at least it's not costing.

Tom: Beautiful. It sounds like a crazy 4 weeks. We're going to miss you here. Then you'll be back for the whole year?

Jacob: Yeah. Then I got to stay in Chicago for a long time.

Tom: Good. Hopefully you'll fail your courses too and then you can be here for even longer.

Tony: I don't think that's going to happen.

Tom: We always wish for the worst. Let's do our little discussion. So are you ready?

Jacob: Yeah.

Tom: Beautiful. Greeks Review? We're going to Greece?

Jacob: No, we're talking about derivatives. We covered most of this material in some level of detail before, but I felt like especially before I leave for a month, it'd be good to just give a good way to actually look at and apply these things.

Tom: I'm pretty sure of two things right now. We're about to give the most complex definition of Greeks in the history of Greeks and you're the first person to ever write Greeks Review, because 99% of all people that ever talked about the Greeks, say, "It's Greek to me."

Tony: That's true.

Tom: I've read 75 option reviews and every single one says, "It's Greek to me." If I saw that on here I was going to cross it out but thank God you did Greeks Review. If you are a new listener, there are a lot of easier Greek reviews that are around. Jacob is a budding young math professor who we decided in conjunction with him that we're going to make the most complex discussions of Greeks and all mathematical formulas so that if you are a little bit of a math geek, this is going to be right up your alley.

Jacob: You can go away with more understanding and more ways to apply these things.

Tom: Or more incentive to learn more stuff. We're not dummy it down, is the easiest way to say it.

Jacob: No. Most of these segments are advertisements for you to go learn something.

Tom: That's right. Everything we do here, we believe that financial content should be just that. We're not investor education, we are financial content. Financial content should be an advertisement of engagement. It should be a marketing tool for engagement. It should be something that you can turn into something investible. I'm not interested in delivering news and/or education. Go ahead.

Jacob: Our discussion of the Greeks … in premise they can all be done for any way you have of valuing options, but in practice we want something where there's a closed-form formula for the value of the option so that we can actually do first-year Calculus type derivatives of it. We start with the Black-Scholes formula which is just up there. The various variables are define, S is your spot price, K is your strike price, R is your risk-free rate of return, tau is your time until expiration, those n's are the cumulative distribution for a normal variable, so those are the odds that a normal random variable is less than whatever the argument is, d1 and d2. D1 and d2, we'll see in a second, are these large piles made of the existing variables that tell you how much you need the return to shift in order to cross the strike price essentially.

Tom: What's my takeaway from this slide?

Jacob: Your takeaway is that the important thin about the Black-Scholes model, which this is, is that unlike a lot of other pricing models, it ends with a the value of the option equals and then a formula, rather than the Binomial model which says, "to find the value option you need to go through this binomial tree process." It doesn't end with a formula. The fact that the Black-Scholes gives you a formula makes it much easier to discuss the Greeks.

Tom: Beautiful. Next slide please. Of course I don't know anybody that's going to discuss the Greeks this way. Next one please. So you made it easier.

Jacob: Yeah. This is just saying those d1, d2 and n were. They were hiding a bunch of mess, but I sort of said what they are and it's just the probability that are random variables, is that less, and then d1 and d2 are how much you need to shift across the strike price from your current value.

Tom: I think we should teach professional athletes option Greeks-

Jacob: This way?

Tom: This way. So when they get asked questions by reporters they don't say anything stupid and they can related everything to Greek … I don't know if that was not at reference there, that was a formula for the Black-Scholes model and then all of a sudden the reporters just look around and they would be totally quiet. This is so applicable to so many different parts of life. Let's go to the next slide. This allows us to figure out how much the value of an option changes as the various parameters change.

The so called "greeks". Since derivatives are linear we could even do this for positions by just summing the greeks for the constituent options of the position. So go ahead.

Jacob: That formula gave a value for how much an option is worth based around the parameters and you can take derivatives of things if you've taken any calculus. But if you have a strangle or a position that is made of several options and the same underlying then you can [inaudible 00:06:36] your total greeks are. So greeks is suppose to measure the value of what you hold or have sold changes as the various parameters changes over time.

So you can do that for a position just because the derivative of a sum is the sum of the derivatives, and so you can just add up the greeks across multiple things of the same underlying and come out with the greek for the whole position.

Tom: Which is essentially what we did ask professional traders, because we traded a single underlying pretty much. But as individual investors what it does is it gives us … I want to say it's almost like a quick little luksy.

Jacob: They reveal a lot of the more important facts about the position or option that you're looking at and we'll go over which ones tell you what.

Tom: Let's go to the next slide. So go ahead.

Jacob: They did a typo on that slide.

Tony: Hold on one second, you found a typo in that slide? We tried to put that in there just to mess you up a little bit. Do you want to tell everybody what it is?

Jacob: The right formula there where it says Del C, Del S that should be Del C, Del sigma.

Tony: Right, see it's Del sigma Thomas. I don't know what's wrong with you, he's eating catch, do you want to know why? Because you're just not paying attention, you're just not that sharp, you're just scalping [inaudible 00:07:54] you think you're like anyone at all can do that. It's Del C.

Tom: I'm going to kill him. Don't worry about him, you're not going to miss him.

Jacob: So the first two greeks you want to consider usually are Delta, which is the first one everyone considers, which is just how much the value of your option changes as the price underlying move, and so that gives a way of saying that this option is like owning half of a business stock.

Tom: You called that directional equivalent.

Jacob: Right. Actual stock has a Delta of one and all the other greeks zero. So that's where you can base these things. Options are much more complicated, so it's value comes from this probability which we can perhaps remember what it was but we can't, that's OK, you can go look it out. But it just have to do with how likely you are to cross the strikes. So the more likely you are to cross the strike the more the change of the underlying affects the change of the option.

Vega, which I feel like I'm complaining, that letter next to vega which is the usual letter used to represent it is not a vega, there is no greek letter vega. It's a new, it looks like a V and I don't know. But it gets called vega, that letter is a new.

Tom: We're not in a position … We're going to-

Jacob: No one is in a position to change this now.

Tom: We're going to rant about a lot of stuff, Tony and I, but we're not going to rant about the V and Vega. Are you Tony?

Tony: No. I will be fine with that.

Tom: We ranted on a high frequency training today and things like that-

Tony: Still new maths that we're talking about.

Tom: Yeah, we're going to let the V and vega go.

Jacob: Vega is less often used but probably for many position more important. Because especially like we have a non directional position you're not going to get much in the way of delta, but what vega is going to tell you is how much the value of your option changes as the volatility changes which is the one thing that you would really want to consider is if you think volatility is low or high, especially because volatility does a better job of exhibiting meaner version so your guess is about, this volatility is probably going to go back down or probably going to go back up, your contrarian view point, it's better applied to volatility than it is to stock price.

Tom: What we do is since we're very much always about selling volatility the discussion topic here on Tasted is always about reversion to the mean but it's never about being long volatility hoping that it goes back to the mean so you could sell higher. It's just about not selling it too cheap.

Jacob: You can get the same thing, right?

Tom: Of course.

Jacob: It's just about where you put your money a lot of the times. It's about knowing how the behavior of the volatility affects the price of the option.

Tom: The difference is for retail investors your vega risk is usually significantly less than your delta risk.

Jacob: Right. This is idea behind making something delta neutral. You can keep adding options together until you get your deltas low and at that point most of your risk will come from your vega.

Tom: The problem with that is for retail investors that is not a classic retails investor, you want to have an assumption. What gets people interested about investing is having an assumption about something.

Jacob: Right, I'm just saying that it's perhaps better rather than have your assumption be that Apple is going up or Apple is going down, say Apple's volatility is going to go up or Apple's volatility is going to go down, that's something your assumption about might be better.

Tony: Dude, you're preaching to the choir. We talk about this for five hours every day, same exact thing.

Jacob: I'm saying that for that reason you might want to put your vega higher in your list of statistics you look at.

Tom: Got it, that's fine. Let's keep going, next slide. So delta and vega are perhaps the most important aspects of an option,since they say how much it's value will change with value and volatility of the underlying. They tell you how to turn ideas like "the stock will go up" or "the volatility will go down" into profitable positions. Beautiful, let's go to the slide.

Jacob: Following delta and vega are gamma and vomma. Vomma is a rarely used one but-

Tom: Very rarely used.

Tony: Vomma?

Jacob: I'll be happy not calling it that but that is apparently its standard name.

Tony: Vomma? [inaudible 00:11:50]

Tom: You can pretty much make a sign [inaudible 00:11:54] out of anything but option and greeks for sure.

Tony: I got enough talent.

Jacob: The important thing here is that these give accelerations and if you've taken a physics course or done a first year calculus course you'll remember that the secondary of those things is all you need is to get a good graph of it going.

Tom: What if most of you take short walks to your car?

Jacob: If you take short walks to your car what you want to remember is the acceleration becomes much more important in some sort of a large shift. So your delta could be very small but if your gamma is high then in the case of a large shift underlying your delta is life here, because while it was small at the beginning of that large shift as it goes out the gamma tells you that delta goes up as you further away from the current price. That means that you want to consider your gamma involvement if they are either high or negative, they're going to tell you that your vega and delta are somewhat misleading in the case of large shift.

Tom: We showed you gamma but unfortunately on the platform we do not show you vomma, we show you mova.

Tom: Keeping in mind both the gamma-

Tony: You didn't watch the [inaudible 00:13:05] I'm sure to figure out which one was-

Tom: Of course, everybody did in America.

Jacob: You might not show vomma but anyone who wanted to could take that formula, throw it into … Google would calculate it for you.

Tony: Somebody hasn't shown him vomma in a long time. Even if they did he couldn't see it.

Tom: Keeping in mind both the gamma and the more rarely used vomma-

Tony: Do you put your glasses on in those situations?

Tom: Keeping in mind both the gamma and the more rarely used vomma is important when making decisions based on the delta and vega since they give the acceleration of the value of the option with respect to the value and volatility of the underlying respectively. This means that in the case of a large shift in either, it is these second-order derivatives that will mostly govern the changes in the value of the option.

One of the reasons we roll our positions relatively early and one of the reasons that we suggest to not to hold everything to the end is because these second-order derivatives start to … As Tony would say, grow hair or grow teeth. All the times you grow hair.

Jacob: Teeth is where they hurt you, right. They would give you behavior you weren't expecting in the case of large moves. You want to make sure you avoid that sort of thing. Unless you looked at him ahead of him in which case you were expecting and that would be great.

Tony: He's getting ready for burning man.

Tom: Even a delta-neutral position can change in value greatly with a major shift in the underlying thanks to a large gamma. That's what we were just talking about. One of the things about options, and Tony and I mention this all the time, is that as you're close to expiration an option that's wrapped around the strike price can go from a delta of zero to a delta of 100 with basically three ticks. So that's the scary thing about waiting till the end of the game.

We just had a discussion for this about certain number of days to expiration and that 45 days to expiration it's much more … It's much easier to see and much more imaginable. Is there another slide?

Jacob: Yeah, because we're also going to Theta.

Tom: Yeah, Theta.

Jacob: The last one we want to talk about is Theta, which is the time derivative. It's how the value of the option changes over time, as you were talking about a moment ago, you could do the secondary derivative time which would actually get you the results of your last segment. About telling you when you noticed acceleration. That doesn't even have a goffy name. There's no Thoma or something. But you could just write … There's a formula, you could take derivative with respect to time again and it would get you a reasonable value and you could look for where that zero and will tell you when you want to get in on this, which might be close to 45 for sort of typical values of sigma S,K, but let you pick the tau that you want in order to get the acceleration behavior that you want.

Tom: So you're telling me our research team could have just used this simple formula.

Jacob: I'm telling you that this formula would hopefully match up with what their research says. These models, hopefully, are describing how things really work. What they did was actually look at what does work and if Black-Scholes is pretty good, which it usually is, then they could have also done this and would have gotten a very similar result.

Tom: I'm going to ask Tony to sip in and bang it out of the weekend.

Tony: I'll bang it out right now if you need me to. I'm strong, I'm still young, I can jump.

Jacob: You spent the last segment talking about beta so we don't need to delay it for a while.

Tom: That's awesome. This is the last slide.

Jacob: This is the last thing we're talking about.

Tom: I didn't know there was-

Jacob: Beta is the mystical last greek but beta is a very different greek and so we can't really talk about in the same discussion.

Tony: Let the beta and greek goes together.

Tom: I would love to have a beta discussion because a lot of people don't understand beta and I think when you come back it would be a great discussion to have.

Jacob: We have had a better discussion, it's in the archive somewhere.

Tom: We have, but I would like to make it just … Now that I think we've gotten through a lot more stuff I'd love to revisit beta because we default to beta wording and I would just like to … I used to have so many questions about beta I think it would be fun to run it by you.

Jacob: Beta is an important idea because once you move off from only having one underlying you sort of need beta to have any meaning. If you add up deltas across positions on different underlying you're doing something meaningless.

Tom: Let me ask you a question. If I could as a 100 investment professionals to beta weight the portfolio of their customers how many do you think could do it out of a 100.

Jacob: I know very little about the market, my guess would be 5, 10.

Tom: Your guess would be off by 5 or 10, I would say the number is 0. I would say there's not a single … Maybe there's one or two pieces of technology in the whole advisory business that would let you beta weight your position to come up with a constant over portfolios, I don't even think it exists. Now that being the case and you just saying how important that is, doesn't that say something about the industry that we're in?

Jacob: Yeah, but you're the one writing new software.

Tony: Before we take a quick break, since you're going to burning man, Gregory who we had on one of our bootstrap from a satellite phone store said that because you're a tastyliver and he's learned so much from you he said that, "Tell Jacob to contact me. Nobody gets any reception at burning man." He said to hook you up with a free phone or data terminal if you want. So he's just paying dividends for you, he's the best. We will be back in 90 seconds with the bootstrap where we will go to a different direction, one that you'll like. We're going to go pork barrel barbecue time. So we will be back in 90 seconds as it gets tastier only on the tastylive network.