There are many ways to model options. But how can the farmer make use of these insights?
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Gabe: So I went and looked at my BMI, body mass index.
Rodney: You shouldn't do that by the way. Number one rule, don't ever do that.
Gabe: Don't ever look at your BMI?
Gabe: So I was curious because I saw what it was somewhere. Podcast is normally audio, so people don't see me. I'm a big guy. I went and looked at what my BMI would be at 100 pounds lower. That's still overweight for me. I was like, there's no way. There's no way.
Rodney: Yeah. Supposedly it doesn't work really well for athletes. So Ryan, our producer, has that up on the screen there. We can see the screenshot. I don't know if you saw the guy that invented it wasn't a doctor.
Gabe: That sounds right.
Rodney: Yeah, that was right in the description. Like, "Hey, by the way, this guy's not a doctor." He's a mathematician. Which I like mathematicians. They've got their own things going, but ...
Gabe: Well, that's like option models, right? They weren't invented by traders. They were invented by physicists.
Rodney: Tell me about how physicists got into the options modeling.
Gabe: Man, I don't know how they got into it, but ... So Black-Scholes, these two guys were physicists. And so the, I would say widely accepted kind of base model for options, it's a modification of the model for heat dissipation. Right? So time and heat are the same, right? Like time decay, heat decay.
Rodney: Okay. Man, there's going to be a thousand questions here. First, Black-Scholes, which I've heard a thousand times, was invented by a guy named Black and a guy named Scholes?
Rodney: Didn't know that. Should have known that. That was baseline knowledge.
Gabe: So sometimes people bring up Merton. So there's Black-Scholes Merton. Merton was a grad student though.
Rodney: So he did all the work.
Gabe: Yeah. But yeah. So generally people talking about Black-Scholes or Black-Scholes Merton, so conveniently the BS model.
Rodney: Nice. So let me get this straight. So they're saying it was based on heat dissipation?
Gabe: The physics model that models how heat dissipates from something is the same model. Obviously did a little bit of change to it, but reapplied it to option models, like volatility and assets and time and all that stuff.
Rodney: Oh, that's interesting. Goes right back to the Medici effect. Right? The Medici effect.
Gabe: That's right. So options existed before Black-Scholes. You and I 100 years ago, maybe I had a horse and you were like, "Dude, I love that horse." I'd be like, "All right. Well, you can pay me a dollar for the right to pay $500 for it over the next three months. But you don't need to do that." I just sold you an option. So that stuff existed beforehand. And what they did was gave a way to think about it, again, this close formed modeling, which allowed for much more complex and deeper understanding of kind of the risks and the interplay of the different inputs into why an option costs what it does.
Rodney: So when you talk about that Black-Scholes model, it's so ingrained in how you think about options, right? That is the model that you think about. Are there other models?
Gabe: Yeah. There's a bunch of different ways to look at it. So Black-Scholes is this closed form. There's another thing you might hear. Monte Carlo. Monte Carlo simulations.
Rodney: I've heard that. Yeah.
Gabe: Yeah. So Monte Carlo, it's not particularly advantageous over the Black-Scholes ... Man, this is super nerdy stuff.
Rodney: I love it.
Gabe: Over the Black-Scholes model for your baseline options. Right? So what we would call an American or European style option. Monte Carlo, basically you take the way the option works. So how it generates a payout. So really basic options. All that really matters is at the end, where is the market relative to the strike and that tells you what you're paid. But there are more complex options where the path that the market travels. So it went up and then down and then up a little bit and down a whole bunch. That matters in terms of calculating the final value.
Gabe: So you would use Monte Carlo basically to take historical volatilities to understand kind of what a market looks like and run an option model through thousands if not hundreds of thousands if not more simulations of markets in terms of what it could pay out, based on current factors to kind of guide what those simulations look like. And then that tells you what the option costs or what it's worth. And that kind of tells you what the risk is in it.
Gabe: And then there's another one, which is the binomial tree. And so that assumes at any given moment, the market can basically go up or down. Either it goes up a quarter cent or down a quarter cent, right?
Rodney: I think this is my favorite model, by the way, this is the one that makes the most sense to me.
Gabe: It is the clearest one. Right?
Gabe: And so then what happens with the binomial model is you basically map out all the possibilities and then you do a probability calculation based on each possibility and its value and use that to pull back into what that option is worth today. I use the binomial model a lot when I'm teaching people kind of how to understand what the impact of time and volatility is on the value of an option. I agree. It's got a fancy name, but it's actually the most intuitive.
Rodney: Well, and for anybody that ever watched any daytime TV, to me, it's Plinko.
Gabe: Yeah, totally. 100%. 100% Plinko.
Rodney: If you're ever going to explain options to people, this is the easiest way.
Gabe: The Plinko model.
Rodney: So you've got Plinko is this gigantic ... The Price Is Right is the show we're talking about.
Gabe: Yeah. It is the show. Yeah.
Rodney: So you've got this huge kind of pegboard with all these buckets at the bottom and all the pegs are offset. So when you drop, I think it's a ball. It might be more like a-
Gabe: I think it's a puck.
Rodney: Yeah. Like a puck. Yeah.
Gabe: It's like a hockey puck.
Rodney: When you drop the [inaudible 00:06:42] in, it's going to kind of randomly bounce. It's going to hit at every level. So there might be like 20 rows down and say 20 across for the way we're talking about this. And then the important thing is the pegs aren't in a line. They're staggered.
Gabe: They're offset. Yeah.
Rodney: At every level.
Gabe: So the puck drops down and it hits in theory, the peg hits the middle of the puck and the puck bounces one way or the other at each peg.
Rodney: That's right. And I assume that Plinko machine was built with razor precision.
Rodney: So it's for sure perfect. So essentially you set this hockey puck down in the center and the carry over to options is that's you're at the money-
Gabe: That's your current market.
Rodney: Current market. Exactly.
Rodney: So you drop that down. And at every level, there is a 50/50 chance that that puck is going to go one way or the other, if it's built to precision accuracy. Which explains why a call that's way out of the money, or in this instance, way to the right of the Plinko thing-
Gabe: Where you start. Yeah.
Rodney: Where you start is cheaper because the odds of it always going to that one side are smaller.
Gabe: Right. Every time it hits the peg going to the right. If you win if the puck goes all the way to the right on Plinko, if you had to buy a spot in the Plinko payouts, that would be the cheapest spot to buy.
Rodney: You would think.
Gabe: You would think.
Gabe: It should be.
Gabe: It's the least likely to hit.
Rodney: So that's essentially the binomial model.
Gabe: That's right.
Rodney: And that's how options I think are taught to people in the beginning. Black-Scholes model is pretty advanced stuff. You're way past the binomial model when you're talking Black-Scholes.
Gabe: Yeah. So yes, but binomials models can get fairly complex. But yes, I think it's more intuitive. Also, I would say absolutely more simplistic modeling generally is more binomial in nature. Right? It's kind of like the people forecast a stock price or something and then say, "Here's the probability that I think it would get there." That's not binomial, but if I give you five different stock price outcomes and ask you to assign probabilities, that's effectively like a binomial model.
Rodney: Yeah. And it's reasonable to say that's my volatility so important with options. So volatility is how much do we think the market can move say in any given day. That's how I think about volatility. Is that the right way? I can tell by your face that it's not, so clue me in.
Gabe: So there's two types of volatility first of all, that we use normally. One is historical vol. So that's historical volatility. So that's how much has the market moved in the past? And that could even be today. Right? The other thing with historical volatility is you have to give a period of time. So you can't just tell me ... If I ask you what the historical volatility is on corn, you should have many questions for me. The first one is what historical volatility do you want? How many days? So it's not uncommon. When you look at a historical vols, as a trader, if for some reason I'm looking at historical vol, I'll generally have a really specific question. Like, "What did this do over the last year?" Or I'll want context. So I'll look at the 20, 50, 100 day historical vol. And it's not that different from thinking about moving averages, right? A moving average is a backward looking analysis.
Gabe: The cool thing, if you're into it-
Rodney: Oh man. We're talking options, man. For sure. Yeah.
Gabe: Is the other type of volatility is implied volatility. And we call it implied volatility because when you trade an option with the underlying market, corn futures are at 325, the strike is at 330, the option has three months of length on it, interest rates are 3%, duh, duh, duh. You can see all these other pieces. But when you're pricing it up, the big question when you price up an option is obviously we all see the same inputs, right? Where is the market right now? And the big thing we don't know is what's the market going to do?
Gabe: And so volatility, as an option trader, is the thing that if you're a good trader, you're good at understanding it and if you're bad, you're not. And so when I'm willing to buy an option at a price that actually implies that I believe volatility will be at or above the level, the volatility I had to plug in to get to that price. So it's implied because the price, the option price, given all the other information we can see, implies that you think the volatility is ... So in corn right now for December, I can tell you it's 19.2%.
Rodney: Which is low.
Gabe: Which is low. It's probably not the lowest it's been in the last five years, but it's absolutely on the low end. And certainly historically on the low end, especially for this time of year.
Rodney: So I'm sure we have a huge following of options traders listening to the podcast every day to hear what we have to say. But let's talk farmers, right? So 19% volatility. I'm a farmer. What does that tell me?
Gabe: The first thing I can do with implied volatility is calculate a rent. And so that's the in cents per bushel for corn, how much we think that market's going to move over some period of time. I'm not going to rattle off the rent formula right now. But I can tell you based on that-
Rodney: Check the show notes. Check the show notes-
Gabe: Check the show notes. Check the show notes.
Rodney: That's probably not true.
Gabe: We should put that in there though.
Gabe: But I can tell you right now, daily rent in corn is about 1%. So probably a little over that. So every day we would expect the corn market to move about three and a quarter cents between now and November.
Rodney: Plinko model though, right?
Gabe: Back to the Plinko. So it's-
Rodney: It could use 3 cents every day and never do anything.
Gabe: That's right. Thank you. That's really important to know. It's market movement, not direction. So volatility tells us how much the market's going to move, not where it's going to move. Now to be fair, in markets that are grains and oilseeds, volatility tends to be higher in higher price markets and lower and lower price markets. And the reason for that is when demand for those things is high, or better said, when people are worried about supply, you start to get a lot of panic. That's where panic shows up in grains and oilseeds is higher prices. And so uncertainty is almost always greater in times of panic. And so that's why you see a correlation there.
Gabe: The Black-Scholes model does not allow you to account for any correlation between market prices and volatilities. So that's why, just to bring it back to that Black-Scholes discussion, if you use Black-Scholes model today, that's probably where you start. But we know a lot more about how markets behave and some of these kind of in practice observable things that the model doesn't account for. And so then more sophisticated option houses basically create their own models that start there, but then start to incorporate a lot of these other differences.
Rodney: Got you.
Gabe: Anyway, so things I can do if I know volatility. So one, I can calculate rent. And like I said, in corn, it's a little over three cents a bushel today. So every day we would expect the market to be up or down about three cents a bushel. When the market prices it there, they believe that with about a 66%, 67% confidence level.
Rodney: I learn a lot during these things, man.
Gabe: You and me both.
Rodney: Yeah. I mean, I think it's worth calling out here, Gabe, so I've gotten some feedback on the podcast. Like, "Hey, sometimes I'm listening to this and some of it is maybe too easy for me or some of it is maybe over my head a little bit." And to that, I would just say that's fine, man. Guys that have been in this industry for a long time still only working on marketing. I don't know anything about growing anything. I planted lettuce seed in my garden two weeks ago and it's showing no signs of life. I come from 150 year farm family and I can't get lettuce to grow in my backyard. So no judgment here for anybody that's not following.
Gabe: And I also say If there are things that we talk about that we don't do a good job going over, we would welcome those questions. We want that and we want to know when there's something worth going deeper on.
Gabe: Grainwaves@indigoag.com. That's where you send your questions. Grainwaves@indigoag.com.
Rodney: Would love to see those questions. I just quickly am trying to do some math. And I really haven't thought about it this way. So I guess what I'm trying to do is help a farmer understand like, "Hey, I've got a crop in a field. I've got three months left to do something with this crop. What kind of price can I expect?"
Gabe: I'm going to ask our listeners to bear with me, because I'm going to walk through this really methodically. And we should probably put notes in the show about this so they can go look at it after. So we know the annualized standard deviation of December 2020 corn, the implied volatility is 19.2%. So the question you're asking is, "Gabe, that's great, but we can't trade December 2020 corn for the next year. That would be an annual period." So really what we need to know is those options last for about three more months. They'll go through about, roughly towards the end of November, but let's call it three months so the math is a little easy.
Gabe: So to back into what that annualized volatility actually means over the remaining period of time for our December corn options, what we need to do is take the volatility and divide it by the square root of time. I'm just going to let that set there for a second.
Rodney: Yeah, please.
Gabe: It's a fun sentence to say.
Rodney: Yeah. Square root of time. My sister's a listener of the show. She's going to love that right there.
Gabe: So what that means is in order to convert that volatility into a period of time that's not a year, you basically take the number of times the period you're talking about fits in a year and take the square root of it. So we all remember from probably about eighth grade, the square root of one is one. So we know to get the annualized, you just take that 19.2% divided by the square root of one. So you just get 19.2%. But if we want to know roughly what's about a quarter of the year, three months, well, there's four quarters in a year. So we take the square root of four instead of the square root of one. Again, I'm going to just do this in my head. The square root of four is two.
Rodney: I went straight to looking to see if there was a square root number on my calculator.
Gabe: On your calculator.
Rodney: Yeah. All right, good. Yep.
Gabe: So the square root of four is two. And so conveniently, we just have to cut that volatility in half. So call it about, I'm going to say roughly about a 10%.
Gabe: So what we've done is converted the implied volatility, which is an annualized number, into what is a quarterly volatility. And so we can take that quarterly volatility, which is about 10%, and it tells us how much the market thinks corn will move either up or down between now and the option expiring. And it will give us what it thinks the high or low over that period of time will be. It doesn't mean it will expire at the high or low. Just means that's kind of the range that we should expect to see.
So market's around 330, so that tells us we got about 30 cents of range is what the market thinks the risk is between now and an option expiration. And so to do that math, we're talking about going down to about three bucks, or in a happy scenario, going up to about $3.60.
And so I always find it really helpful when I'm actually sitting across the table from a farmer. That's a really good tool for me. To your point, that's not my opinion. The reason that that number is powerful is that literally what the world market thinks about the risk currently in corn futures in the December 2020 contract. That is the world's opinion handed to you on a platter in a very clear numerical way. And so you're staring at about 30 cents up or down. Then you can have opinions on that, right? Like, do you think it's going to go up? Do you think it's going to go down? Why?
Rodney: Sure. Yeah. Because also we backed into that number. That's still 67% likelihood. That is actually what's happening. Yeah.
Gabe: That's right. The market thinks there's a two thirds chance that we go up or down 30 cents.
Gabe: And so beyond that would be less than two thirds chance.
Rodney: Well, Gabe, I think that's all the time we have for today. So thanks everyone for tuning into the Grain Waves podcast, where Gabe and I bring real time analysis of grain marketing decisions directly to you. If you're new to the podcast, remember to subscribe, leave us a five star rating and share with your friends and family.
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