The Most Important Options Pricing Model Has a Fatal Flaw. Dr. Jim Grades All 6 Assumptions.

Added: 2026-05-09

[00:00:00]Jim Schles here for Calculated Risk. And don't forget before we get started, the best ways you can help us are by liking the video, subscribing to the channel.

[00:00:05]Either one of those really uh helps us out a lot. So, option traders all around the world are leaning on the option pricing models to help them analyze the markets and make decisions. And without question, the poster child of all option pricing models is the Black Scholes model. So what I want to do today, let's break down the assumptions of the black shells model. Because every mathematical model, I don't care how great it is and I don't care how elegant the mathematics might be, they all have to make assumptions to track to the messy real world that we all live in. No research design is capable of replicating what we all do in the here and now every single day. So assumptions always have to be made with all these models. So what I want to do, let's take the six primary assumptions of the black souls model.

[00:00:52]Let's break them down. Let's talk about them. And then I want to give my verdict as to whether or not that assumption is realistic. So let's go. So the first assumption of the black souls model, stock prices follow a logn normal distribution. And honestly, this might be the best assumption that the black souls model puts out there when it comes to the different assumptions that it has to make. Because a logn normal distribution in English simply means that stock prices can't go below zero.

[00:01:19]It simply means that stock prices are concentrated to only the positive side of the distribution. And just think about that intuitively. Just use kind of common sense. Stock prices can't go below zero because that would mean, hey, here is some shares in our company and here's $30, here is $50, here is $100 per share or whatever it is. So it makes sense to assume that stock prices are going to follow a logn normal distribution. Now, with all that being said, we all know when it comes to curtosis and the leptocurrentic nature of the distribution, I know you guys were thinking about that probably when you clicked on this video that distributions in the stock market in equities have fatter tails. They have more outlier moves than a normal distribution would predict. So, the logn normal distribution assumption is not capturing that. So the fat tails is still an issue, but at the end of the day, I would actually give this a verdict of yes, this actually is pretty realistic. So the black souls model appears to be off to a pretty good start. Okay, so assumption number two, European style exercise only. Now, this one is assuming that assignments and exercises can only happen at expiration.

[00:02:29]That is what European style options means. This is not necessarily tracking too closely to what we all trade every single day because most of the options that we're trading, even the indexes, spy, QQQ, IWM, what have you, those are American style options where you can you can you can have assignments and exercises prior to expiration. And so the realism of this assumption, it's kind of tracking off base at least a little bit. Now, to be fair, in highly active, highly liquid options, is the pricing differential between a European style model and an American style model that different that's going to make a significant impact on what we're doing every single day? I would say no. But this is an example of one of those concessions that models have to make where the math just becomes much easier when you actually pin assignment or exercise to one point along the timeline as opposed to allowing it to essentially happen at any point prior to expiration.

[00:03:24]That makes the math way more complicated. And there are models that have gone to great lengths to actually fix this problem and extend the black souls model when it comes to this European style exercise assumption that may not necessarily be realistic. But just to stay focused on the task at hand here, I would say that the European style exercise assumption is not that realistic, but it's also not going to cause a big difference for us in our day-to-day trading. Okay, so assumption number three, prices follow geometric brownie in motion. Now, geometric brownie emotion simply means that there are two components to a financial assets price. There's a drift component and there's a shock component. So, the drift component when it comes to equities, that's going to be your positive drift.

[00:04:07]That's going to be kind of the upward trajectory of the market over time in some capacity. The shock component, this is going to be when you have volatility shocks in the marketplace, whether it be a news event, whether it be a geopolitical thing, whatever it might be. This is going to be the uncertainty that we all obviously know and love and some of us don't necessarily love, but that is in the marketplace every single day that can't necessarily be predicted or that can't necessarily be modeled in a precise way before the fact. But that's actually kind of the point of geometric bounty motion. Very similar to an efficient markets hypothesis in that regard. It's that prices are independent, right? Like you're not going to find any discernable patterns in the day-to-day noise of the marketplace. And so you've got the drift piece and you've got the shock piece.

[00:04:51]And essentially dayto-day there's a lot of randomness and there's a lot of unpredictability. So I would actually say that this assumption of the blacks model is very realistic when it comes to asset prices following geometric brownie emotion. Okay. So assumption number four frictionless markets. So that means no bides spread differential, no transaction costs, no commissions, no exchange fees like everything is frictionless. A lot of financial models actually make this assumption, which is a little bit odd to me because I don't think it would be that difficult mathematically to assume some type of friction in the marketplace. You can just choose some static, you know, flat tax and kind of use it across the board.

[00:05:30]But a lot of models do this. And man, wouldn't this be nice? Like, wouldn't it be nice if we didn't have commissions?

[00:05:36]Wouldn't it be nice if we didn't have exchange exchange fees? If we didn't have bid ask spread differentials, but sadly, we do have all these things. we have to deal with all the frictions in the marketplace on a day-to-day basis with all the trading that we do. So obviously assumption number four, frictionless markets. That's not necessarily too realistic and I would say so far it is the least realistic of the bunch. Okay, so assumption number five, the risk-free rate is going to be constant over the life of that trade. Is that a realistic assumption? This one can kind of go either direction in my opinion, right? You can make the case that this is not that realistic because interest rates are moving every single day. I mean, traders who are trading fixed income products, traders who are trading, you know, the bond products and, you know, the note products and what have you, they're moving around the 10-year, they're moving around the 2-year, they're moving around the 30-year, what have you. And so, interest rates are obviously changing on a dayby-day, minute-by-minute basis in a lot of ways. But then the other side to that same story is simply the fact that is this really going to impact option prices too drastically. I mean this is what row captures when it comes to the option Greeks and the reality is daytoday like in most cases row is just not going to have that big of an impact on an options price. Now can it have an impact? Absolutely. And if there's a big move in rates will it have you know a discernable impact a meaningful impact?

[00:06:56]Absolutely. but mostly daytoday it's just not going to be that big of a difference when it comes to a 30-day time horizon a 45day time horizon or what have you. So I would actually say whether this assumption is realistic or not actually doesn't really matter. So we'll kind of put this one as like an NA or a TBD or you go ahead and fill in the blank at home with whatever you want for the realistic nature of assumption number five that interest rates are constant. Okay, assumption number six and this is it. This is the coup d'etra.

[00:07:26]This is the grand pooa of them all.

[00:07:28]Volatility is constant. In my opinion, in my humble, professional, even personal opinion. This assumption is the least realistic of the bunch. And it is the most critical flaw of the black shells option pricing model because if you've traded for any longer than I don't know, six, seven minutes, you know that volatility is not constant. The VIX is moving. Volatility futures are moving. individual IVs for individual stocks are moving. They're moving all the time. So volatility is anything but constant. And in fact, since that's what we do at Tasty, that is what we trade inside the Tasty ecosystem. It's a good thing it's not constant, right? Because if it were constant, there wouldn't be too much to do. Like again, I mean, yeah, it'd be great to have the frictionless markets, but man, if we had constant volatility, like we're all out of a job. Like there's nothing to do. So thankfully volatility does move and thankfully markets do move and things do change. When it comes to volatility, this thing changes all the time and it obviously presents us at Tasty with tremendous opportunities almost on a daily basis. So the black shells model has six assumptions. Some of them are workable and realistic and some of them are not so practical and maybe not so realistic. And when it comes to understanding this, is this going to help you adjust a strangle today? No. Is this going to help you make your next earnings trade? No. But now the next time you're at a cocktail party and somebody just says, "Man, does anybody know if the black shells model assumptions are realistic?" Man, you are ready. You are equipped for that conversation and you are ready to go.

[00:08:57]So, we'll see you guys next time.