In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. Black-Scholes is used in the opposite way: traders deduce the implied volatility from the observed option prices. This volatility is a representation of the risk-neutral probability distribution that the markets puts on the underlying returns. From that distribution we can price other financial products for which prices are not directly observable.
I have seen the insides of an options market maker, and can say this is not really true (at least for some regions of the market). Black-Scholes is used to derive theoretical prices for options. Good option traders will have an opinion on volatility and won't just take whatever the market says.
However, one of the interesting aspects of serious option trading is that Black-Scholes is merely your bread and butter. There is a lot of information that goes into option pricing, including supply/demand signals. The mix of signals also depends on the time scale on which you are trading.
What rings true to me with this comment is the correlation between products. Option traders are often concerned with many relationships between product pricing: between underlying and option, across expiries, across strikes, between products in indices, between products in sectors, etc .
>In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand.
I'm not sure what your point is. Yes, actual market prices are determined by...the market. The Black-Scholes formula is widely used in modern finance to MODEL the price of an option given different sets of inputs in theoretical situations.
The way the article is written, it appears that the formula is used as: 1. Observe market parameters (volatility of the underlying and risk free rate) 2. Plug into formula 3. Deduce a price for the option.
My point is that it is used in the opposite way: observe prices to deduce market parameters. You claim my point is obvious, but I'm not sure it would be obvious to a reader unfamiliar with modern finance reading this article, which is the target audience.
> 1. Observe market parameters (volatility of the underlying and risk free rate) 2. Plug into formula 3. Deduce a price for the option.
In the FX market (interbank), the quoted and "traded" number is Implied Vol - the price of the option then follows from there (via the Black–Scholes model).
Sure, but isn't most of supply and demand in the market driven by large investors who use such formulas to derive the fair price of the option?
That is, if the real price ever differred significantly from what Black-Scholes predicts, wouldn't algorithmic trading very quickly correct this deviation?
If there was a way to directly formulate every parameter of the black Scholes formula you would be correct. The problem that you run into is how to calculate volatility itself? Without the volatility value, your algorithm cannot trade on it.
Using history of volatility is insufficient, because volatility is a forward looking measure. Just because the stock was volatile in the past does not mean it will be in the future, and vice versa. There are even more nuances with this, as volatility is a smile (or a surface), not a singular number https://en.wikipedia.org/wiki/Volatility_smile.
TLDR Trading in volatility is a very complicated topic. However, volatility is a useful parameter, and black Scholes is typically used to deduce the forward looking volatility from option price, in addition to volatility -> option price.
That article says that implied volatility is inconsistent, with options at strike prices that are very far from the current market price having costs that imply a different level of volatility than options at strike prices that are close to the current price. The cute question here is "should an option be priced according to the actual level of volatility in the price of the underlying asset, or should it be priced according to the level of volatility that exercising the option would require?"
In a sense, BS and the option market enable trading in volatility itself.
Specifically, you trade in the estimate of the stock's volatility over the time from now to expiry of the option.
If you don't want to trade options directly to do that (it is cumbersome, as it involves "continuous" delta hedging), you can trade in VIX futures for the same purpose. Or variance swaps.
> traders deduce the implied volatility from the observed option prices.
I've only ever seen one thing:
Black-Scholes models say IV should be less but your broker/brokerage/the market are overpaying for it.
I always figured it was closer to a Vegas juice/vig.
I never understood the benefit really.
Complicated math to tell you lots of people want to play roulette on NVDA earnings and whatever you are going to pay for it is going to be "overpriced/overvalued" in at least one way.
I've never seen the opposite where it helps you find an edge and something was undervalued.
Black Scholes is not used for any otc option pricing, except perhaps to provide an instantaneous estimate to get in the ballpark, but no one would use it for the final price.
European and American calls cost the same on non-dividend paying stocks (on dividend paying stocks, it might make sense to exercise an American just before the ex-date).
Either way, as was pointed out, in reality BS is used as a deterministic one-to-one mapping between option prices and BS vols. Then, from market quotes (either as prices or as BS vols) a vol-surface is fitted (as a function of strike and expiry time), from which a stochastic process is fitted that correctly re-prices all these points (using a model such as "local vol" or "stochastic vol" or a combination of those two, or others), and then everything is priced of that.
American style options are inherently more valuable. Imagine you had options on a stock that experienced a sharp but possibly temporary move. As a holder of an American style option, you could benefit from that temporary move, making it more valuable.
By put-call parity, C - P = S - df K, thus C = S - df K + P > S - K.
This is contingent only on the discount factor df being <= 1, and P >= 0, which is basically always the case. Thus, the value of the call exceeds the exercise value, making exercise never optimal.
Exercise for the reader: Understand why the same argument doesn't work for puts (or calls on dividend paying stocks).
> European and American calls cost the same on non-dividend paying stocks
All else being equal, I would prefer to buy an option contract I can exercise at any time vs one I can only exercise on a certain date. It doesn’t make intuitive sense they would be priced the same, can you please elaborate?
The parent is assuming that you can always sell your option to someone else for its fair value. If that's the case, there would never be a time where it's optimal to exercise a call option, because the optionality will always make the option value higher that the value of owning the stock.
This is shown in the article: the curved lines representing the option value are always above the straight lines of the final option payoff (the value if exercised).
This is not necessarily true for put options or for call options if the stock pays dividends. In those cases the option value can be below the payoff line and early exercise would be better than selling the option.
For valuing financial products with no directly observable price, BS or its descendants matter quite a lot. For actually pricing a transaction on those, it becomes more complex but model value is typically an important input.
The website argues that using a flag for a language may confuse or even offend users. It argues English would most appropriately be represented by the flag of England, but few people know the flag of England, so English is usually represented by the flag of the UK or the US, neither of which are appropriate because other languages are spoken in the UK and English does not originate from the US.
I would argue that using either the UK or US flag is less likely to confuse anyone than not using any flag, and that anyone offended by this needs to grow a tougher skin.
The fact that any mapping from a language to a flag is to some extent arbitrary does not imply that no mapping at all is better. This sounds like a variation of the Sorites paradox.
Furthermore, I find it amusing that a website dedicated to languages, which are roughly sets of arbitrary conventions we use to communicate, is offended by the choice of another arbitrary convention to communicate.
I know a person from Ireland that doesn't take well to being associated with the "Butcher's apron" as he refers to the flag of Great Britain. Ireland has its own flag and they are very proud of it. And they'll object to any suggestion that they are English.
And of course England has its own flag, which is not the same as that of Great Britain. And of course quite a few countries still using English because they were formerly colonized/oppressed/etc. (take your pick) and might have a thing or two to say about having to deal with the British flag.
There are a lot more languages than countries. And language variations, dialects, etc. And a lot of flag / language combinations are confusing, insulting, historically incorrect, or not that helpful. Like the British, the French were all over the place and there are lots of places that speak French that don't use the French flag. Likewise Spanish is used all over the Americas. India has about 21 official languages (I think, might be more). One of which is English. So, it's complicated for English and it doesn't really get any better for other languages.
Telling people to grow a tougher skin isn't particularly user friendly or that helpful.
> And of course quite a few countries still using English because they were formerly colonized/oppressed/etc. (take your pick) and might have a thing or two to say about having to deal with the British flag.
What about the fact that their language would be listed as "English", therefore reminding them it originated in England? Is listing the language as "English" significantly different from listing it as "<UK flag> English"? Should we rename the language to "Irish" ? Then what about the inhabitants of Ireland who don't identify as Irish?
You can always take the most offensive interpretation "This flag is claiming that Irish people are English, therefore contribute to historical oppression, etc".
But you can also take a more natural and charitable interpretation, which is that most people associate the UK flag to English, and the flag is therefore a convenient visual indication.
> it's complicated for English and it doesn't really get any better for other languages.
I agree, there is complexity and arbitrariness in any "language -> flag" mapping. I am arguing that you can make practical decisions even in the presence of complexity.
> Telling people to grow a tougher skin isn't particularly user friendly or that helpful.
Arguing you can't do something because someone will be offended is also not very helpful: you can almost always find some offensive interpretation of anything.
> Arguing you can't do something because someone will be offended is also not very helpful: you can almost always find some offensive interpretation of anything
You mentioned the sorites paradox earlier. Do you think it could be applied here as well?
> you can almost always find some offensive interpretation of anything.
This is the "perfect is the enemy of good" fallacy. We may not be able to find something that is not offensive to anyone in the world, but we can pick a convention that doesn't actively force hundreds of millions of people to identify themselves with colonial powers that committed genocide against their ancestors.
If this sounds hyperbolic to you, I strongly recommend reading up on the history of English treatment of the Irish over the centuries. Then follow that by learning more about African colonization. This isn't just a matter of growing thicker skin, the intergenerational trauma these people feel is very very real.
What’s reasonable for some is hyperbolic for others. So it feels like emotional abuse / bullying; or at least as a real world example of a utility monster: Someone gets so much harm from a little inconvenience that all people are supposed to bow down to them.
> I strongly recommend reading up on the history of English treatment of the Irish over the centuries. Then follow that by learning more about African colonization.
We're not talking about some your-grandpa-defrauded-my-grandpa historical slight, we're talking about genocide systematically executed under the authority of that flag. The emotions experienced by these people are in the same category as those experienced by Jews when they see a swastika. If you don't see how that's a bigger deal than you're making it sound then I don't know how to help you.
If you don’t see why censoring a British flag that represents a language literally called _English_ seems entirely pointless and laughable to some people then I don’t know how to help you.
> Are you saying this with the personal experience of being from a country that now speaks the language of its colonizer?
And to be clear, the US is excluded from this. Our cultural memory of our colonial history is an outlier—for most Americans our sense of our relationship with Britain is more that of friendly rivals than colonizer-colonized. The difference is largely because most of us are descended from the colonists (or people who arrived much later), not from the people that were there first, so the abuses that our ancestors suffered barely even register on the scale of colonial abuse.
That contrasts sharply with how the Irish or most Africans feel towards their former colonial powers. It's hard to feel positively towards a flag that represents a power that repeatedly committed genocide against your people.
To give you an example of flags being offensive: most people who would ever choose Belarusian anywhere in any computer system will find the current Belarusian flag offensive because it represents the government that oppresses their culture and represses people who dare use the language in public.
Another example: a lot of people speak Russian outside of Russia. Many of them have nothing to do with Russia and never lived there, and even without the devastating war that Russia is currently waging against Ukraine they don't want to associate their language with Russia and its flag.
Thanks, these are indeed good arguments. This made me reconsider but I am still not entirely convinced. I would argue that the association of the flag with the current government rests largely in the mind of the reader, not in the convention itself.
The website makes further arguments: English is the official language in many other countries, therefore choosing the UK is arbitrary.
You could define a complicated rule to make it less arbitrary, but then the choice of the rule itself would be arbitrary. I think the point that any mapping will be to some extent arbitrary is correct.
The problem for me is arguing that because any arbitrary convention will be offending or confusing to some, then no convention should be chosen. As opposed to the practical idea of just picking a convention that makes sense.
LLMs such as ChatGPT are very useful to craft or explain command lines for you. It doesn't replace knowing the tools and reading the man pages, but great to get started.
The CV of Thomas Vidick, one of the two people that found the bug, is quite impressive. Undergrad at ENS in France (ranked 1st), PhD at Berkeley (3.97/4.0), postdoc at MIT under Scott Aaronson, and now full professor at Caltech. He literally wrote a book on the topic (Introduction to Quantum Cryptography). So, yeah.
Thomas is indeed a beast - he was considered one of the smartest profs in the department when I was doing my PhD at Caltech. Just FYI, he left Caltech and moved to Israel a few years ago.
For context, as far as I am aware, ENS is the most prestigious non-engineering institute in France and is known for its extreme rigor. And l’X is the top engineering institute.
I believe Newton's flaming laser sword applies, so I would ask:
"What set of observations do you consider would establish the truth of your claim?"
From https://philosophynow.org/issues/46/Newtons_Flaming_Laser_Sw...
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Newton made his philosophical method quite clear. If Newton made a statement, it was always going to be something which could be tested, either directly or by examining its logical consequences and testing them. If there was no way of deciding on the truth of a proposition except by interminable argument and then only to the satisfaction of the arguer, then he wasn’t going to devote any time to it. In order to derive logical consequences that could be tested, it was necessary to frame his statements with a very high degree of clarity, preferably in algebra, and failing that Latin. Nowadays we drop the Latin option.
In choosing to exclude all propositions which could be argued about but not decided by a combination of logic and observation, Newton changed, quite deliberately, the rules of the game. An argument about, for example, whether cats or rocks have rights, the same as people do, would not be entered into until some clarification has been obtained.
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Birth rate is not a law of nature that can be naively extrapolated. Increased pace of technological development implies an increased pace of societal changes, which will impact birth rate.
Predicting birth rate for 2060 from today might be roughly equivalent to someone in 1850 trying to extrapolate birth rate to 1950. They would have been completely wrong because there was no way they could predict the level of development.
Even ignoring that, shouldn't we expect birth rate to be autocorrelated, as the impact of having children, and therefore people's decisions to do so, would depend on the population count itself?
2060 is 36 years from now, not 100. People having kids in 2060 are alive today or will be born in the next 20 years. Not crazy to make predictions about those people.
