It's worth reflecting on what options markets were like before Black-Scholes: a lot smaller and valued through qualitative, "over-the-counter" measures. More like handshake one-off business deals than liquid markets.
Regardless of how you feel about options trading or the role of liquidity in financial markets, Black-Scholes was an intellectual achievement and should be remembered as such, even as newer better techniques replace it.
To his credit, Ed Thorp also realized this at the same time as Black-Scholes but chose the money-management route and didn't feel the need to publish his strategies as papers for the academic community (and probably giving up the Nobel Prize in Economics).
My two favorite books on these people are Perry Mehrling's biography of Black and Ed Thorp's autobiography.
Fischer Black: https://www.amazon.com/Fischer-Black-Revolutionary-Idea-Fina...
Ed Thorp: https://www.amazon.com/Man-All-Markets-Street-Dealer/dp/0812...
Multiple wall street firms (at US Government urging) needed to urgently inject massive capital into the markets to contain a near-systemic collapse.
PBS produced a phenomenal documentary, The Trillion Dollar Bet, which covers the development of Black-Scholes and the rise and fall of LTCM. Highly recommended.
So this isn't a knock on the BS model necessarily, but human greed.
This is all from the excellent book "When Genius Failed."
Two ways. Gradually and then suddenly.”
How quaint. In 2019, tech companies burn through billions of dollars of capital every single year, and we call them business "successes".
In the case of LTCM the government needed to bail out LTCM positions. That is why it is different.
The banks keep dealing with high levels of leverage. It keeps predictably blowing up in their faces. The government/Federal Reserve is responding by making it easier to borrow money and then VC/Unicorns etc borrow.
The links aren't perfectly causal, but I bet that under normal conditions (if interest rates were allowed to rise into the 2-6% band in a sustained way and the government stopped handing out free money) then suddenly the unicorns would be subjected to market logic such as a need to make money to receive a high valuation.
I quote, “ Technically, the Fed didn't bail out LTCM. It used no federal funds. It merely brokered a better deal than the one Buffett offered.”
> Tech firms are losing cash but generally gaining value towards an IPO.
...but they don't always. This makes the original statement sensationalist nonsense as it's happened multiple times (over the time period mentioned).
Valuation is screwed up in both "types" of businesses, but the methodology is irrelevant to the claim when it's apples to apples for the market.
But the part about money having a positive time value shouldn't be. That indicates a major problem in the system.
It's somewhat orthogonal to how financial organisations actually fair value their rates volatility. All the market makers had to move away from log normal vols years ago as negative forwards have been around for a long time in other currencies.
So you have your counterparty on the phone or in group chat and you arent using the same formulas in the same way then its difficult to get same pricing
If it had never been published would it still have been as accurate? Who knows.
When you dive deep it's easy to think of economics in terms of math and forget the fact that, unlike physics, it is a social field and there is no right and wrong aside from what people agree on.
I think if prices didn’t follow the model, there will be arbitrage opportunities either in the options or the underlying.
We will continue to arbitrarily create money, and create incentives which force us into subpar investments in order to motivate people to take out loans they otherwise wouldn't have, in order to work to create products there wasn't otherwise enough demand for, and in the meantime the middleman will collect the fees for their "work" in managing these "investments".
Really kind of reminds me of Rick and Mortys microverse episode.
It's number 58: http://www.jewfaq.org/613.htm
They also have a mitzvot that one shall not lend to another jew with interest. It's number 171
To be clear. I acknowledge there is a difference between lending with interest and usury
Without interest (or fees) on loans then anyone lending money would have to take an active interest in the business as a proper partner or shareholder, which is a lot of overhead and headache for everyone involved.
Though I suppose keeping it impersonal and at arm's length like this has pros and cons, I think it's what I would prefer personally in most cases as a borrower.
Another alternative of course is not borrowing money but that would tend to limit business ventures to those with minimal setup costs that start nearly cash-flow positive - or initiated by the already wealthy elite.
So, basically what you mentioned. And yes, it does involve more work. But that's how life is if you want to be fair. The alternative with lending money with interest is that now the lendee owes you money just for simply borrowing money. We see what this practice gave us when we look at the current financial situation (in its many forms, bonds for example are a form of usury). It is a predatory practice. Simply making money for having money is extremely dangerous and unethical. You have to work to make money, either by putting in effort to do physical labor, or by doing your research in deciding whom to invest your money with, etc. You can't get money "for free" (I realize that nothing is 100% guaranteed, e.g. if the lendee declares bankruptcy, but the contract itself is predatory).
Its not some nefarious scheme, its just the best way that has arisen to do things thus far. It wasn't "designed" or "planned" and in order to make the system more efficient, a new method of transactions needs to be established, and many groups are working hard to come up with a cryptocurrency to solve this problem.
Regarding interest and "usury" there is no difference, because there is no definition for "unreasonable" interest. I have an irresponsible friend, that I know if I give $100 to, there's a 1% chance that I will get my money back. So than why would I give him money at a rate that would be unprofitable for me when I can do other more useful things with it? Say I have another friend who I have good reason to believe will give me back my money 99% within our agreement. Obviously the second would get a better interest rate because there is less risk and he might be more useful with the money than I could be.
How do you calculate risk? Well let 10,000 other people with money offer him better terms (driving down the interest rate) if they think my judgement is wrong, and if it turns out to be the case they make money, if not they lose money.
Its not for you to say, ALL Investors you have to get involved with the business, for one, the person receiving the money might not want to give up control, nor the investor give it, because that might not be his area of expertise. Then again, maybe it is, and you have specific investors called VC's that do get involved.
Its actually ridiculous that people in the 21st century could consider the usury argument valid and actually praise Dogmatism. The greater concern is actually about creating and maintaining a competitive marketplace of creators and investors, then about the rates they charge -which is determined by simple supply and demand.
Try limiting the rates to your definition of "Fair", see what happens. Hint: Google "the cobra effect".
His claim seems to be that usury is when interest is charged on loans where the lender has full recourse to the borrower in case of default.
It seems a little overblown to me. If you were setting up a new spreadsheet(!) you'd tend to call some counterparties and hear what they thought of how to value things. It's not something they'd keep secret from you, maybe you'd even get a free meal out of it. If course you still have to think for yourself whether what they said makes sense.
As for BS model, I think of it as a demo tool. Everyone knows the underlying assumptions are not met, but it still illustrates the so called stylised facts that people in social sciences tend to be fond of.
They might well tell you how they think you should value things ...
Now, it's a whole different story if you are not a trader, for example you run a massive pension fund, a university endowment, a government treasury, etc. In that case, the investment bank's attractive salespeople will invite you to golf at a famous country club, a helicopter tour of the city, dinner at the best steakhouse in town, all while lying through their teeth about the value and safety of the financial product you're about to purchase.
Black-Scholes is basically the textbook model taught in schools. But modern finance has more complex models to address its flaws. In particular, Black-Scholes assumes that Call-options and Put-options are symmetrical, but in reality, people value put-options more than call-options. (In laymans terms: protecting against market drops is more valuable than protecting against market upswings).
You assume a normal curve. You define "volatility" (the market's uncertainty to the price of something) as Geometric Brownian motion with some standard-deviation / variance, and then perform differential equations on that to determine the "proper price" of an option.
After all: Options grow more valuable in times of uncertainty, and grow less valuable when everyone can accurately predict future prices.
The part that "brakes" because of negative rates is the "risk free rate", predicting the future value of money. To me, it seems like there are a variety of obvious extensions you can do to fix this problem. You could redefine Black-Scholes to operate on "Real" terms, and then convert everything back into "normal" terms later.
Black Scholes doesn't "fundamentally" require postivie interest rates for the risk-free rate. It was just an assumption that they had in the original model. But as a differential equation, its pretty easy to tweak your assumptions around and fix these issues.
But any such tweak means you're no longer working with classic Textbook Black Scholes. Sure, it served as the basis of the theory, but you gotta account for more real-world variables than the original textbook model.
Interestingly, the Schrodinger equation works about the same way. Just assume a handful of reasonable and "obvious" things about physics, and out pops the equation.
Under normal circumstances, a call option is always more valuable than the stock itself. The exception is of course, the dividend. True owners of the stock will receive the dividend, but call option holders will NOT.
However, for any stock without a dividend (ex: AMD, Tesla, etc. etc.) American vs European style doesn't seem to matter. Its always better to hold onto the option of buying a stock, rather than being "forced" to buy the stock.
Tax laws change that equation significantly.
1. Black-Scholes was originally designed to describe the price of assets like equity (which tend to move proportionally to their price). So applying to rates was already using it for something it was not meant to. And everybody knew it. A lot of people had developed normal models instead of lognormal models.
2. Black Scholes has been broken for years. Pricing with a volatility smile has been around since the 90s. It's a way bigger hack than what's needed to make black scholes work for rates.
3. If the problem is that R can go below 0, you can just model R+2%, and voila, you get a process that's never negative
4. The negative rates problem dates back to crisis, so of course people have already found ways to make it work.
Was it painful? Well it required tweaking the models for sure. But this is neither high-flying math nor out of "business-as-usual" activity.
The Black Scholes equation is a tad too complicated to say whether something like that will happen but it's too simple to just conclude everything breaks because of one complex logarithm.
There is no such assumption about positivity of the interest rate in BS.
The CIR model is broken yes because of the square root, and people started to use the old Vasicek model instead.
Nothing in the HJM framework forbids negative interest rates neither.
Edit: ah they meant model the IR directly with BS like SDE?
Its not "controversial". Its just that with negative rates, you can't take the log(interest rate) anymore, so the math literally breaks.
I don't think its a particularly difficult problem to solve, there are probably going to be a bunch of easy extensions to account for negative rates of the modern era.
edit: Actually took at look at the model. Looks like the issue is with a negative strike or current price, not the risk free rate.
Negative interest rates are wealth redistribution. Keeping money in account would cost more money, so instead, you are forced to lend it out to people who need it (presumably poorer) for less money in the future. Thus the rich who have lots of cash lose money and the poor, who need cash, can use their cash, start businesses, and have to do less work to make their business profitable, after paying back the loan
This will never happen.
So are positive interest rates, just in the opposite direction.
Yes. This is why venture capital is a thing, why it's so easy to get funding for a variety of businesses, and why hedge funds that have very modest returns are popular.
> If so, this would seem to be a pretty clear argument for wealth re-distribution in the name of poverty alleviation and reducing economic inefficiency.
Inflation is wealth redistribution. By reducing the real value of money, it benefits those who are engaged in economic activity and makes sitting on money a losing proposition.
Actual wealth redistribution is a bad idea because it reduces incentives to invest or engage in economic activity and encourages capital flight.
In other words, LTCMs collapse was the fault of the investors in LTCM, not the fault of the model. There are hundreds of hedge funds that have continued using the same basic model as LTCM, and have lasted through two recessions and several global financial shocks. They have achieved that by learning from LTCM: keep the model, dump the stupidly overleveraged investors.
Counterparties, on the other hand, very different story, if they didn't force LTCM'S hand, they would be stuck with an empty bag.
You're correct that many of LTCM trades did eventually work out positively. But when you're driving a car at 200 mph, a mundane pothole is deadly. When your hedge fund levered 30x, a temporary liquidity crisis is also fatal.
But that wasn't some incidental thing; it indicated that the core idea behind their arbitrage was flawed -- that there is a reason that the more liquid (US) bonds were consistently overpriced: to account for the fact that, during the occasional crisis, investors flee to them!
I know in 2002 Nomura Securities was using some extension of the SABR vol model to address it.
For this reason the model breaks down well before the rate actually becomes negative, and practitioners have had to worry about this for quite some time! Using a shifted lognormal model is a quick fix, as the article mention. Then you just need to pick a shift size...
Not an expert either.
I borrow $1000 and promise to pay back $1050. Lender now has a $1050 IOU which he will likely put into circulation (borrow against it, trade it etc.). Monetary supply just increased by $50.
The same can be stated about Markowitz portfolio optimization, a product of hype in the operations research space at the time. It obviously doesn't work because portfolio optimization isn't a simple convex optimization problem in the real world. Yet anyone who studies finance is forced to learn it and other empirically failed bullshit.
By that measure we'd better stop learning and teaching Newtonian gravity, too.
Way to find an example that supports my point.
A lot of financial models have never, ever worked in any sense when put to use in real markets.
It is completely different. These are mathematical models predicting the outcome of complex systems, not physical laws that are observable in every day life (even if the intuition can be wrong, only work above the subatomic level etc).
There's no "unifying theory" to uncover. A lot of the research is just plain garbage. Otherwise it would be easy to become wealthy through pure academic pursuit, wouldn't you agree? But markets don't work that way, and these theories can be easily tested and fail every time.
That is to say, he anticipated the force to be a function of the mass.
> Granted, the current state of affairs is more a nuisance than a serious problem.
What a poorly written article. Must be a slow financial news day.
As an analogy in high school physics they give you a problem like someone 2 meters tall shoots a gun and the bullet is moving so many meters per second, how far does the bullet go before it hits the ground. You use your formula for gravitational acceleration and figure it out, and Yeah! you get the right answer.
But you can't use this formula if you really want to calculate how far the bullet goes. You have to take into account air resistance and then you need differential equations and you probably need to approximate an answer with a PDE solver.
That's just the difference between a tool to explore foundational concepts and something that attempts to be actually be useful in the real world...