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Negative Rates Are Rewriting the Rules of Modern Finance (bloomberg.com)
185 points by megacorp 21 days ago | hide | past | web | favorite | 113 comments

Before Black-Scholes gets bashed too hard, people should keep in mind that it's nearly 50 years old. Of course it's going to be outdated and inaccurate (as all models are).

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...

Myron Scholes was heavily involved in LTCM, a hedge fund whose strategy was to apply statistical models to trading. It was one of the most spectacular business failures of the last few decades, losing $4.5 billion in value.


Losing $4.5B in value really understates the impact LTCM's failure had on the public markets.

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[1], which covers the development of Black-Scholes and the rise and fall of LTCM. Highly recommended.

[1] http://watchdocumentaries.com/trillion-dollar-bet/

In their defense, they were fine until they stopped paying attention to risk and correlated positions.

So this isn't a knock on the BS model necessarily, but human greed.

It's true that they were very profitable for several years, and then lost a ton of money at the end. Some of their worst losses were due to "style drift" into strategies that they were not experienced in, such as an unhedged bet on the Russian ruble before it was devalued. However, their core strategies involved exploiting very small profits with 25X leverage. Very few strategies can survive with that much leverage. Obviously a 4% decline in asset prices wipes you out, but in the case of LTCM it didn't take that large of a move. Since they were large and well-known when they started to lose money other traders figured out their positions and bet against their specific positions, knowing that LTCM would be forced to sell.

This is all from the excellent book "When Genius Failed."

“How did you go bankrupt?

Two ways. Gradually and then suddenly.”

Also true

>It was one of the most spectacular business failures of the last few decades, losing $4.5 billion in value.

How quaint. In 2019, tech companies burn through billions of dollars of capital every single year, and we call them business "successes".

But the government hasn't yet needed to bail out a VC, a Unicorn or a stockholder. Each may lose money, but that happens all the time.

In the case of LTCM the government needed to bail out LTCM positions. That is why it is different.

Although true, the money that the tech companies are burning through is probably related to the bail-out money that the trading firms are getting.

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.

That’s incorrect.

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.”

From https://www.thebalance.com/long-term-capital-crisis-3306240

While there’s lots to complain about this practice, those aren’t really the same thing. Tech firms are losing cash but generally gaining value towards an IPO. Whereas the investments were simply losing value.

> It was one of the most spectacular business failures of the last few decades, losing $4.5 billion in value.

> 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.

There’s an excellent book called “An Engine, Not a Camera: How Financial Models Shape Markets” that lives up to its title.

>Before Black-Scholes gets bashed too hard, people should keep in mind that it's nearly 50 years old. Of course it's going to be outdated and inaccurate (as all models are).

But the part about money having a positive time value shouldn't be. That indicates a major problem in the system.

Even more modern models like SABR got broken by negative rates and the quants adjusted in the same way, they just shifted it.

I worked in an investment bank (Barclays Capital) in 2008, and at the time we were already developing models which could handle negative interest rates. The idea that this is somehow a new problem that has "broken the pillars of modern finance" is bizarre.

The vanilla European swaptions market has always quoted wrt the Black model. If you strip out the hyperbole, I think this article is suggesting that they're looking for a cheap and cheerful model that accepts negative forwards.

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.

As the article states, this is more about getting two people to agree on the price of illiquid derivatives

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

That's a good way to put it. As my economics professors liked to point out, Black-Scholes was a self-fulfilling prophecy in that the success of the model was determined by the fact that everyone was using it (or some variation of it) to price derivatives.

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.

> If it had never been published would it still have been as accurate? Who knows.

I think if prices didn’t follow the model, there will be arbitrage opportunities either in the options or the underlying.

One of the key problems with HW was that rates could go negative, and quite negative -- this was considered in 01/02 if not before.

I think the argument is funny:

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 no wonder interest (usury) is banned in Judaism, Christianity, and Islam. It's absolutely at the root of the financial problems we're seeing today.

Judaism has a mitzvot to lend to gentiles with interest (mandatory)

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

What are the reasonable alternatives? In terms of business investment I mean, personal loans are a whole other problem.

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.

Alternatives include engaging in a partnership (basically investment). Someone wants to start a business, they gather interest from investors who put in money for a share of the business. The founder contributes effort (and perhaps some money), and the investors contribute money. If the business succeeds, great, everyone wins. If it doesn't, the founder(s) are not stuck with debt + interest to pay back.

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).

You misunderstood the meaning of my post. Whats funny is the idea that you could somehow "create" money out of nothing by simply printing it, then attempt to balance its value by creating incentives for people to use. The part I think is funny, is that the people that have the prerogative to lend out the recently printed money, don't have to take the same risk as the people who have borrow it to create value. The "unfair" part is the part where money is printed, and given away for "free" to "investors" who don't "deserve" it, but make the argument that without them, the system will collapse because market valuations have been distorted for so long that only prolonged distortion can stabilize it.

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".

Usury is not interest in general, but rather, unreasonably high interest

Zippy Catholic has a FAQ on this : https://zippycatholic.wordpress.com/2014/11/10/usury-faq-or-...

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.

Modern day Christianity strayed from the early teachings. If I'm not mistaken even during Shakespeare's time, money lenders were loathed (because of them charging interest), and it was prohibited then.

Not in the context of Abrahamic religions.

Strange then that so many millions of Christians and Jews worldwide engage in money lending and borrowing.

People also use profanity, work on their rest days, drink alcohol, eat pork and shellfish, covet other people's things, and do lots of other things they're not supposed to according to their religion.

People do lots of things that they acknowledge are against their religion. However I’ve never heard a Christian (or Jew for that matter) tell me that their religion prohibits lending or that it’s a sin. It’s not that they simply do it anyway, but that they aren’t even supposed to avoid it. In this respect it seems that lending isn’t like consuming pork for Jews but like drinking caffeine for Christians.

It could simply be that they are not aware that it's prohibited. If you look up early Christianity, they definitely loathed money lending due to interest.

If you look at modern Christianity, they don’t. You cannot hold a religion to an outdated set of beliefs they do not hold themselves to.

There are Christians today that still uphold the rules in the Old Testament (e.g. not eating pork), as early Christianity still followed Judaic law before straying away from those teachings.

Borrowing if you have no choice, and lending if you know it's wrong (according to your religion) are two different things. Many people participate in the shit system they find themselves, without trying to make the system worse. I'd say this doesn't just apply to interest, but all sorts of things. Climate activists acknowledge that plastic and consumerism are bad for the planet, and yet the vast majority continue to purchase and use products that rely on pollution, single use plastic, and resource waste.

It just means they're not following the teachings of their respective religion.

Or they don’t believe that those are teachings of their religions. You don’t get to define what other religions should hold themselves to, even if they did in the past.

You read their original teachings and see what they said. It's clear that there was deviation from them. This is acknowledged by those who studied the subject well.

You don’t get to define what other religions should hold themselves to, even if they did in the past.

I'm referring to charging money on money, at any rate no matter how small. There is no difference.

Sounds like they are doing everything they can to not do the helicopter drops they should probably be doing.

When I first got into finance, it was working for a professor who'd come up with one of, if not the first, reasonably good fixed income option model. Our original implementation allowed for negative interest rates since as he put it, they're not unheard of (this was in the 1980s, so long term interest rates in the US were well over 10% at the time). Everywhere we demo'd the model, practitioners complained that you can't have negative interest rates, so our next iteration got rid of them. Interesting times.

I used to trade all the instruments mentioned in the article.

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.

> you'd tend to call some counterparties and hear what they thought of how to value things

They might well tell you how they think you should value things ...

Traders want deal flow. They also need to trust counter-parties. It really isn't in anyone's interest to have a market participant who mis-prices everything, because they won't be able to both buy and sell (and they will likely soon be out of work). Even pretty dumb traders will quickly realize when it's me, it's not everybody else, whose model is wrong.

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.

Yes of course. But you have more than one counterparty. And not everything is a thing you're currently considering to trade. You might well use them to calibrate.

I'm no financial expert, but based on discussions with them years back, it seems like Black-Scholes has all sorts of issues and isn't actually used in practice anyway.

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).

People ~5 years ago were certainly using Black Scholes where I worked, just with a lot of caveats. The volatility smile you describe only really applies to out-of-the-money puts - people trading with black scholes as a signal will look at the at-the-money strikes.

At the end of the day, excepting edge cases, the spread on most listed equity options absorbs any difference between model pricing.

it is used everywhere as the foundation, all the more recent models (stochastic vol/Heston, Local volatility, SABR, SLV, SVI etc) are just incremental extensions and generalization of Black-Scholes

At its core, Black Scholes is a set of "obvious" differential equations.

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.

> At its core, Black Scholes is a set of "obvious" differential equations.

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.

Isn't Black-Scholes based on a normal distribution? Is that an appropriate probability distribution?

Additionally, Black-Scholes does not account for the possibility of early exercise in American options (versus European options, which it was designed for)

More like Black-Scholes fails to account for dividends, which is the only reason why you'd want to exercise early.

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.

> Its always better to hold onto the option of buying a stock

Tax laws change that equation significantly.

It is used for quoting between market participants. People may use more complex models for the underlying pricing and risking, but they will quote option prices in black/black-scholes format as an implied vol.

This is an ill-informed vulgarisation article.

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.

It's a bit weird to just throw up your hands just because you need to take a logarithm of a negative number. Plugging ina negative number might cause the solution to become complex but as far as I can tell it should remain a solution of the corresponding differential equation. So either the partial differential equation has no real solutions or the complex part cancels out or can be removed. Some information seems to be missing to truly determine Black Scholes to be broken.

I wonder how you transfer a complex amount of cash through the banking system...

Well, to illustrate my point the differential equation f'(x) = 1/x has the solution log(x) for positive x. If you let x become negative then that particular solution ends up becoming complex, however there is still a real solution namely log(-x) (which only differs by a constant).

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.

Presumably the cash amplitude can be taken as positive.

I don’t understand why the Black Scholes model is broken for negative interest rates.

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?

Most of the criticisms regarding Black-Scholes that I've seen has to do with the assumption that the probability distribution of future prices is a normal distribution. I didn't think using the risk free to account for the time value of money was that controversial. Have there been suggestions on alternative ways to factor in the time value of money?

> I didn't think using the risk free to account for the time value of money was that controversial.

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.

Gotcha, the "short cut" doesn't work any more.

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.

For people asking why is there even such a thing as negative interest rate (lend $100, get back $99), NPR Planet Money has a good explainer. TL;DR: There's a lot of cash in search of investment. While waiting for opportunity, you could stash it under the mattress. But that's not safe, you'd probably have to buy a safe, hire some guards. Also it's not very liquid. So you pay a bank to hold it for you, put it in their safe, use their transfer system, etc. Tah-dah: negative interest rate.


In another sense, doesn’t the existence of long-term negative interest rates suggest that some people/institutions have more money than they can productively use? 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.

In a sense, that is precisely what low/negative rates do. If cash-holders' future purchasing power is diminished, it effectively redistributes future purchasing power to those earning money and making things now and in the future.

In theory. In reality low income people do not have access to loans and therefore no access to low interest rates.

> If so, this would seem to be a pretty clear argument for wealth re-distribution

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

> you are forced to lend it out to people who need it (presumably poorer) for less money in the future

This will never happen.

Um what? Negatvie interest rates already exist in some european countries and exactly this is happening.

It will never be lent out to poor people.

It will be lent out to people who can pay. If poor people can't then they won't, but I mean, it will be lent out to people less rich than the ones lending. That may mean middle class too. Still transfers from upper to middle are indeed wealth redistribution.

> Negative interest rates are wealth redistribution.

So are positive interest rates, just in the opposite direction.

Sure, but the commenter was asking if negative interest rates indicated that we need wealth redistribution from rich to poor. Also, in the recent past, we have had a negative 'real' interest rate. You'd be hard-pressed to find funds paying more than inflation on your cash.

> In another sense, doesn’t the existence of long-term negative interest rates suggest that some people/institutions have more money than they can productively use?

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.

What you wrote might be true for warehousing physical gold but not for (mostly digital) fiat money because the cost of digitally storing $1 and $10,000 is the same.

according to nicholas Taleb, Black-Scholes was always broken. I tend to believe him based on results achieved by Scholes https://en.wikipedia.org/wiki/Long-Term_Capital_Management

Taleb's funds aren't any more impressive.. LTCM blew up very publicly but Empirica shut down after many years of losses and Universa isn't exactly a high performer. He's still out there banging the drum about hyperinflation!

Just wait until the paleo/deadlift bubble pops, he’ll be wiped out completely.

But LTCM wasn't based on options trading, its main strategy (the one that failed) was arbitrage of bonds with different maturity dates: https://en.wikipedia.org/wiki/Long-Term_Capital_Management#F... That hasn't got much to do with Black-Scholes

LTCM cracks me up because it should have been obvious that linking a massively liquid market with a not very liquid market was going to be trouble. IIRC when the crisis came it turned out there were only three or four buyers on the tight side, and when they sat on the sidelines it was game over for LCTM.

You should take a closer look at what actually happened to LTCM. Their model remained profitable even after the crash, and recovered value far quicker than other hedge funds did. The real cause of the systemic failure had more to do with the actions of investors than the fundamentals of the model. The investors were heavily overleveraged across the board, and when they started losing money elsewhere, they initiated a flight to liquidity within LTCM. The flight to liquidity caused them to liquidate positions before they converged, compounding losses. Those positions for the most part actually did converge, but were prematurely exited. Had those investors not liquidated, they would have continued making strong returns.

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.

Not true. LTCM had some of the most restrictive covenants among similar funds. Minimum lockup of at least 2 years, and redemption notice of 3 or 6 months (hey its been 20 years) - in other words, if you wanted to redeem, you had to give multiple month notice. The investors had no way of forcing LTCM to liquidate any holdings in a panic, in fact the covenants were to protect against that exact scenario, so the firm could ride out their positions.

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.

I don't think that's right, at least this is not the way I learned it: the terms on which you borrow money to fund your investments should be considered a part of the model. So if you borrow short term and invest long term, your model itself now includes maturity transformation, and it can blow up just like any such model. Sure you can then construct a different model that's basically the same but without the maturity transformation, and that's okay, you'll get different returns. Thinking about it this way I think it's still fair to blame LTCM, their investors were free to do whatever their contract allowed them to do.

That's true, and very important. And while I think (or, at least, I hope) large investors keep that in mind after so many high profile explosions like LTCM, I think small time retail investors tend to forget that, and that there's a reason Vanguard (for example) suggests 70% stocks and 30% bonds. Doesn't seem too important, until you need the money...

>The flight to liquidity caused them to liquidate positions before they converged, compounding losses.

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!

This fact is luckily slowly leaking into higher education of finance, and is preventing hundreds of poor finance students from attempting to reinvent the wheel.

Also, options were priced (and this price agreed upon both parties) long before the formula. So, the formula is just a technical so to say after-the-fact explanation of the pricing. Interesting as a technical tool, but not mind-shattering per se.

Japanese rates have been negative or near zero a number of times over the past 20+ years. This is not a new problem.

I know in 2002 Nomura Securities was using some extension of the SABR vol model to address it.

Even when today's rates are positive the black-76 model doesn't price in the possibility that rates will become be negative in the future.

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...

Aren't negative interest rates deflationary by design? When an entity already in debt borrows money at negative interest rates the debt will keep shrinking, thus destroying monetary supply.

The negative interest rates discourages holding money and encourages spending (and investment), which drives inflation. I do not believe negative interest rates destroy money, but I am not an expert. I cannot find any literature to prove or dispute that.

You're right, it does encourage spending and investment. However a part of the money does eventually go into negative interest rate assets (due to regulations etc.) and I believe that shrinks the money supply.

Not an expert either.

You get $1000. You pay back $950. The monetary supply increased by $50.

Uhm... no.

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.

Which financial model actually works in the real world? A lot of what is studied seems to be nonsense from more than 60 years ago, because computers and algorithmic thinking started to come into vogue in economics research.

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.

> 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.

Huh? That's a terrible example, gravity is easily observable here on Earth, hence why the theory was formulated using empirical experiments.

Way to find an example that supports my point.

Newtonian gravity is empirically wrong. sigh

That's not the same. It has held up quite well, wouldn't you agree?

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.

Nope. If you take the time to read Newton, you will discover he never wrote F=ma. His formula was equivalent to F=dmv/dt.

That is to say, he anticipated the force to be a function of the mass.

Newtonian gravity put men on the moon.

> Negative interest rates have quite literally broken one of the pillars of modern finance.


> 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.

Black Scholes isn't a bad approximation for pricing short term call options that are either in-the-money or not too badly out of it. For anything else, the assumptions that go into it mean that it's wildly inappropriate. It needs to go away, and if this is the final nail in the coffin, then that's a good thing.

Maybe I agree if by go away you mean don't really use it for pricing derivatives for real. However it's still a very useful intellectual tool to understand how to generate a price for a very simple derivative.

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...

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