
Negative Rates Are Rewriting the Rules of Modern Finance - megacorp
https://www.bloomberg.com/news/articles/2019-09-30/how-negative-rates-broke-black-scholes-pillar-of-modern-finance
======
loganfrederick
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 Of course it's going to be outdated and inaccurate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...](https://www.amazon.com/Fischer-Black-Revolutionary-Idea-
Finance/dp/0471457329/)

Ed Thorp: [https://www.amazon.com/Man-All-Markets-Street-
Dealer/dp/0812...](https://www.amazon.com/Man-All-Markets-Street-
Dealer/dp/0812979907/)

~~~
camjohnson26
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.

[https://en.m.wikipedia.org/wiki/Long-
Term_Capital_Management](https://en.m.wikipedia.org/wiki/Long-
Term_Capital_Management)

~~~
navigatesol
> _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".

~~~
georgeecollins
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.

~~~
roenxi
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.

------
avvt4avaw
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.

~~~
rolltiide
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

~~~
frausto
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.

~~~
alfiedotwtf
> 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.

------
zarro
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.

~~~
apta
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.

~~~
adeelk93
Usury is not interest in general, but rather, unreasonably high interest

~~~
simula67
Zippy Catholic has a FAQ on this :
[https://zippycatholic.wordpress.com/2014/11/10/usury-faq-
or-...](https://zippycatholic.wordpress.com/2014/11/10/usury-faq-or-money-on-
the-pill/)

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.

~~~
apta
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.

------
bwanab
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.

------
lordnacho
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.

~~~
twic
> 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 ...

~~~
listenallyall
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.

------
dragontamer
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).

~~~
bra-ket
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

~~~
dragontamer
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.

~~~
Xcelerate
> 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.

------
d--b
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.

------
contravariant
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.

~~~
cm2187
I wonder how you transfer a complex amount of cash through the banking
system...

~~~
contravariant
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.

------
rq1
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?

------
choiway
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?

~~~
dragontamer
> 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.

~~~
choiway
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.

------
devchix
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.

[https://www.npr.org/2019/09/20/762748958/episode-940-interes...](https://www.npr.org/2019/09/20/762748958/episode-940-interest-
rates-why-so-negative)

~~~
selimnairb
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.

~~~
tathougies
> 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

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

This will never happen.

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

~~~
cheez
It will never be lent out to poor people.

~~~
tathougies
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.

------
ptah
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](https://en.wikipedia.org/wiki/Long-
Term_Capital_Management)

~~~
darksaints
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.

~~~
conistonwater
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.

~~~
owenversteeg
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...

------
JackFr
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.

------
fancyfredbot
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...

------
neonate
[https://outline.com/ZNWx2n](https://outline.com/ZNWx2n)

------
samsonradu
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.

~~~
Litmus2336
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.

~~~
samsonradu
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.

------
codesushi42
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.

~~~
pixelpoet
> 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.

~~~
codesushi42
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.

~~~
pixelpoet
Newtonian gravity is empirically wrong. _sigh_

~~~
codesushi42
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.

------
munificent
_> 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.

------
joker3
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.

~~~
rdm70
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...

