James Purchase and Nick Constantine.

In 1995, Fischer Black, an economist whose ground-breaking work in financial theory helped revolutionise options trading, confidently stated that “the nominal short rate cannot be negative.” Twenty years later this assumption looks questionable: one quarter of world GDP now comes from countries with negative central bank policy rates. Practitioners have been forced to update their models accordingly, in many cases introducing greater complexity. But this shift is not just academic. Models allowing for a wider distribution of future rates require market participants to hedge against greater uncertainty. We argue that this hedging contributed to the volatility in global rates in early 2015, but that derivatives can also play an important role in facilitating monetary policy transmission at negative rates.

A brief history of negative rates

Negative nominal interest rates are not new phenomena. As early as the 19th century, economists discussed imposing taxes on money (e.g. Gesell’s tax), and in the 1970s the Swiss National Bank experimented with negative rates to curb capital inflows in a bid to prevent the Swiss Franc appreciating. But in recent years, an unprecedented number of central banks have adopted negative policy rates (Chart 1). We discuss the drivers of long-term rates and volatility (Chart 2) later on.

The trend towards negative rates follows a decade of significant growth in financial derivatives. According to the BIS, the total notional outstanding of global FX, interest rate and equity-linked derivatives rose from $72 trillion in 1998, to $522.9 trillion in 2015. The vast majority (nearly 80%) are interest rate derivatives whose theoretical underpinnings are often predicated on the assumption that risk-free rates are bounded at zero. These baked-in assumptions have made it more complicated for financial markets to adjust to life below 0%, particularly where derivatives were priced and risk-managed as if negative rates were not possible.

Chart 1: International central bank policy rates*

Source: Bloomberg

*The policy rates are as follows: Sweden, Switzerland and Eurozone (deposit rates), Denmark (CD rate), Japan (balance rate, introduced in 2011).

Chart 2: 10-year European swap rate and implied volatility*

Source: Bloomberg

*10-year rate normalised implied volatility from 3-month swaption.

Shaded area (from July 2014 to July 2015) highlights the fall in rates and subsequent sharp reversal along with a spike in implied volatility.

Model shift

In the world of derivatives, the industry standard model to price options on interest rates (the ‘SABR’ model) relies on an assumed distribution of possible rates. Traditionally, this distribution is lognormal, meaning rates do not go below zero. The simplest way to adapt the model to allow for negative rates is to ‘shift’ the distribution of rates lower, such that the lower bound is no longer zero, but somewhere between say -1% and -3%. Chart 3 below illustrates a stylised shift.

But this ad hoc approach has side effects: ‘shifting’ SABR mechanically changes the shape of the entire distribution, including the portion above 0%, in potentially unrealistic ways. More advanced, proprietary approaches attempt to marry together a world of sustained negative rates with the world of positive rates, and include a ‘stickiness’ around 0% based on the Swiss experience where market rates hovered around 0% for a time before falling below it. A highly stylised version of this distribution is shown in Chart 4. These kinds of changes have been necessary for banks to price and hedge options on negative rates. But they come at the cost of increased complexity and model risk.

Chart 3: normal (red), lognormal (blue), and 150bps-shifted lognormal (dash blue) PDFs.

Source: Bank calculations.

Chart 4: the same shifted-lognormal PDF, with a stylised “sticky” SABR model PDF (green).

Source: Bank calculations.

Systems and legal issues

As well as pricing issues, negative rates have had a number of other disruptive effects. As noted in the WSJ, computer systems from “Spain to Sweden” have struggled to cope with negative rates. There has also been uncertainty around the legal agreements that cover interest rate swap collateralisation.

Hedging impact

The shift in modelling assumptions described above has real world implications. After the ECB implemented negative interest rates in early 2015, banks set out to update their option pricing models by relaxing the assumption that rates could not be negative. Dropping this assumption implied that the distribution of potential interest rates was considerably wider than previously thought (e.g. anything from -1% to 3%, rather than 0-3%). Models incorporating distributions with non-zero probabilities assigned to negative rates imply greater uncertainty. And this uncertainty had to be hedged.

Hedging of so-called ‘exotic’ derivatives, also known as structured notes, compounded the problem. These included derivatives sold to investors searching for higher returns in an otherwise low yield environment. In particular, some structured notes, such as ‘Constant Maturity Swap’ (CMS) linked notes were designed such that the buyer would not be required to pay the issuer if the floating coupon falls below zero. This risk was typically held by banks, and according to our contacts, many sought to hedge their unintended and growing exposures to negative rates.

The obvious hedge was to protect oneself against lower rates and higher volatility, for instance by buying bonds, entering interest rate swap contracts, and buying options. However the process of hedging likely amplified the fall in yields, as greater demand resulted in higher bond prices and increased volatility. Chart 2 shows the 10-year European swap rate and the expected volatility of the 10-year swap rate implied by 3-month options. The fall in rates in Q1 2015, and the subsequent spike in volatility occur during the same period that banks were reportedly undertaking changes to modelling assumptions.

FRNs and the monetary policy transmission mechanism

The prevalence of financial instruments with floors at 0% has been a complicating factor in the markets’ transition to negative rates. Floating rate notes (FRNs) are a good example. A buyer of an FRN receives a coupon that varies with interest rates. So what happens when rates become negative? Do negative coupons mean the investor has to pay the debtor? In practice, no. Legal and operational practicalities have meant FRN coupons are effectively floored at 0%.

This 0% floor is important. As noted by Ippolito, et al (2016), FRNs are a significant channel through which the monetary policy transmission mechanism works. But companies must contend with the prospect of having the cost of their FRN liabilities floored at 0%, whilst seeing returns on investible assets fall below zero. This means that rate cuts may not be fully passed on to debt issuers in terms of lowered funding costs. In an extreme case, it could even raise systemic concerns around bank business model viability, with net interest margins already compressed by the low rate environment.

At present, €350bn of euro-denominated FRNs referencing Euribor (28% of total outstanding) are affected by this 0% floor. If Euribor falls by a further 25bps, we estimate that around half of all EUR FRNs would be affected (~€670bn).

Market participants have begun to adapt to negative rates by issuing new FRNs paying elevated coupons, but asking investors to pay more upfront (at a so-called ‘premium to par’). But it is unclear whether this is a panacea. And in any case, there are €1.5 trillion in outstanding FRNs with a weighted-average maturity of around 4.5 years.

A solution to the problems with existing debt may lie in the derivatives market. Market contacts report growing demand in recent months by banks and other companies to hedge their FRN liabilities with interest rate options (which as discussed above now account for negative rates). In this way, financial derivatives perform a useful function in facilitating the pass-through of monetary policy at negative rates. But we should be mindful of the risks that greater use of certain derivatives pose to the financial system – for instance, as noted by Liu et al (2015), greater inter-bank connectedness means that shocks tend to transmit more rapidly across the financial system.

Conclusions

The increasingly widespread adoption of negative policy rates by central banks has led to a shift in the assumptions used to model interest rate derivatives. Market participants attribute the amplified interest rate volatility in 2015 to pro-cyclical hedging flows arising from this model shift.

The pass-through of negative rates, and therefore the effectiveness of monetary policy at increasingly negative rates, may be constrained by 0% floors embedded in a variety of debt instruments. Specifically, FRN issuers’ funding costs may not be able to fall lower than zero. In an extreme case, there could be financial stability implications, if concerns around bank net interest margin compression and business model sustainability become systemic. But the market has already begun to adapt: new FRNs are being issued above par with elevated coupons to avoid negative rates, and issuers are making greater use of derivatives to hedge outstanding FRNs.

James Purchase and Nick Constantine works in the Bank’s Foreign Exchange Division.

If you want to get in touch, please email us at bankunderground@bankofengland.co.uk. You are also welcome to leave a comment below. Comments are moderated and will not appear until they have been approved.

Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.