Across-the-Curve Credit Spread Index (AXI)

• AXI is a credit-sensitive index derived from observable unsecured funding transactions across maturities from overnight to 5 years.
• The index is constructed by aggregating dollar-volume-weighted median spreads with a 21-business-day average to smooth daily volatility.
• AXI restores the credit sensitivity lost in SOFR by adding a risk premium, and empirical results highlight its strong linkages with market stress and macro variables.

The Across-the-Curve Credit Spread Index (AXI) is a daily measure of the marginal unsecured wholesale funding cost of U.S. banks over a risk-free base rate. It is presented as a transparent, transaction-based measure of wholesale bank funding costs that is IOSCO-aligned and operationally compatible with SOFR-based infrastructure. In the post-LIBOR setting, AXI is designed not as a replacement for SOFR but as a credit spread that can be added to SOFR in order to restore the credit sensitivity that LIBOR embedded through unsecured bank funding (Tsyrennikov, 3 Sep 2025).

1. Definition and post-LIBOR rationale

AXI is defined as a credit-sensitive benchmark component rather than as a standalone reference rate. The intended contract form is

$$\text{credit-sensitive rate} = \text{reference rate} + \text{fixed spread} + c \cdot \text{AXI},$$

with $c \in [0,1]$. In the paper’s notation, $c=0$ corresponds to a pure SOFR-style rate with no credit sensitivity, $c=1$ corresponds to full credit sensitivity, i.e. SOFR + AXI, and intermediate values correspond to partial credit sensitivity. The recommended structure is therefore

$$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$

This formulation is central to the paper’s treatment of AXI: it is a credit-sensitive “add-on” to SOFR rather than a substitute for SOFR (Tsyrennikov, 3 Sep 2025).

The economic motivation is the loss of credit sensitivity in the LIBOR transition. LIBOR was linked to unsecured interbank funding and therefore embedded bank credit risk. SOFR is robust and transaction-based, but it is nearly risk-free and therefore does not capture banks’ marginal term funding costs. The paper argues that this matters particularly for lenders that fund themselves with unsecured wholesale debt and that face draw-sensitive revolving credit lines. If a lender’s own funding costs rise during stress, a benchmark that rises as well can help preserve net interest margin and reduce incentives for borrowers to draw heavily on revolving credit lines.

A common misconception is that AXI is meant to recreate LIBOR directly. The paper’s position is narrower: AXI is meant to restore a funding-risk-sensitive component while avoiding reliance on thin short-term markets. This suggests that the relevant comparison is not “AXI versus SOFR,” but rather “SOFR alone versus SOFR plus a credit-sensitive spread.”

2. Construction from observable unsecured funding transactions

AXI is built from observable unsecured wholesale funding transactions across both short- and long-term maturities. The transaction set includes certificates of deposit (CDs), commercial paper, wholesale term deposits, interbank loans, and, for longer maturities, corporate bonds and notes issued by banks. The key distinguishing feature is that the index spans short- and long-term maturities, from overnight to 5 years (Tsyrennikov, 3 Sep 2025).

Component	Specification
Short-term bucket	$0$–$1$ year
Long-term buckets	$1$–$2$, $2$–$c \in [0,1]$0, $c \in [0,1]$1–$c \in [0,1]$2, $c \in [0,1]$3–$c \in [0,1]$4 years
Transaction types	CDs, commercial paper, wholesale term deposits, interbank loans, bank bonds and notes

For a given maturity bucket $c \in [0,1]$5, the paper uses a dollar-volume-weighted median spread. The short-term spread is the $c \in [0,1]$6–$c \in [0,1]$7-year bucket. The long-term spread is the volume-weighted average of the median spreads across the four long-term buckets. Daily aggregation then uses maturity-weighted dollar volume so that longer maturity and larger volume both receive more weight. For day $c \in [0,1]$8, the weights are

$c \in [0,1]$9

and

$c=0$0

The daily spread is then

$c=0$1

AXI itself is a 21-business-day average of these daily spreads:

$c=0$2

The paper states that this smoothing makes AXI more stable and operationally comparable to common SOFR averaging conventions; it also notes that 21-business-day averaging is numerically similar to a 30-calendar-day average.

The “across-the-curve” property is not cosmetic. The paper argues that U.S. banks fund themselves much less with short-term unsecured borrowing than in the LIBOR era and more often term out funding through bonds and notes. In the sample, the long-term share is always significant and above 36%, while the long-term and short-term maturity-weighted volumes are only weakly correlated, at about 0.076. The paper further emphasizes that the effective tenor of AXI lengthens in stress periods, because long-term issuance becomes more important when conditions tighten.

3. Relation to SOFR, LIBOR, and the fallback index FXI

AXI is paired with SOFR precisely because the two components supply different information. SOFR contributes a robust nearly risk-free base, while AXI supplies the unsecured-bank-credit component. This division of labor is explicit in the proposed pricing structure. The paper reports that over the sample SOFR + AXI is always above LIBOR, with an average basis of about 0.37%. It also states that

$c=0$3

and that with $c=0$4, the average spread between SOFR + $c=0$5AXI and LIBOR is approximately -0.01%. The correlation between daily changes in SOFR+AXI and LIBOR is reported as 0.133, rising to 0.878 quarterly (Tsyrennikov, 3 Sep 2025).

The paper also introduces the Financial Conditions Credit Spread Index (FXI) as a broader-market companion and fallback for AXI. FXI measures the marginal cost of unsecured wholesale debt funding faced by U.S. institutions more broadly and uses the same basic methodology and filters as AXI, but with a larger transaction pool. The stated implications are that FXI is more statistically robust, is a natural fallback benchmark if AXI becomes unavailable, and is more suited for broader derivatives or macro use.

FXI generally runs above AXI except during bank-specific stress. The paper treats divergence between the two as informative: if AXI rises more than FXI, the stress is more bank-specific; if both rise together, stress is spilling into the broader economy. The full-sample correlation of daily changes is reported as

$c=0$6

During stress episodes, co-movement strengthens further: 93.6% during the COVID onset (March 1–June 30, 2020) and 80.0% during the SVB episode (March 1–June 30, 2023).

4. Empirical relationships with credit, stress, and macro variables

The paper reports that AXI behaves like a credit-spread measure rather than merely a funding-market statistic. It is positively related to standard credit-spread measures and market-stress indicators, and negatively related to financial-sector performance. The reported lag structure is also notable: the strongest correlations occur when other indicators lead AXI by about one week, which the paper interprets as evidence that AXI is reflecting funding conditions that respond quickly to market stress (Tsyrennikov, 3 Sep 2025).

Variable	Reported relationship with AXI
Markit North American IG credit index	Positive lagged correlation around $c=0$7
Bloomberg FRN OAS	$c=0$8 at a one-week lag
Bloomberg U.S. corporate OAS	$c=0$9 at a one-week lag
LIBOR-OIS spread	$c=1$0 at a one-week lag
TED spread	$c=1$1 at a one-week lag
NFCI	$c=1$2 at a one-week lag
Credit market distress index	$c=1$3 at a one-week lag
EPU	About $c=1$4 at a one-week lag
VIX	About $c=1$5 at a one-week lag
XLF	About $c=1$6 at a one-week lag

These relationships are described as economically meaningful but not perfect. The paper reads this as evidence that AXI captures bank-funding-specific conditions rather than merely replicating broad-market credit spreads. With respect to macroeconomic variables, the paper compares SOFR+AXI and LIBOR against DFAST macro variables. The strongest positive correlations for SOFR+AXI are with the Prime rate at 0.913 and the 3-month Treasury bill at 0.881. Moderate positive correlations are reported for the BBB spread at 0.406 and the Mortgage rate at 0.403. SOFR+AXI is reported as negatively correlated with CPI inflation at -0.363, while correlations with GDP growth, unemployment, housing prices, and equity performance are described as weaker and mostly insignificant.

The paper also reports Granger-causality-style evidence: several drivers Granger-cause changes in AXI at the 99% confidence level, while there is no evidence of reverse causality from AXI to those drivers. This is used to support the view that AXI responds to financial conditions rather than generating them.

5. Stress episodes and the significance of the long end of the curve

The paper emphasizes two episodes: the COVID-19 onset and the Silicon Valley Bank collapse. Both are used to illustrate why a benchmark confined to short-term unsecured borrowing may fail to track banks’ marginal funding conditions in stress (Tsyrennikov, 3 Sep 2025).

At the onset of the pandemic, AXI’s long-term component rose from about 0.4% to 3.9%. The paper states that long-term funding became much more important while revolving credit lines were drawn heavily. It further reports that C&I loan balances increased by about \$c=1$7738 billion above pre-stress levels eight weeks later. In the paper’s interpretation, this demonstrates why a credit-sensitive benchmark matters: if loans had been priced only off SOFR, their yields would not have risen in step with funding costs.

During the SVB crisis, the reported pattern again favored the long end. Banks increased cash positions and borrowed from emergency facilities, but they also probed longer-term fixed-income funding markets. AXI’s long-term transaction volume rose sharply on the first two business days after the collapse, by factors of 2.8x and 4.8x relative to the prior 21-business-day average, while short-term volume fell by 20% and 30%. The paper presents this as direct evidence that AXI responds to bank-funding stress in a way that a short-term-only benchmark would not.

A plausible implication is that AXI’s construction embeds not only a level effect but also a state-dependent maturity-composition effect. The paper itself states this operationally by noting that AXI’s effective tenor lengthens in stress periods.

6. Loan-pricing implications and related term-structure research

The paper’s loan-pricing argument is that a lender indexing loans to SOFR + AXI bears less funding risk than a lender indexing only to SOFR. Because part of the lender’s funding-cost risk is already embedded in the benchmark, the fixed spread can be reduced while maintaining the same expected risk-adjusted return. Using sample calibration from June 2016 to April 2025, the paper reports

• $c=1$8
• $c=1$9
• $\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$0
• $\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$1

Under these assumptions, and with an initial SOFR-only fixed spread of 1%, the bank can reduce the contractual spread substantially when switching to SOFR+AXI. The paper reports spread reductions up to 65 basis points. At an estimated optimal credit sensitivity of $\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$2</strong>, the fixed spread can be cut by about <strong>48 basis points</strong>, from <strong>100 bps</strong> to roughly <strong>52 bps</strong>. It also notes that, using a price elasticity of <strong>25</strong> from cited literature, a <strong>48 bp</strong> reduction would increase demand by about <strong>12%</strong> (<a href="/papers/2509.03035" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Tsyrennikov, 3 Sep 2025</a>).</p> <p>The paper further compares a \$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$3370 billion*<em>, this would have meant about *</em>\$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$418.5 billion** in total bank profit in Q1 2020, that is about <strong>2.7$$6.471 billion, or roughly 34% of total banking profit in that quarter. A specific warning is that in stress, a bank relying on SOFR-only pricing can fail to recover as much as 15 basis points on revolving credit lines over as little as three months.

A related but distinct line of research appears in "Bayesian Estimation of Corporate Default Spreads" (Papenkov et al., 4 Mar 2025). That paper does not build an AXI as a standalone cross-sectional index in the sense of aggregating many issuer spreads into a market index. Instead, it develops the core machinery needed to construct one by estimating an issuer-specific default spread curve / credit spread term structure from daily corporate bond prices using a Bayesian Vasicek exponential-spline yield-curve model. It defines the corporate spread curve as

$$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$5

with

$$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$6

and derives

$$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$7

It also gives an aggregate horizon measure,

$$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$8

That work uses daily TRACE corporate bond prices, FISD issue characteristics, and Treasury yields; limits the sample to vanilla, senior, fixed-coupon, nonconvertible, non-optioned, on-the-run bonds; and employs a Normal-Inverse-Gamma Bayesian regression framework to obtain posterior means and credible intervals for spread curves. The paper’s own synthesis describes it as yielding the closest analogue to an AXI in the form of an across-the-curve spread term structure $$\text{SOFR} + c \cdot \text{AXI} + \text{fixed spread}.$$9 across maturities. This suggests a methodological precursor: issuer-level term-structure estimation for corporate default spreads and bank-level transaction aggregation for unsecured wholesale funding spreads address different objects, but both center the credit signal in the full maturity profile rather than in a single short-dated point estimate.