Synthetic Basis Spread Calculation for Short-term Cross-currency Swaps

For cross-currency basis spread curves, there are usually no quotes available below 1Y time point (for 3M and 6M) and there might be a need to implement the appropriate calculation methodology for the missing data. This post will explain one possible calculation methodology based on Covered Interest Parity and presents the most relevant test results for this applied methodology.

Methodology

We will use adjusted version of traditional Covered Interest Rate Parity (CIP) for calculating synthetic quotes for short-term cross-currency basis spreads. First, in the absence of any arbitrage opportunities, CIP is assuming that the following parity will hold:



Assuming EUR/USD currency pair, we may consider the following two separate investment strategies:

1. Converting EUR amount to USD by using FX spot rate, then investing received USD amount by using USD interest rate for a given period and finally, converting resulting USD amount back to EUR by using FX forward.

2. Investing directly into EUR currency by using EUR interest rate for a given period.

As empirical evidence is strongly suggesting, CIP does not hold, since there is always some basis spread for a given currency pair for a given period. In order to take this basis spread properly into account, adjusted CIP is assuming the following parity to hold:



Where S is cross-currency basis spread for a given period. Finally, we can solve this cross-currency basis spread S for a given period by using the following analytical formula:

Test I: snapshot

As a first test for evaluating this methodology, we used formula for calculating short-term basis spread for a few liquid/major currency pairs. We used comparison data for this specific date from Bloomberg and/or ICE. We present the results in the following tables. Note, that even the curves are up to 5Y, only 3M and 6M points have been estimated by using Adjusted CIP.

For these specific liquid/major currency pairs, applied calculation methodology is able to re-produce snapshot market quotes for the short-end relatively accurately. General hypothesis is, that the more liquid/major the currency pair, the more accurate results will be produced by Adjusted CIP.

Test II: time-series

At this point in our analysis, we are interested about the consistency of the proposed methodology. We want to know, whether this methodology produces consistent results as market changes over time. As a second test, we calculated short-term basis spread time-series for EUR/USD pair since the beginning of the year of 2014. We have used Bloomberg market quotes for this period as benchmark. The following table shows time-series data for 3M cross-currency basis spread.

While there are clearly some periods with larger difference between market quote and estimated spread, applied calculation methodology is still able to re-produce market quotes consistently and relatively accurately over time.

Sensitivity

Generally, calculated basis spread estimate is highly sensitive for the interaction of specific variables (∆t, FX spot and FX forward). More specifically, as tenor ∆t will approach to zero, the relative change in spread estimate will generally increase. The following analysis was made for EUR/USD currency pair. All the other parameters were held constant, while FX spot was stressed to both directions in order to see the effect. In practice this means, that basis spread estimate might be heavily biased if, for example, market variables used in parity formula are not captured exactly at the same time.

Practical implementation notes

Assume the following parameters and market data. As we estimate spread for 3M tenor, we can use adjusted CIP formula as follows:

Note, that when estimating spread for 6M tenor, the formula above can still be used, but domestic and foreign interest rate quotes must be adjusted accordingly by using 3v6 tenor basis spreads. Since there is no explicit basis spread quotes available for 3M and 6M, 1Y quote can be used as relatively close proxy.

Finally, the following Excel/VBA function implements the calculation presented above. Thanks for reading my blog.
-Mike

Public Function GetXCCYBasisSpread( _
    ByVal FX_spot As Double, _
    ByVal FX_forward As Double, _
    ByVal BaseDepositRate As Double, _
    ByVal TermDepositRate As Double, _
    ByVal Tenor As String, _
    ByVal BasisSign As Integer, _
    ByVal ScaleRates As Boolean, _
    ByVal UseForwardPoints As Boolean, _
    ByVal ConvertToBasisPoints As Boolean) As Double
    
    ' tenor conversion from string ("3M") to double (0.25)
    ' handling for FX spot and forward, rate scaling
    Dim tenorInYears As Double
    If (VBA.UCase(Tenor) = "3M") Then tenorInYears = (3 / 12)
    If (VBA.UCase(Tenor) = "6M") Then tenorInYears = (6 / 12)
    If (UseForwardPoints) Then FX_forward = FX_spot + FX_forward
    If (ScaleRates) Then
        BaseDepositRate = BaseDepositRate / VBA.CDbl(100)
        TermDepositRate = TermDepositRate / VBA.CDbl(100)
    End If

    ' calculate cross-currency basis spread from given market data
    ' by using modified FX-IR-parity :
    ' (FX_spot / FX_forward) * (1 + R_domestic * dt) = (1 + [R_foreign + spread] * dt)
    
    ' solve the previous parity formula for spread
    Dim spread As Double
    spread = (((FX_spot / FX_forward) * (1 + TermDepositRate * tenorInYears) - 1) * _
            (1 / tenorInYears)) - BaseDepositRate
    
    If (ConvertToBasisPoints) Then spread = spread * 10000
    GetXCCYBasisSpread = spread * VBA.CDbl(BasisSign)
End Function