Description
Return zeroRate+maturity×zeroRateSlope as instantaneousForward and the slope contribution separately.
A financial model connects supplied rates, discount factors, cashflows or prices under a particular convention. A local identity or residual is not a complete valuation, an observed market relationship or a promise of future returns.
Return zeroRate+maturity×zeroRateSlope as instantaneousForward and the slope contribution separately.
When to use this tool
Use Yield Curve Forward Slope Term when you need one transparent financial-model term.
How to use the tool and how it works
- Enter zeroRate, maturity, zeroRateSlope. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read instantaneousForward, slopeContribution. Use the output convention below.
Require nonnegative maturity. Return zeroRate+maturity×zeroRateSlope as instantaneousForward and the slope contribution separately.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| zeroRate | Continuously compounded zero rate on the maturity time basis. | Required. Finite number. |
| maturity | Maturity | Required. Finite number; minimum 0. |
| zeroRateSlope | Derivative of zero rate with respect to maturity, in rate per time. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| instantaneousForward | Instantaneous Forward | Required. Finite number. |
| slopeContribution | Slope Contribution | Required. Finite number. |
{
"input": {
"zeroRate": 0.03,
"maturity": 2,
"zeroRateSlope": 0.01
},
"output": {
"instantaneousForward": 0.05,
"slopeContribution": 0.02
}
}Limitations and assumptions
- The zero rate is continuously compounded on a common time basis, and its derivative is rate per time. This local curve identity does not estimate a curve or forecast rates.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete model matching the instrument, cashflows and market conventions. Review compounding, timing, currency, uncertainty and omitted costs before using a local estimate in a financial decision.
References
Similar or alternative tools
- Forward Rate Discount Factor Two Dates
Divide log discount ratio by time gap for continuous rate, or take its reciprocal-gap power minus one otherwise.
- Discount Factor Log Derivative Term
Return exp(-rate×time) or (1+rate)^(-time), and derivative of log discount with respect to rate as -time or -time/(1+rate).