Description
Return exp(-rate×time) or (1+rate)^(-time), and derivative of log discount with respect to rate as -time or -time/(1+rate).
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 exp(-rate×time) or (1+rate)^(-time), and derivative of log discount with respect to rate as -time or -time/(1+rate).
When to use this tool
Use Discount Factor Log Derivative Term when you need one transparent financial-model term.
How to use the tool and how it works
- Enter time, suppliedRate, continuous. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read discountFactor, logDerivative. Use the output convention below.
Require nonnegative time and, for discrete compounding, rate above -1. Return exp(-rate×time) or (1+rate)^(-time), and derivative of log discount with respect to rate as -time or -time/(1+rate).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| time | Time | Required. Finite number. |
| suppliedRate | Supplied Rate | Required. Finite number. |
| continuous | Continuous | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| discountFactor | Discount Factor | Required. Finite number. |
| logDerivative | Derivative of log discount factor with respect to suppliedRate, not with respect to time. | Required. Finite number. |
{
"input": {
"time": 2,
"suppliedRate": 0.1,
"continuous": true
},
"output": {
"discountFactor": 0.8187307530779818,
"logDerivative": -2
}
}Limitations and assumptions
- Time matches the rate period. The derivative is rate sensitivity, not a derivative in time or elasticity; no cashflow valuation or rate forecast is performed.
- 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
- Discount Factor Elasticity
Return -periods×rate/(1+rate).
- 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.