Interpolation
Controls how zero rates are displayed from discount factors.
Used when date mode is enabled.
Base date for year fractions.
Bonds use price per 100 notional.
| # | Type | Maturity (years) | Rate % | Coupon % | Price | Freq | Action |
|---|
Results
| Maturity (y) | Discount Factor | Zero Rate % | Instrument Source |
|---|
Zero rate is derived from DF using the selected convention. Example: continuous r = −ln(DF)/t.
Curve Fitting (Nelson–Siegel / Svensson)
Fitting targets continuous zero rates rc(t) derived from discount factors; τ bounds, long‑end anchor, clamps, and frozen tail improve stability and extrapolation.
Instrument Analysis (IRR / Par Check)
| # | Type | Maturity | Market Quote | IRR / Par % | Model PV / Par % |
|---|
IRR for bonds solves yield matching price with periodic discounting at the stated frequency. For swaps, “Par %” shows the model par rate from bootstrapped discount factors.
Formulae Used
- Discount factor from deposit/zero:
DF(t) = exp(−r t) for continuous; DF(t) = (1 + r/m)−m t for periodic; DF(t) = 1/(1 + r t) for simple.
- Coupon bond price:
P = Σi=1..n−1 ci·DF(ti) + (F + cn)·DF(T). Last DF: DF(T) = [P − Σ ci DF(ti)]/(F + cn).
- Par swap rate S:
S = (1 − DF(T))/A with A = Σ Δi DF(ti). Rearranged: DF(T) = [1 − S Σi=1..n−1 Δi DF(ti)]/(1 + S Δn).
- Zero rate from DF:
rcont = −ln(DF)/t.
- Piecewise‑constant forwards:
Between nodes ti, ti+1: f = −ln(DF(ti+1)/DF(ti))/(ti+1−ti).
- NS/NSS fits & health:
We check monotonic DF(t) and DF(t)≤1 for t>0 on the overlay grid; tail extrapolation can freeze the last forward for stability.