Valuation models
Yield toolkit
Every yield measure for a bond, conversions between rate conventions, and Treasury bill yields.
Bond
Call schedule (optional)
Yields
Methodology
Conventions
- Yields are compounded at the coupon frequency and solved from the dirty price on the settlement date.
References
- Fabozzi, Bond Markets, Analysis and Strategies, ch. 3
Formulas
- Yield to maturity
- P_dirty = Σ CFₖ / (1 + y/f)^(f·tₖ)
- Yield to call
- same, with the call price paid on the call date
- Yield to worst
- min(YTM, YTC₁, …, YTCₙ)
Bond yield measures run on the analytics core.
Convert
Default day counts: ACT/360 for simple and discount rates, ACT/365F for compounded and continuous rates.
Result
Methodology
Conventions
- Two rates are equivalent when they give the same growth over the term.
References
- Hull, ch. 4
Formulas
- Simple
- G = 1 + r·τ
- Discount
- G = 1 / (1 − d·τ)
- Compounded m times
- G = (1 + r/m)^(m·τ)
- Continuous
- G = e^(r·τ)
Rate conversion runs on the analytics core.
Bill
Yields
Methodology
Conventions
- Bank discount and money-market yields on the bill's day count; bond-equivalent yield on a 365-day year.
References
- US Treasury, Interest rate statistics: bill rates
Formulas
- Price from discount
- P = F (1 − d · days/360)
- Money-market yield
- r = (F/P − 1) · 360/days
- Bond-equivalent
- r = (F/P − 1) · 365/days (≤ 182 days)
Bill yields run on the analytics core.