Valuation models
Bond pricer
Price a fixed-rate bond from its yield, or solve the yield from a price, with duration, convexity and DV01.
Inputs
Valued on a coupon date, so clean and dirty prices coincide. Yield compounds at the coupon frequency.
Analytics
Methodology
Conventions
- Settlement on a coupon date, so accrued interest is zero and clean equals dirty price.
- Yield compounded at the coupon frequency f.
- Coupon c = face × coupon rate / f, paid at the end of each of the n = years × f periods.
- DV01 is the price change for a 1bp move in yield, per the face value entered.
References
- Fabozzi, Bond Markets, Analysis and Strategies
- Hull, Options, Futures and Other Derivatives, ch. 4
Formulas
- Price
- P = Σₖ₌₁ⁿ CFₖ / (1 + y/f)ᵏ
- Macaulay duration
- D = (1/P) Σ (k/f) · CFₖ / (1 + y/f)ᵏ
- Modified duration
- D* = D / (1 + y/f)
- Convexity
- C = (1/P) Σ k(k+1) · CFₖ / (f² (1 + y/f)ᵏ⁺²)
- DV01
- DV01 = D* · P · 0.0001
- Yield from price
- solve P(y) = P_market for y (bisection)
Dated bonds with accrued interest and day counts are priced by the analytics core.