Module pik
Expand description
The accretion seam and the fixed-rate payment-in-kind bond.
An accreting-principal bond is modelled as par cashflows on a constant
face multiplied by a per-flow ratio, never as a per-period notional: the
face stays scalar and the whole per-100 surface stays on one basis. The
inflation-linked bond takes its ratio from a market index; a PIK takes it
from a contractual rule — the coupon capitalises into the principal each
period instead of paying in cash, so the face grows by ∏(1 + c·τᵢ) and
the single cash event is the accreted redemption at maturity.
Because the accretion is contractual it needs no market data: every factor is fixed by the bond’s own terms, so the accreted face at any date is computable with no curve, and the ratio is passive — it enters the pricing mode as a constant, never as an input.
Quote bases. Price, yield and accrued are offered on two named bases — per 100 of accreted face (the market convention) and per 100 of par face — with explicit conversion by the accretion ratio at settlement. No entry point returns a price whose basis a caller must infer.
A PIK is not credit-taggable here: the defaulted claim is the accreted
face at default, a time-varying notional the recovery kernel does not
express, so there is no issued_by to misuse. Floating and elective
(toggle) capitalisation are not representable by the type at all.
Structs§
- Capitalisation
- One capitalisation: the coupon rolled into the principal rather than paid, carrying the rate applied and the face it produced. Reported so the accretion is reconstructable from the events; never a cash flow.
- Contractual
Accretion - A contractual accretion rule: par face grown by the compounded period
factors
∏(1 + c·τᵢ)over the capitalisation dates elapsed to a date. - Payment
InKind Bond - A fixed-rate payment-in-kind bond.