Swaps and discounted cashflows

An interest-rate swap is valued by projecting its floating coupons and discounting the payments on both legs. Historical fixings determine coupons whose observations are already known; forward curves supply the remaining rates. The discount policy selects the curve appropriate to each payment.

For the payments included in the valuation, we can write

\[ V=\sum_{\ell}s_\ell\sum_i C_{\ell i}\,P_{d,\ell}(0,T_{\ell i})\,X_{\ell i}. \]

Here \(s_\ell\) is leg direction and \(X_{\ell i}\) is the applicable conversion factor when the pricing policy calls for conversion. The pricer’s payment-selection and currency-conversion conventions determine which terms enter the sum. The generic implementation’s conventions are described below.

Regular fixed–floating swaps

MakeSwap builds fixed leg zero and floating leg one; SwapTrade supplies position metadata. A receive-fixed contract uses LongReceive on its fixed side. For simple fixed coupons, \(C_i=NK\tau_i\); other compounding conventions use the coupon’s compound factor instead.

A regular floating coupon has a single observation. The pricer uses required historical fixings for past observations and otherwise projects from the forward curve. The spread is then added under the coupon’s conventions. Missing required history is an error. Choosing SOFR as the index does not change this into overnight daily accrual.

Projection and discounting are separate. A Term SOFR coupon can project from TermSOFR3m while a USD CSA discounts it on SOFR. Without an explicit discount policy, the generic pricer attempts to infer curves from leg identities; ambiguous choices can fail. Production multi-curve setups should make collateral assumptions explicit.

Payment selection and reporting

The generic DiscountedCashflowPricer iterates the cashflows supplied by the instrument; it does not apply a universal payment_date > evaluation_date filter. Do not use it as an implicit settlement/seasoning filter for an arbitrary existing leg. Specialized bond and loan pricers apply their own payment-selection conventions.

The default HandleCashflows report shows signed amounts, including principal and initial disbursements where present. It applies leg direction and reverses disbursements: receipts are positive and payments are negative. Use its payment dates, leg indices, currencies and observations to inspect the contract. Reconciling the table to PV also requires payment selection, discount factors and any currency conversion.

In the first valuation, the builder produces principal exchanges on both sides, giving 24 rows in the cashflow table.

Fair fixed rate

For a vanilla fixed-versus-floating coupon swap under a specified market, the familiar expression is

\[ K^\ast=\frac{PV_{\rm float}}{A},\qquad A=\sum_iN_i\tau_iP_d(0,T_i). \]

Request::FairRate(index) selects a zero-based leg. Target 0 solves the fixed coupon and target 1 the floating spread on a vanilla swap. The scalar result makes total trade PV zero, retaining all other legs’ quotes, principal exchanges, projection indices, discount policy and leg signs. Selected fixed or floating coupons are replaced by a common coupon/spread; mixed coupon types in one selected leg, daily spread compounding and legs without rate exposure are rejected. Request one target per evaluation. The same selection applies to linear basis and cross-currency legs under a compatible native discount policy.

Overnight index swaps

MakeOvernightIndexSwap constructs OvernightIndexSwap with coupon-only legs and index-specific overnight conventions:

#![allow(unused)]
fn main() {
extern crate quantsupport;
use quantsupport::prelude::*;

let rd = Date::new(2026, 1, 2);
let ois = MakeOvernightIndexSwap::<DualFwd>::new(
    MarketIndex::SOFR, rd, Period::new(5, TimeUnit::Years), 0.04,
)
.with_identifier("USD_SOFR_OIS_5Y".into())
.with_notional(10_000_000.0)
.with_side(Side::LongReceive)
.build()?;
let _trade = OvernightIndexSwapTrade::new(
    ois, rd, 10_000_000.0, Side::LongReceive,
);
Ok::<(), QSError>(())
}

For standard future compounding the overnight accumulation telescopes to a discount-factor ratio. Seasoned periods combine weighted historical daily observations with projected remainder. Lookback, lockout, observation shift, daily spread treatment and payment lag are separate inputs; the calibration chapter explains their market presets and the legacy XVA conversion limit.

Basis swaps extend the same logic to two floating indices. Their value and quote risk depend on both projection curves and the policy-selected discount curve. They are also calibration instruments, so a basis curve’s derivative can carry parent OIS risk through the IFT.

Related linear products

Deposits and floating-rate notes share leg-based mechanics. Straight bonds require settlement, quote anchors and yield/spread analytics and therefore have a specialized bond pricer. Listed rate futures use RateFuturesPricer: implied rate is the decimal \((100-Q)/100\), and contract size is value per futures price point, not per basis point. A one-basis-point rate change changes a 100-100r quote by 0.01 price points. These unit distinctions are essential before comparing their risk with swap sensitivities.