ZAR RATES DESK · ZARONIA OIS · JIBAR

OIS Swap Strip — Fair NACQ vs ZARONIA Daily Compounded, Paid Quarterly

JIBAR Vanilla Swap Strip — Fair NACQ

OIS Fair Rate Curve (%)

JIBAR Fair Rate Curve (%)

OIS/JIBAR Basis Spread (bp)

Implied Forward ZARONIA vs JIBAR (%)

Single Swap Valuation

Rate Sensitivity

Discount Factor — OIS Curve

NPV vs Rate Shift (ZAR m)

Cashflow Profile — Fixed & Float

PV01 / CS01 Attribution by Quarter

Full Cashflow Schedule

Qtr	Leg	Start	End	DCF	Fwd NACC%	Comp Factor	Cashflow (ZAR)	DF	PV (ZAR)	CS01

JIBAR Discount Factor

JIBAR Zero Rate NACC (%)

JIBAR Forward Rate NACC (%)

JIBAR Bootstrapped Curve — Full Term Structure

Period	Tenor(y)	Instrument	Mkt Rate%	Fwd NACC%	Zero NACC%	DF	Par Rate%

ZARONIA / JIBAR Basis — OIS vs JIBAR Fair NACQ Swap Rates

📐 OIS / IBOR Basis Theory

Post-2008, OIS and IBOR rates diverged due to credit and liquidity risk embedded in panel-bank IBOR fixings (Mercurio, 2009; Bianchetti, 2010). This gave rise to multi-curve pricing. Basis (bp) = Fair_OIS_NACQ − Fair_JIBAR_NACQ) × 100 In ZAR: ZARONIA (risk-free, overnight compounded) trades below JIBAR 3M (credit-risky, term rate) — hence negative basis is normal. The spread represents the JIBAR term/credit premium. Ref: Mercurio (2009) "Interest Rates and the Credit Crunch"; Bianchetti (2010)

🔁 QuantLib Multi-Curve Bootstrap

QuantLib separates discounting curve (OIS/CSA) from projection curve (JIBAR): oisCurve → discounts all cashflows via DF_ois(t) jibarCurve → projects JIBAR 3M forwards via DF_jib(t) Fair NACQ rate for OIS tenor T: r_fair = [ N·(1−DF_ois(T)) / (N·Σᵢ DF_ois(tᵢ)) ] × 4 Fair NACQ for JIBAR swap (same formula, JIBAR DFs): r_fair = [ (1−DF_jib(T)) / Σᵢ DF_jib(tᵢ) ] × 4 Ref: QuantLib MakeVanillaSwap; Ametrano & Bianchetti (2013)

OIS vs JIBAR Fair Rates (%)

OIS/JIBAR Basis Spread by Tenor (bp) — negative = OIS below JIBAR

Basis Detail Table — All Spreads in Basis Points · bp = (OIS−JIBAR)×100

Tenor	JIBAR Fair NACQ%	OIS Fair NACQ%	Basis (bp)	JIBAR DF(T)	OIS DF(T)	JIBAR PV01 (ZAR)	OIS PV01 (ZAR)	DF Spread (bp)

Implied ZARONIA Forward Rates (3M×3M, NACC%)

Implied JIBAR Forward Rates (3M×3M, NACC%)

Implied SARB Repo Path (NACM→NACC, %)

OIS vs JIBAR vs Repo Forward Comparison

Implied Forward Rate Table — OIS, JIBAR, Repo

Period	Start(y)	End(y)	OIS Fwd NACC%	OIS Comp Rate%	JIBAR Fwd NACC%	JIBAR Comp Rate%	Repo Implied%	OIS-Repo Spread (bp)	JIBAR-OIS Spread (bp)

SARB Repo Analysis — Rate Convention Mathematics

📐 Compounding Convention Theory

All nominal rate conventions are equivalent representations of the same effective annual rate (EAR). The no-arbitrage identity (Hull, 2022; Brigo & Mercurio, 2006): (1 + r_m/m)^m = (1 + r_q/4)^4 = (1 + r_a) = e^(r_c) where m = compounding frequency. SARB quotes repo as NACM (m=12) — monthly. Conversions are exact — no approximation. Ref: SARB Monetary Policy Framework; ISDA 2006 Definitions §6.2

🔄 NACM → Other Conventions

Given repo rate r_m (NACM, as quoted by SARB): NACC: r_c = 12 · ln(1 + r_m/12) NACQ: r_q = 4 · (e^(r_c/4) − 1) Eff Ann: r_a = (1 + r_m/12)^12 − 1 Key insight: NACM < NACQ < NACC < Eff Annual for positive rates — higher compounding frequency requires a lower nominal rate to achieve the same effective return. Ref: Fabozzi (2012), Fixed Income Mathematics §2; QuantLib ActualActual

📊 Spread to Swap Rates (basis points)

Spread is computed on comparable conventions (NACQ), since swap fixed rates are NACQ: Spread (bp) = (r_swap_NACQ − r_repo_NACQ) × 100 A positive spread means swap rates exceed the repo rate — the market prices credit/liquidity/term premium over the policy rate. The OIS rate should trade above repo by the OIS-repo spread (historically ~15–25bp in ZAR), reflecting the difference between overnight compounding and the monthly repo fixing. Ref: SARB Working Paper WP/23/01; Duffie & Stein (2015)

🏦 QuantLib Implementation

In QuantLib, the SARB repo maps to: ql.SimpleQuote(repoNACM) ql.FlatForward(today, repoHandle, ql.Actual365Fixed(), ql.Monthly) The OvernightIndex (ZARONIA) uses: ql.OvernightIndex("ZARONIA", 0, ql.ZARCurrency(), cal, ql.Actual365Fixed()) OIS swap pricing via MakeOIS: ql.MakeOIS(tenor, oisIndex, fixedRate, ql.Period("0D")) Ref: QuantLib docs §InterestRateSwap; Ametrano & Bianchetti (2013)

Repo Rate Conversions — All Conventions (%)

Spread of OIS & JIBAR over Repo NACQ across Term (bp)

Repo Rate Convention Table — All Spreads in Basis Points

Convention	Rate%	Eff Annual%	Spread to OIS 1Y (bp)	Spread to JIBAR 3M (bp)	Mathematical Definition & Notes

NPV Heatmap — OIS Swap · Curve Shift (rows) × Fixed Rate (cols) · ZAR m

NPV Sensitivity — OIS Swap (ZAR m)

OIS Fair Rate Sensitivity to Curve Shifts

Scenario Strip

📋 JIBAR FRN Pricing — QuantLib FloatingRateBond Methodology

A JIBAR-linked FRN pays quarterly coupons = (JIBAR₃M_reset + spread) × N × DCF. The current coupon is locked in at the last reset date's JIBAR fixing; future coupons are projected using the JIBAR forward curve. Dirty Price = Σᵢ [ CF_i × DF_jibar(tᵢ) × e^(−dm × τᵢ) ] + N × DF_jibar(T) × e^(−dm × T) where dm = discount margin above JIBAR curve, τᵢ = ACT/365 tenor to payment date. Accrued Interest = (days_since_reset / days_in_period) × coupon_rate × N Clean Price = Dirty Price − Accrued Interest The ZARONIA equivalent note replaces remaining JIBAR-projected coupons with ZARONIA overnight-compounded coupons, using ZARONIA_spread = issue_spread + OIS/JIBAR_basis and OIS discount factors from the ZARONIA curve. Ref: QuantLib FloatingRateBond; Fabozzi (2012) §FRN Valuation; ISDA 2006 §6.2 Reset Convention

Bond Terms

Face Value (ZAR)

Issue Date

Maturity Date

Issue Spread bp

Day Count

Trading / Settlement

Settle Date

Trading Spread bp

Last Reset JIBAR %

Last Reset Date

Next Reset Date

ZARONIA Conversion

Conversion Date

OIS/JIBAR Basis bp

ZARONIA spread = Issue spread + Basis.
Remaining cashflows re-projected on OIS curve.
Equivalent note shows OIS-discounted dirty/clean price.

JIBAR FRN — Valuation at Settle Date

ZARONIA Equivalent Note — Valuation from Conversion Date

JIBAR FRN — Projected Coupon Strip (%)

ZARONIA Equiv — Coupon Comparison (bp spread)

Cashflow PV Profile — JIBAR vs ZARONIA Equiv (ZAR)

Clean Price vs Trading Spread Sensitivity

Full Reset Schedule — JIBAR FRN & ZARONIA Equivalent

Prd	Reset Date	Start Date	Pay Date	DCF	JIBAR Reset%	Cpn Rate%	JIBAR CF (ZAR)	JIBAR DF	JIBAR PV	OIS Equiv%	OIS CF (ZAR)	OIS DF	OIS PV	Status