Contents
1. What is Rijeka
2. Pricer — Rates (IRS, Swaption, Cap/Floor, Callable, Basis, Amort)
2b. OIS Curve Construction & Interpolation Methods
3. Pricer — Credit (CDS, CDX, RPA)
4. Pricer — FX & Commodity
5b. Hybrid — Convertible Bond (Andersen-Buffum 2004)
5. Pricer — Crypto Derivatives BETA
6. XVA Engine — CVA, DVA & FVA
7. SIMM Overview & Regulatory Context
8. SIMM — Interest Rate Risk
9. SIMM — Credit, Equity, Commodity & FX
10. SIMM — Aggregation & Concentration
11. Rijeka Crypto IM — Proprietary Methodology BETA
12. Limitations & Disclaimer
13. Change Log
1. What is Rijeka
Rijeka (Croatian: river) is a port city on the Adriatic coast — a place where trade routes converged, goods flowed, and value was exchanged for centuries. The engine takes its name from that idea: that beneath every financial transaction is a flow — of risk, of funding cost, of collateral — that must be measured, priced, and managed. This engine surfaces that flow.
Rijeka is a full-stack derivatives pricing and risk engine covering trade pricing, counterparty valuation adjustments (XVA), and initial margin (SIMM). It is designed for front-office traders, risk managers, and quantitative analysts who need a single system that moves seamlessly from clean price to risk-adjusted all-in cost to regulatory margin requirement.
Pricer
14 instruments across Rates, Credit, FX, Commodity and Crypto. From vanilla IRS to DeFi interest rate swaps. Every product outputs a full XVA waterfall — NPV → CVA → DVA → FVA → all-in price — alongside indicative SIMM IM and funding cost.
XVA Engine
Monte Carlo simulation under the Hull-White one-factor model. Computes CVA (counterparty credit cost), DVA (own default benefit), and FVA (funding valuation adjustment) along with EPE and PFE exposure profiles at each monthly time step.
IM Calculator
Full ISDA SIMM v2.8+2506 implementation covering IR, Credit, Equity, Commodity and FX risk classes. Concentration risk add-on. Cross-asset aggregation with ISDA correlation matrix. Proprietary Rijeka Crypto IM for crypto portfolios.
The river metaphor
A river flows — cash flows, exposure curves, discount curves all move through time. A river has currents beneath the surface — CVA and FVA are the hidden costs beneath a clean price. Rivers have delta — where they meet the sea, where they branch. Every derivatives trader knows delta.
| Module | Instruments | Models | Outputs |
|---|
| Rates | IRS, Basis swap, Amortising, Cap/Floor, Swaption, Callable swap | Hull-White MC, Black normal vol, LSM Bermudans | NPV, DV01, XVA waterfall, EPE/PFE, SIMM IM |
| Credit | CDS, CDX index, Risk Participation Agreement | Hazard rate (flat), ISDA CDS standard model | NPV, CS01, survival probs, XVA waterfall |
| FX | FX forward, FX vanilla & barrier option | Garman-Kohlhagen, closed-form barriers | NPV, delta, XVA, forward points |
| Commodity | Commodity swap, Commodity option | Forward curve, Black-76 | NPV, DV01, Cmdty01, schedule |
| Crypto BETA | Perp futures, Vanilla option, DeFi IRS, Quanto option | MtM + funding, Garman-Kohlhagen, Quanto-adj BS | P&L, Greeks, VaR, liquidation, protocol CVA |
2. Pricer — Rates
The rates pricer covers six interest rate derivative products. All products share a common Hull-White one-factor short rate model for Monte Carlo simulation and a flat OIS discount curve (configurable via Market Data). The XVA waterfall is computed for every product using the same CVA/DVA/FVA engine described in Section 6.
Vanilla IRS
Fixed vs floating interest rate swap. NPV = PV(fixed leg) − PV(float leg) under the flat OIS curve.
Par rate: fixed rate that makes NPV = 0.
DV01: $ change per 1bp parallel rate shift.
MC paths: 200–2,000 for XVA simulation.
Endpoint: /price/irs
Basis Swap
Floating vs floating swap between two rate indices (e.g. SOFR vs EURIBOR). Par spread = rate differential at which NPV = 0.
Each leg discounted at the index-appropriate all-in rate. Spread DV01 measures sensitivity to basis widening.
Endpoint: /price/basis-swap
Amortising Swap
IRS with scheduled notional reduction. Supports linear, bullet, and mortgage-style amortisation.
WAL (weighted average life) = Σ(notional_t × t) / initial notional.
Full payment schedule output per period.
Endpoint: /price/amortising-swap
Cap / Floor
Series of caplets/floorlets priced using Bachelier (normal) model. Each caplet = call/put on the forward rate at each reset date.
Vol surface: flat normal vol input (bps). Parity check: Cap − Floor = swap value (verified).
Endpoint: /price/cap-floor
Swaption
Option to enter a swap at expiry. Priced using Bachelier model on the forward swap rate.
European: closed-form. Bermudan: Longstaff-Schwartz Monte Carlo with regression.
Vega: $ per 1bp change in normal vol.
Endpoint: /price/swaption
Callable Swap
Vanilla IRS with embedded cancellation option at one or more call dates. Value = vanilla NPV − embedded swaption.
The embedded option is a receiver swaption (counterparty's right to cancel). Option cost expressed in bps/year of remaining maturity.
Endpoint: /price/callable-swap
IRS NPV = N · [ (1 − DF_T) − K · Σ_i DF_i · Δt_i ] (pay fixed)
where K = fixed rate · DF_i = exp(−r · t_i) · N = notional
Par rate K* solves NPV = 0: K* = (1 − DF_T) / Σ_i DF_i · Δt_i
2b. OIS Curve Construction & Interpolation v4.3
Rijeka builds four overnight index swap (OIS) curves: USD SOFR, EUR €STR, GBP SONIA, and JPY TONAR. Each curve has 13 pillars spanning O/N through 30Y. Between pillars, five interpolation methods are available, selectable per currency from the Market Data tab.
Log-Linear on Discount Factors Default · Bloomberg match
Interpolates log(DF(t)) linearly between pillars. Equivalent to linear interpolation on r(t)×t. Produces smooth, positive discount factors and is the standard method for OIS curve construction. Verified to match Bloomberg SWPM NPV to <1bp on standard SOFR IRS.
DF(t) = DF(t₀)^(1−α) × DF(t₁)^α
r(t) = −ln(DF(t)) / t
Smooth Forward (Natural Cubic Spline)
Fits a natural cubic spline through all zero rate pillars. Produces a smooth, differentiable forward curve — no kinks at pillar dates. Best for visual forward curve analysis. Can produce slight oscillations in sparse curve regions (e.g. 15Y–30Y). Recommended for curves with 8+ liquid pillars.
Step Forward (Flat Forwards)
Instantaneous forward rate is held constant between adjacent pillars. Zero rate at tenor t is computed as the weighted average of all flat forward segments up to t. Produces a piecewise-constant forward curve — the most conservative assumption. Standard in some regulatory stress-testing frameworks.
f(t₀,t₁) = (r₁t₁ − r₀t₀) / (t₁−t₀)
Linear on Zero Rates
Simplest method — linear interpolation directly on zero rates. Does not preserve discount factor monotonicity as strictly as log-linear but is intuitive and transparent. Produces slightly different DV01 profiles vs log-linear, particularly at short tenors where the curve is steep.
| Method | Forward Curve | DF Monotone | Bloomberg Match | Best For |
|---|
| Log-Linear DF | Smooth, positive | ✓ Always | ✓ Best | Standard OIS pricing |
| Smooth Forward | Very smooth, C² | ✓ Usually | Close | Forward curve analysis |
| Step Forward | Piecewise constant | ✓ Always | Conservative | Stress testing |
| Linear Rates | Piecewise linear | ✓ Usually | Close | Simple benchmarking |
| Piecewise Linear | Piecewise linear | ✓ Usually | Close | Equivalent to Linear |
Bloomberg SWPM equivalence: Bloomberg's standard OIS curve construction for SOFR uses log-linear interpolation on discount factors with actual/360 day count conventions. Rijeka's default matches this. Remaining NPV differences (<1bp on standard tenors) are attributable to holiday calendar adjustments and settlement date conventions which Rijeka approximates using year fractions.
3. Pricer — Credit
The credit pricer covers three instruments: single-name CDS, CDX index trades, and Risk Participation Agreements. All credit products use the ISDA standard hazard rate model for default probability and a flat credit curve for simplicity. Survival probabilities are output at standard tenors (1Y, 3Y, 5Y, 10Y).
CDS — Credit Default Swap
NPV = Protection PV − Premium PV
Hazard rate: h = CDS_spread / (1 − Recovery)
Survival prob: Q(t) = exp(−h·t)
CS01: $ per 1bp spread widening.
Par spread = rate at which NPV = 0.
Endpoint: /price/cds
CDX Index
CDX priced as a portfolio CDS on 125 equally-weighted names (CDX.NA.IG) or 100 names (CDX.NA.HY).
Intrinsic spread: equal-weighted average of constituent par spreads.
Index basis: CDX spread − intrinsic spread. Positive basis = index is cheap.
Endpoint: /price/cdx
Risk Participation Agreement
Bank A sells a share of credit risk on a reference obligor to Bank B. B receives a fee in exchange for absorbing losses if the obligor defaults.
Funded RPA: B posts cash upfront.
Unfunded RPA: B provides contingent guarantee.
Par fee = break-even annual premium in bps.
Endpoint: /price/rpa
Protection PV = (1−R) · Σ_t Q(t−1,t) · DF(t)
Premium PV = spread · Σ_t Q(t) · DF(t) · Δt
Risky annuity = Σ_t Q(t) · DF(t) · Δt (DV01 per bp of spread)
4. Pricer — FX & Commodity
FX Forward
Forward rate = Spot · exp((r_d − r_f) · T) by covered interest parity.
Forward points: (forward − spot) × 10,000.
NPV: notional × (forward − agreed_rate) × DF.
P&L per pip: notional / 10,000.
Endpoint: /price/fx-forward
FX Option
Garman-Kohlhagen model (Black-Scholes with continuous foreign dividend yield r_f).
Barrier options: closed-form knock-in / knock-out via reflection principle.
Full Greeks: Δ (FX delta), Γ, Vega/1%, Θ/day.
CVA on counterparty default risk included.
Endpoint: /price/fx-option
Commodity Swap
Fixed price vs floating (spot-referenced) commodity swap. Supports 10 commodities: WTI, Brent, TTF, Henry Hub, Gold, Silver, Copper, Corn, Wheat, Soybeans.
Cmdty01: $ per $1 spot move.
Forward schedule output per reset date.
Endpoint: /price/commodity-swap
Commodity Option
Black-76 model pricing options on commodity forward prices.
Call / put on forward price with log-normal vol assumption.
Intrinsic value: max(F−K, 0) × units.
Time value: option price − intrinsic.
Endpoint: /price/commodity-option
5. Pricer — Crypto Derivatives BETA
The Rijeka Crypto Pricing Engine prices four crypto derivative types using market-standard models adapted for crypto-specific dynamics. All products use live BTC/ETH market data (spot, vol, funding rate, borrow rate) updatable via /crypto-market-data. Crypto derivatives carry unique risks not present in traditional finance: funding rate volatility, liquidation cascades, protocol hack risk, and fat-tailed return distributions.
Crypto Perpetual Futures
Perpetual futures have no expiry. Price tracks spot via a funding mechanism paid every 8 hours.
MtM P&L: (spot − entry) / entry × notional
Funding P&L: ±rate_8h × notional × (days × 3)
Liquidation: entry × (1 − 1/lev + 0.5%) for long
VaR 1D 99%: notional × (σ/√252) × 2.326
Endpoint: /price/crypto-perp
Crypto Vanilla Option
Garman-Kohlhagen treating the borrow rate as a continuous foreign yield.
F = S · exp((r − r_borrow) · T)
d1 = (ln(F/K) + ½σ²T) / (σ√T)
Full Greeks: Δ, Γ, Vega, Θ, ρ.
CVA: exchange default risk (zero recovery).
Endpoint: /price/crypto-option
DeFi IRS — Fixed vs Floating
Fixed vs floating rate swap on DeFi protocols (Aave, Compound). Floating rate = live protocol borrow rate.
Discount: OIS flat rate + 200bps crypto premium.
Protocol CVA: notional × T × 2%/yr hack prob × 30% severity.
Protocol premium: 50–60bps/yr smart contract risk.
Endpoint: /price/crypto-irs
Crypto Quanto Option
Option on a crypto asset settled in a different currency. The quanto adjustment corrects for the correlation between asset price and FX rate.
F_Q = F · exp(−ρ · σ_asset · σ_FX · T)
ρ = correlation between crypto and FX (default 0.85)
σ_FX = vol of crypto/USD rate (default 9.5%)
Endpoint: /price/crypto-quanto
SIMM IM in Pricer: Each priced trade displays an indicative SIMM IM using IM = |DV01| × RWtenor and a FIM (Margin VA) = IM × funding spread — the annualised cost of posting that margin. For crypto products, the Rijeka Crypto IM methodology (Section 11) applies. Full multi-asset SIMM is on the IM Calculator tab.
6. XVA Engine — CVA, DVA & FVA
XVA (valuation adjustments) are the corrections applied to a clean derivative price to account for counterparty credit risk and funding costs. The Rijeka XVA engine computes three adjustments: CVA (cost of counterparty default), DVA (benefit of own default), and FVA (cost of funding uncollateralised positions). The XVA waterfall — NPV → CVA → DVA → FVA → all-in — is displayed for every applicable product.
Hull-White Rate Simulation
dr = a(θ(t) − r)dt + σ dW
a = mean reversion speed (default 0.10)
σ = short rate volatility (default 0.015)
θ(t) = time-varying drift consistent with initial OIS curve
Monte Carlo paths: 200 / 500 / 1,000 / 2,000
Time steps: 60 monthly steps over trade maturity
Exposure Profiles
EPE(t): E[max(V(t), 0)] — expected positive exposure. Used for CVA.
ENE(t): E[min(V(t), 0)] — expected negative exposure. Used for DVA & FVB.
PFE 95%(t): 95th percentile of positive exposure at time t. Regulatory capital proxy.
Profiles output at each monthly step and plotted in the Pricer.
CVA — Credit Valuation Adjustment
CVA = −(1−R) · Σ_t EPE(t) · PD(t−1,t) · DF(t)
Hazard rate: h = CDS_spread / (1 − Recovery)
Marginal PD: PD(t−1,t) = exp(−h·t₋₁) − exp(−h·t)
Recovery R: default 40%
CVA is always negative — it is a cost to the bank.
DVA & FVA
DVA = +(1−R_own) · Σ_t |ENE(t)| · PD_own(t−1,t) · DF(t)
DVA is positive — a benefit, controversial in accounting.
FCA = Σ_t EPE(t) · fs · dt · DF(t) (funding cost of assets)
FVB = Σ_t |ENE(t)| · fs · dt · DF(t) (funding benefit of liabilities)
FVA = −(FCA − FVB) · fs = funding spread (default 80bp)
All-in price = NPV + CVA + DVA + FVA
Net XVA = CVA + DVA + FVA (typically negative for an out-of-the-money receiver)
XVA % of NPV = |Net XVA| / |NPV| × 100 (measures relative adjustment significance)
7. SIMM Overview & Regulatory Context ISDA SIMM v2.8+2506
The ISDA Standard Initial Margin Model (SIMM) is the industry standard methodology for calculating initial margin (IM) under the Uncleared Margin Rules (UMR) mandated by BCBS/IOSCO. It is used by over 1,000 financial institutions globally across Phase 1–6 of UMR implementation.
Rijeka implements SIMM v2.8+2506, effective 6 December 2025, calibrated using 3 years of market data to 30 June 2025. The "+2506" suffix denotes the June 2025 calibration date under the semi-annual cycle introduced in 2025.
Regulatory basis
BCBS/IOSCO Margin Requirements for Non-Centrally Cleared Derivatives (2015, revised 2020). Implemented via ISDA 2016 Credit Support Annex for Variation Margin and Phase 1–6 IM thresholds.
Calibration methodology
Risk weights calibrated to a 99th percentile 10-day VaR over a stressed period. 3–5 year lookback window ending 30 June 2025. Semi-annual updates: June and December effective dates.
SIMM v2.8+2506 key changes
Energy commodity RWs decreased vs v2.7+2412 (calm June 2025 data). IR RWs broadly stable. Semi-annual calibration cycle formalised. HVR maintained at 0.74.
Source documents
ISDA SIMM Methodology v2.8 (December 2025). ISDA SIMM Calibration Results v2.8+2506. ISDA CRIF Standards v2.5.
IM = Aggregate( K_b ) across asset classes using cross-class correlation matrix Ψ
where K_b = sqrt( Σ_i WS_i² + Σ_{i≠j} ρ_{ij} · WS_i · WS_j )
and WS_i = sensitivity_i × RW_i × CR_i (concentration risk factor)
8. SIMM — Interest Rate Risk
IR risk is decomposed into three components: delta (DV01 sensitivity to parallel rate shifts), vega (sensitivity to implied vol changes), and curvature (second-order rate sensitivity). Tenors: 2W, 1M, 3M, 6M, 1Y, 2Y, 3Y, 5Y, 10Y, 15Y, 20Y, 30Y.
IR Delta — Sensitivity definition
s_k = change in portfolio value per 1 basis point parallel shift in the risk-free rate at tenor k. Units: $ per bp (DV01). Positive = portfolio gains when rates fall.
Low vol currencies (USD, EUR, GBP, AUD, CAD, CHF etc.) — individually calibrated RWs. USD 5Y: 41bp · EUR 5Y: 20bp · GBP 5Y: 27bp.
Regular vol (JPY, BRL, CNY, INR, MXN, ZAR etc.) — uses EUR/JPY schedule. 5Y = 20bp.
High vol (ARS, CLP, NGN etc.) — uses USD schedule. 5Y = 41bp.
| Currency group | 5Y RW | Concentration threshold | Key currencies |
|---|
| Low vol | 20–41bp | $14M–$230M | USD, EUR, GBP, AUD, CAD, CHF, DKK, HKD, NOK, NZD, SEK, SGD |
| Regular vol | 20bp | $1M–$20M | JPY, BRL, CNY, CZK, HUF, IDR, INR, MXN, PLN, RUB, SAR, THB, TRY, ZAR |
| High vol | 41bp | $1M | ARS, CLP, COP, PEN, NGN, PKR, BDT |
IR Vega RW = 18%. Intra-bucket correlation for delta: 0.999 (same currency, adjacent tenors) to 0.13 (different currency, far tenors). Cross-currency correlation = 0 for low-vol vs high-vol pairs. Curvature uses the same risk weights as delta, applied to the second-order convexity sensitivity.
9. SIMM — Credit, Equity, Commodity & FX
Credit: CS01 sensitivity ($ per 1bp spread move) bucketed into 12 sectors. Separate IG (qualifying) and HY (non-qualifying) risk weights. Intra-bucket correlation 0.35–0.97 depending on sector.
| Bucket | Sector | IG RW | HY RW |
|---|
| 1 | Sovereigns, central banks | 70bp | 179bp |
| 2 | Financials, govt-backed | 81bp | 232bp |
| 4 | Non-financial corporates, consumer | 103bp | 309bp |
| 7 | Basic materials, energy, agriculture | 163bp | 457bp |
| 8 | Consumer staples, transport | 238bp | 566bp |
Equity: $ PnL per 1% spot move. 13 buckets by market cap and geography. RW 18–34%. Intra-bucket ρ 18–62%. Equity Vega RW = 28%.
Commodity: 17 buckets. RW 13–53%. High intra-bucket ρ within energy (crude 98%), low for base metals (10%). Commodity Vega RW = 45%.
| Bucket | Commodity | RW | Intra ρ |
|---|
| 2 | Crude oil (Brent, WTI) | 29% | 98% |
| 6 | Natural gas EU/NA | 22% | 92% |
| 10 | Base metals (copper, aluminium) | 53% | 10% |
| 12 | Precious metals (gold, silver) | 21% | 64% |
| 13–15 | Agricultural | 13–15% | 19–71% |
FX: $ PnL per 1% spot move. RW depends on currency volatility category pairing. Regular/Regular (G10): 13.6%. High/Regular (EM): 10.6%. High/High: 7.4% (high-vol currencies move together, providing natural offset). FX Vega RW = 47%. Concentration threshold = $8.1B.
10. SIMM — Aggregation & Concentration
After computing IM per risk class, total SIMM IM is aggregated using the cross-asset class correlation matrix Ψ, providing diversification benefit when risk classes offset each other.
Total IM = sqrt( Σ_b K_b² + Σ_{b≠b'} Ψ_{b,b'} · K_b · K_{b'} )
| IR | Credit Q | Credit NQ | Equity | Commodity | FX |
|---|
| IR | 1.00 | 0.29 | 0.07 | 0.21 | 0.15 | 0.10 |
| Credit Q | 0.29 | 1.00 | 0.17 | 0.52 | 0.42 | 0.33 |
| Equity | 0.21 | 0.52 | 0.13 | 1.00 | 0.37 | 0.36 |
| Commodity | 0.15 | 0.42 | 0.25 | 0.37 | 1.00 | 0.26 |
| FX | 0.10 | 0.33 | 0.17 | 0.36 | 0.26 | 1.00 |
Concentration risk: CR_i = max(1, √(|net_WS_i| / Threshold_b)). Positions below the threshold: CR = 1, no add-on. Above the threshold: IM scales with the square root of position size, reflecting the cost of unwinding illiquid positions under stress.
Example: USD 5Y DV01 = $10M → WS = $10M × 41bp = $410k → CR = max(1, √(410k / 230M)) = 1.0 (no add-on)
DV01 = $100M → WS = $4.1M → CR = max(1, √(4.1M / 230M)) = 1.0 (still below threshold)
DV01 = $1B → WS = $41M → CR = max(1, √(41M / 230M)) = 1.34 (+34% IM add-on)
11. Rijeka Crypto IM — Proprietary Methodology BETA
Important: Rijeka Crypto IM is a proprietary methodology. It is not endorsed by ISDA, is not part of any regulatory framework, and must not be used for UMR compliance. It is intended as a directional estimate only. Validate against institution-specific VaR models before operational use.
No industry standard equivalent to ISDA SIMM exists for crypto. Rijeka fills this gap by adapting the SIMM delta framework to crypto assets using historically calibrated risk weights derived from 2-year realised volatility.
Risk weight derivation — 4 steps
Step 1: Calculate 2-year annualised realised vol for each asset (daily log returns Jan 2023–Dec 2024).
Step 2: 99th %ile 10-day VaR = vol × √(10/252) × 2.326 (parametric normal).
Step 3: Apply 1.15× fat-tail scalar for crypto leptokurtosis.
Step 4: Round to nearest 5%, floor at 75% (majors), 100% (mid-caps), 200% (DeFi tokens).
| Asset | 2Y Realised Vol | 99th %ile 10D VaR | Fat-tail scalar | Rijeka RW |
|---|
| BTC Bitcoin | 72% | 66% | 1.15× | 80% |
| ETH Ethereum | 95% | 87% | 1.15× | 100% |
| SOL Solana | 140% | 128% | 1.15× | 150% |
| BNB / XRP | 90–110% | 83–101% | 1.15× | 95–115% |
| DeFi tokens (UNI, AAVE, CRV, MKR) | 150–200% | 138–184% | 1.15× | 200% (capped) |
Crypto IM = sqrt( Σ_i (s_i × RW_i)² + Σ_{i≠j} ρ_crypto · (s_i × RW_i) · (s_j × RW_j) )
where s_i = $ PnL per 1% spot move · RW_i = Rijeka RW · ρ_crypto = 0.65
(65% inter-asset correlation from median pairwise Pearson across BTC, ETH, SOL, BNB, XRP, ADA, AVAX 2023–2024)
5b. Pricer — Hybrid: Convertible Bond v4.8
Convertible bonds are hybrid securities combining a fixed-income bond with an embedded equity conversion option. Rijeka prices convertibles using the Andersen-Buffum risky discounting model solved on a Cox-Ross-Rubinstein (CRR) binomial tree.
Model: Andersen-Buffum (2004)
The entire convertible value V(S,t) is discounted at the risky rate r(t) + λ(S,t), where λ is the issuer credit spread. This contrasts with the Tsiveriotis-Fernandes (1998) approach which splits the value into two components. Rijeka follows the unified risky discounting approach, consistent with the industry standard for credit-sensitive convertibles.
Reference: Andersen, L. and Buffum, D. (2004). "Calibration and implementation of convertible bond models." Journal of Computational Finance 7(4), 1–34.
Stock-Linked Credit Spread
The issuer hazard rate is modeled as stock-dependent per Andersen-Buffum:
λ(S,t) = λ₀(t) · (S₀/S)^p
where λ₀ is the base credit spread (from CDS or assumed), S₀ is the reference stock price, and p ≥ 0 is the decay exponent. When p=0 the spread is flat. Higher p creates a strong equity-credit linkage — as the stock falls, the spread widens, creating the default corridor.
Binomial Tree Backward Induction
Standard CRR lattice with u = e^(σ√Δt), d = 1/u. At each node, the holder maximises value between holding and converting. The issuer exercises the call when the convertible value exceeds the call price. Default recovery is applied as a floor V ≥ R·F where R is recovery rate and F is face value.
Default tree steps: 400 (standard). Calibrated to ±0.3% of benchmark.
Valuation Decomposition
Fair Value — full convertible price including optionality
Bond Floor — pure debt value (σ → 0), also called Investment Value
Equity Premium — Fair Value − Bond Floor (the option component)
Parity — S × conversion ratio (current equity value if converted)
Point Premium — Fair Value − Parity (premium over conversion)
Conversion Premium % — (K_conv/S − 1) × 100
| Greek | Definition | Unit |
|---|
| Delta (outright) | ∂V/∂S — sensitivity to 1 dollar stock move | $/share |
| Delta (hedge) | Shares of stock to short per $100 face to delta-hedge | shares |
| Gamma (1%) | Change in delta for 1% stock move | $ |
| Vega (1pt) | Change in fair value per 1 vol point (e.g. 45% → 46%) | $/vol pt |
| Rho (100bps) | Change in fair value per 100bps credit spread widening | $/100bps |
| Theta (1d) | Time decay per calendar day | $/day |
Benchmark validation: Rijeka replicates the ZS (Zscaler) 0% Convertible Jul 2028 at σ=45%, spread=75bps, S=$156.48: Fair Value $91.93 vs benchmark $92.18 (Δ = 0.27%), Bond Floor $90.41 vs $90.79 (Δ = 0.42%), Parity $35.60 exact match.
12. Limitations & Disclaimer
Disclaimer: Rijeka is an independent pricing tool. Results must be independently validated before use in regulatory reporting, margin calls, or trading decisions. Rijeka accepts no liability for losses arising from reliance on these calculations.
| Limitation | Impact | Workaround |
|---|
| Single-curve discount (flat OIS) | Medium — IRS NPV may differ from multi-curve by 5–30bp in par rate | Use full multi-curve bootstrapping for precise NPV |
| Hull-White one-factor model | Low–Medium — adequate for vanilla IRS, insufficient for Bermudan swaptions or CMS | Use SABR vol surface for swaption pricing |
| Static credit curve in XVA | Medium — CVA assumes constant hazard rate; does not track credit migration | Bootstrap full hazard curve for precision |
| Crypto IM — no regulatory basis | High — cannot be used for UMR compliance | Directional use only; apply 1.25× stress buffer |
| SIMM runs ~9 months behind market | Medium — calibrated to June 2025 data; acute market dislocations not captured | Apply manual overlays for known dislocations |
13. Change Log
16 Mar 2026
v4.3 — IRS Trading Terminal: full two-leg SWPM-style entry (counterparty, CCP, trade/effective/maturity dates, fixed freq, float freq, day count ACT/360|ACT/365|30/360, float spread, CSA collateral currency). Curve-consistent pricing using OIS discount factors per tenor. Bucketed DV01 (Front O/N–2Y, Belly 3Y–7Y, Tail 10Y–30Y). Cashflow schedule with zero rates, discount factors, forward rates. EPE/PFE exposure chart. XVA waterfall sidebar. SIMM IM indicative. 7-scenario shock analysis. CSV export (trade summary + cashflows + scenarios). Tooltip engine on all metrics.
16 Mar 2026
v4.3 — Curve interpolation engine: 5 methods selectable per currency — Log-Linear on Discount Factors (default), Linear on Zero Rates, Smooth Forward (natural cubic spline), Step Forward (flat forwards), Piecewise Linear. API endpoint PUT /market-data/curves/{ccy}/interp. NPV verified to match Bloomberg SWPM to <1bp on standard SOFR OIS swaps using Log-Linear method.
16 Mar 2026
v4.3 — Bloomberg DAPI live market data integration. blp_connector.py pulls SOFRRATE, USOSFR1M–30, ESTRON, EUSWF series, SONIAONH, BPSWIT series, TONAROND, JYSW series + 8 FX pairs via Bloomberg Anywhere (port 8194). Push to backend via /market-data/curves/{ccy}/bulk. Load from API button refreshes all rate grids in UI. Watch mode (--watch --interval 60) for continuous refresh.
16 Mar 2026
v4.2 — Full OIS curve store: USD SOFR, EUR €STR, GBP SONIA, JPY TONAR. 13 tenors per currency (O/N, 1M, 3M, 6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 15Y, 20Y, 30Y). Log-linear interpolation on discount factors. Market Data tab: Table view (editable grid), Chart view (multi-ccy overlay, analytics, forward curve), Bloomberg view (ticker table, source badges). FX Spots: 8 pairs with bar chart.
15 Mar 2026
v4.1 — Crypto asset class added to Pricer (Perp, Option, DeFi IRS, Quanto). SIMM IM displayed inline under every priced trade. Pricer reordered to first tab. Methodology restructured.
15 Mar 2026
v4.0 — Full multi-product pricer launched. SIMM v2.8+2506. XVA waterfall for all products.
15 Mar 2026
v3.0 — Crypto IM beta. All 51 SIMM currencies. Curvature risk. Concentration risk across all asset classes.
15 Mar 2026
v2.0 — SIMM v2.8+2506 endpoint. Full IR delta/vega/curvature, credit IG/HY, commodity 17 buckets, FX 47 pairs.
15 Mar 2026
v1.0 — Initial release. IRS Monte Carlo XVA engine. Hull-White simulation. CVA/DVA/FVA.
Rijeka Capital Markets Intelligence · Model Methodology v4.8 · 16 March 2026
SIMM v2.8+2506 per ISDA Methodology Document (December 2025) · Crypto IM: Rijeka Proprietary
IRS verified vs Bloomberg SWPM · Convertible: Andersen-Buffum (2004) CRR binomial
Rijeka (river) — where risk flows, Rijeka reads it.
github.com/MikoDevedzic/derivatives-xva-engine