Roadmap: Path to Production¶

VALAX today covers standard equity options, vanilla rates derivatives, four pricing methods, and three stochastic models — all with autodiff Greeks and JIT compilation. This is roughly 5-10% of feature parity with production quant libraries at major banks (JPM Athena, Goldman SecDB, etc.), which have been built over 20-30 years by hundreds of quants.

The good news: the architecture (pure-functional JAX, autodiff-first, pytree data model) is arguably more modern than most bank stacks. The gap is breadth, not depth.

This roadmap organizes every missing piece into prioritized tiers. Each tier unlocks the next.

Current State¶

Area	What We Have
Instruments	`EuropeanOption`, `ZeroCouponBond`, `FixedRateBond`, `FloatingRateBond`, `Caplet`, `Cap`, `InterestRateSwap`, `Swaption`, `OISSwap`, `FXForward`, `FXVanillaOption`, `FXBarrierOption`
Models	Black-Scholes, Heston (MC), SABR (analytic + MC), LMM (MC with PCA factors)
Pricing	Black-Scholes, Black-76, Bachelier analytic; Monte Carlo (GBM, Heston, SABR, LMM); Crank-Nicolson PDE; CRR binomial tree
Greeks	1st order (delta, vega, rho) and 2nd order (gamma, vanna, volga) via autodiff; key-rate durations via curve pytree differentiation
Curves	`DiscountCurve` with log-linear interpolation, flat extrapolation
Dates	Act/360, Act/365, Act/Act, 30/360; ordinal-based date arithmetic; coupon schedule generation
Calibration	SABR and Heston calibration with LM, BFGS, and Optax solvers; parameter constraint transforms
Portfolio	`batch_price()` and `batch_greeks()` via vmap
Market Data	`MarketData` container, `MarketScenario` / `ScenarioSet` for risk factor shocks
Risk	Curve shocks (parallel, steepener, butterfly, key-rate), parametric/historical/stress scenarios, VaR, ES, sensitivity ladders with waterfall P&L

Instrument Coverage Matrix¶

A snapshot of every instrument class relevant to production bank systems, with implementation status and blocking dependencies.

✅ Implemented¶

Instrument	Asset class	Module	Pricing available
`EuropeanOption`	Equity	`instruments/options.py`	BSM, Black-76, Bachelier, SABR, MC (GBM/Heston), PDE, Lattice
`ZeroCouponBond`	Fixed income	`instruments/bonds.py`	Curve discounting
`FixedRateBond`	Fixed income	`instruments/bonds.py`	Curve discounting, YTM, duration, convexity, KRDs
`FloatingRateBond` / FRN	Fixed income	`instruments/bonds.py`	Forward projection + single-curve discounting, seasoned fixings
`Caplet`	Rates	`instruments/rates.py`	Black-76, Bachelier
`Cap` (and Floor)	Rates	`instruments/rates.py`	Black-76, Bachelier (strip pricing)
`InterestRateSwap`	Rates	`instruments/rates.py`	Analytic (replication), curve discounting
`Swaption`	Rates	`instruments/rates.py`	Black-76, Bachelier
`OISSwap` / `SOFRSwap`	Rates	`instruments/rates.py`	Telescoping float-leg identity + fixed-leg annuity (single-curve)
`BermudanSwaption`	Rates	`instruments/rates.py`	Longstaff-Schwartz MC on LMM paths
`FXForward`	FX	`instruments/fx.py`	Covered interest rate parity
`FXVanillaOption`	FX	`instruments/fx.py`	Garman-Kohlhagen, implied vol, 3 delta conventions
`FXBarrierOption`	FX	`instruments/fx.py`	Instrument defined; analytical pricing TBD
`AmericanOption`	Equity	`instruments/options.py`	Binomial tree (CRR), European/American exercise
`EquityBarrierOption`	Equity exotics	`instruments/options.py`	MC with sigmoid smoothing, knock-in/knock-out parity
`AsianOption`	Equity exotics	`instruments/options.py`	MC arithmetic and geometric averaging
`LookbackOption`	Equity exotics	`instruments/options.py`	MC floating-strike and fixed-strike variants
`VarianceSwap`	Volatility	`instruments/options.py`	Analytic (BSM), MC realized variance, seasoned pricing

🟠 Missing — Medium Priority (specific desks)¶

Instrument	Asset class	Complexity	Blocked by	Notes
`CallableBond` / `PuttableBond`	Fixed income	High	Short-rate models (P1.4)	OAS, effective duration. Most corporate bonds are callable
`CrossCurrencySwap`	Rates / FX	High	Cashflow engine + multi-curve	Notional exchange, basis spread, two currencies
`CDS`	Credit	Medium	Survival curve / hazard rates	Prerequisite for XVA (CVA). Huge market
`InflationSwap` (ZC and YoY)	Inflation	Medium	Inflation curve	Liability hedging. Growing market
`InflationCapFloor`	Inflation	Medium	Inflation curve	Black-76 on forward CPI ratio
`TotalReturnSwap`	Equity / prime brokerage	Medium	Cashflow engine	Funding + equity combined
`QuantoOption`	FX / equity cross	Medium	Correlated 2-asset MC	FX-equity correlation adjustment
`SpreadOption`	Multi-asset	Medium	2-asset MC or Kirk approx.	Option on spread (Margrabe, Kirk)

🟡 Missing — Lower Priority (structured / exotic)¶

Instrument	Asset class	Complexity	Blocked by	Notes
`Autocallable` / Phoenix	Structured products	High	SLV model, correlated MC	Multi-hundred-billion dollar market. Path-dependent, multi-asset
`WorstOfBasketOption`	Structured products	High	Correlated multi-asset MC	Correlation-sensitive, multi-asset
`RangeAccrual`	Rates / structured	Medium	MC with path monitoring	Coupon accrues while index in range
`CMSSwap` / `CMSCapFloor`	Rates	Medium	Replication or SABR integration	CMS rate with convexity adjustment
`CDOTranche`	Credit correlation	High	CDS + copula simulation	Gaussian copula, base correlation
`ConvertibleBond`	Equity-credit hybrid	High	PDE or tree with credit	Equity + credit + optionality
`TARF`	FX structured	High	MC with early termination	Target accrual range forward
`Cliquet` / Ratchet	Equity structured	Medium	Forward-starting option pricer	Popular in structured notes
`MBS`	Securitized	Very high	Prepayment models, OAS	Very US-market-specific
`CompoundOption`	Exotic	Low	BSM extension	Option on an option. Rare in practice
`ChooserOption`	Exotic	Low	BSM extension	Choose call/put at a future date

Production Priority Roadmap (Snapshot: June 2025)¶

The tier-based feature inventory below is comprehensive but feature-area oriented. This section reorganizes the most critical work into execution priorities — what a bank evaluating VALAX would need to see, in roughly the order it should be built.

This is a point-in-time snapshot. Priorities will shift as items are completed and real user feedback arrives.

Priority 1 — Foundational Infrastructure (Blocks Everything)¶

These items are hard prerequisites. Every downstream feature, product, and integration depends on them.

#	Task	Why It's Critical	Tier Ref
P1.1	Business Calendars & Date Adjustment	Every trade in a bank settles on business days. Wrong dates = wrong cashflows = wrong P&L. Precomputed holiday arrays (TARGET, NYSE, SOFR/Fed, London, Tokyo) with modified-following/preceding and end-of-month conventions.	1.3
P1.2	Cashflow Engine (Legs, Stubs, Compounding)	Real swaps have short/long stubs, compounding-in-arrears, amortizing notionals, fixing histories. The current schedule generator can't represent production trades. `FixedLeg` / `FloatingLeg` pytrees with full convention support.	1.4
P1.3	CI/CD Pipeline	No bank adopts a library without automated testing. GitHub Actions with: lint, type-check, full test suite, QuantLib comparison, coverage reporting. A gate before anything else ships.	—
P1.4	Short-Rate Models (Hull-White, G2++)	Backbone of every rates desk — needed for callable bonds, Bermudan swaptions (backward induction alternative to LSM), and IR exotics. Analytic bond prices + swaption calibration.	2.1

Priority 2 — Production Pricing Capabilities¶

These unlock entire asset classes and bring pricing to the speed and accuracy required by trading desks.

#	Task	Why It's Critical	Tier Ref
P2.1	Heston Semi-Analytic (COS / Fourier)	MC-only Heston is ~1000x too slow for real-time pricing and calibration loops. The COS method gives microsecond pricing — essential for any equity desk.	2.2
P2.2	Local Volatility + SLV	Local vol (Dupire) is the minimum standard for exotic equity pricing. SLV (Heston + leverage function) is the actual industry standard. Without this, no structured products desk can use VALAX.	2.3, 2.4
P2.3	FX Derivatives (Garman-Kohlhagen, Barriers, Delta Conventions)	FX is one of the largest derivatives markets with unique conventions (delta-space quoting). Unlocks an entire asset class.	3.3
P2.4	Credit Derivatives (CDS, Survival Curves)	Survival curves are a prerequisite for XVA (CVA). CDS pricing and hazard rate bootstrapping are foundational. Unlocks credit trading and the entire XVA workstream.	3.4

Priority 3 — Risk & Regulation (Required for Sign-Off)¶

Banks cannot go live without regulatory compliance. These items satisfy Basel requirements and complete the risk framework.

#	Task	Why It's Critical	Tier Ref
P3.1	XVA Suite (CVA, DVA, FVA at minimum)	XVA is now a first-class P&L line at every bank. CVA alone changes pricing by 10–50 bps on uncollateralized trades. This is where JAX's GPU acceleration creates the biggest competitive advantage (nested MC).	4.3
P3.2	FRTB Standardized Approach	Basel III.1/IV mandates FRTB for market risk capital. The Standardized Approach (SA) is the minimum — sensitivity-based with prescribed risk weights. Banks need this for regulatory capital reporting.	—
P3.3	Marginal / Component / Incremental VaR	Current VaR is portfolio-level only. Desks need to attribute risk to individual trades and see the marginal impact of new trades.	4.1

Priority 4 — Service Layer (Required for Integration)¶

VALAX is currently a Python library. Banks integrate pricing engines as services. This priority turns the library into a deployable system.

#	Task	Why It's Critical	Tier Ref
P4.1	API Server (gRPC + REST)	Banks integrate pricing via services, not Python imports. A gRPC server (low-latency inter-service) + REST (UIs/dashboards) with OpenAPI docs is the delivery mechanism.	—
P4.2	Market Data Adapters & Persistence	Production systems consume Bloomberg/Refinitiv feeds and store EOD snapshots. Need adapters for market data ingest and a storage layer for curves, surfaces, and fixings.	6.1
P4.3	Audit Logging & Observability	Regulatory requirement: every pricing must be reproducible. Structured logging (who priced what, when, with which market data), OpenTelemetry tracing, Prometheus metrics.	—
P4.4	Docker + Helm Deployment	Containerized deployment with GPU support, health checks, graceful shutdown, resource limits. Helm charts for Kubernetes — the standard bank deployment platform.	—

Priority 5 — Competitive Differentiators (Leverage JAX Advantages)¶

These are the features that make VALAX not just another pricing library but a fundamentally better one. They exploit the JAX-native architecture in ways traditional C++ stacks cannot replicate.

#	Task	Why It's Critical	Tier Ref
P5.1	Neural Surrogate Pricers (Differential ML)	XVA nested MC is the most compute-intensive task in banking. Neural surrogates trained with autodiff Greeks reduce compute 100–1000x. Same framework for training and deployment — VALAX's killer feature.	5.1
P5.2	GPU/TPU Benchmark Suite	Prove the value proposition with numbers. Benchmark VALAX on GPU vs QuantLib on CPU for: batch European pricing, MC VaR, XVA exposure simulation. Publish results.	—
P5.3	Deep Hedging	RL-based hedging with transaction costs is a frontier area. JAX makes the entire training loop differentiable. Positions VALAX at the cutting edge.	5.3

Recommended Execution Order¶

Q1 (Foundation):
  ├─ [P1.1] Business Calendars ──→ [P1.2] Cashflow Engine
  ├─ [P1.3] CI/CD Pipeline
  └─ [P1.4] Short-Rate Models (Hull-White)

Q2 (Pricing Depth):
  ├─ [P2.1] Heston COS / Fourier
  ├─ [P2.2] Local Vol → SLV
  ├─ [P2.3] FX Derivatives
  └─ [P2.4] Credit (CDS, Survival Curves)

Q3 (Risk & Regulation):
  ├─ [P3.1] XVA (CVA / DVA / FVA)
  ├─ [P3.2] FRTB Standardized Approach
  └─ [P3.3] Advanced VaR Decomposition

Q4 (Production Delivery):
  ├─ [P4.1] API Server (gRPC + REST)
  ├─ [P4.2] Market Data Layer
  ├─ [P4.3] Audit & Observability
  └─ [P4.4] Docker / K8s Deployment

Ongoing (Differentiators):
  ├─ [P5.1] Neural Surrogates
  ├─ [P5.2] GPU Benchmarks
  └─ [P5.3] Deep Hedging

Assessment¶

VALAX has excellent bones. The pure-functional JAX architecture is genuinely superior to what most banks run internally (mutable C++ object graphs built 20+ years ago). Autodiff Greeks, vmap batching, and GPU portability are structural advantages that compound with every new feature added.

The most urgent gap is foundational infrastructure (P1: calendars, cashflows, CI/CD) — not because it's glamorous, but because every downstream feature depends on it. A bank quant evaluating VALAX will immediately ask: "Can it handle modified-following date adjustment on a 10Y EUR swap with short front stub and compounding-in-arrears on the floating leg?" — and today the answer is no.

The highest-ROI parallel investment is short-rate models + Heston COS alongside calendars/cashflows, because they unlock the most actively traded products (callable bonds, fast equity vol calibration) while the plumbing is being built.

Tier 1: Critical Infrastructure¶

These are foundational pieces that block almost everything else. They should be built first.

1.1 Multi-Curve Bootstrapping¶

[x] Sequential bootstrap from deposits, FRAs, and par swap rates — analytic solve per pillar
[x] Simultaneous bootstrap via optimistix.root_find (Newton) in log-DF space — handles overlapping instruments
[x] Multi-curve framework — MultiCurveSet with OIS discount curve + tenor-specific forward curves, dual-curve swap bootstrap
[x] Jacobian of discount factors w.r.t. input rates via autodiff (free with JAX, verified in tests)
[ ] Basis curve support (e.g., 1M vs 3M SOFR basis)
[ ] Turn-of-year effects and stub handling

Why: Every rates product needs proper forward curves. Manual pillar specification doesn't scale.

Approach: Root-finding via optimistix.root_find on the system of bootstrapping equations. Each instrument (deposit, swap) provides one equation. The curve is a pytree — autodiff gives the Jacobian for free.

Status: Core bootstrapping implemented in valax/curves/bootstrap.py and valax/curves/multi_curve.py. Bootstrap instrument pytrees (DepositRate, FRA, SwapRate) in valax/curves/instruments.py. Both sequential and simultaneous methods produce DiscountCurve objects compatible with all existing pricing functions. Dual-curve bootstrap supports OIS discounting with separate forward projection curves.

1.2 Volatility Surface Construction¶

[x] Vol surface object — GridVolSurface with bilinear interpolation on (strike, expiry) grid
[x] SABR smile per expiry — SABRVolSurface with per-expiry SABR calibration and parameter interpolation
[x] SVI parametric fitting — SVIVolSurface with Gatheral's SVI parameterization and LM calibration
[ ] SSVI — global arbitrage-free parameterization (Gatheral-Jacquier)
[ ] Sticky-strike vs sticky-delta conventions
[ ] Local vol extraction from implied vol surface (Dupire formula)

Why: Every option product needs a vol surface. Scalar vol is a toy assumption.

Approach: Store the surface as an eqx.Module pytree with pillar data. Interpolation via cubic splines (or SABR per expiry). SVI fitting via optimistix.least_squares. The surface must be differentiable for Greeks.

Status: Three surface types implemented in valax/surfaces/: GridVolSurface (interpolated grid), SABRVolSurface (SABR per expiry with calibration), SVIVolSurface (SVI per expiry with calibration). All are callable, JIT-able, differentiable pytrees. See the Vol Surfaces guide.

1.3 Business Calendars and Holiday Schedules¶

[ ] Holiday calendar objects for major markets: TARGET, NYSE, SOFR (Fed), London, Tokyo
[ ] Date adjustment conventions: modified following, modified preceding, end-of-month
[ ] Business day counting (e.g., Bus/252 for Brazil)
[ ] Calendar combination (union/intersection for cross-currency)

Why: Every real trade settles on business days. Wrong dates = wrong cashflows = wrong prices.

Approach: Precomputed boolean arrays of holidays (JIT-compatible, no runtime lookups). Calendar as a pytree with a jnp.array of holiday ordinals. Adjustment functions operate on integer ordinals.

1.4 Trade Representation and Cashflow Engine¶

[ ] Leg abstraction — fixed leg, floating leg with compounding conventions (in arrears, in advance, compounded, averaged)
[ ] Cashflow schedule generation with proper date adjustment, stub periods (short/long front/back stubs)
[ ] Fixing histories — realized fixings for partially-settled floating legs
[ ] Amortization schedules — notional step-down for amortizing swaps
[ ] Accrued interest calculation

Why: Real swaps and bonds have complex cashflow structures. The current simplified schedule generation can't handle production trades.

Approach: FixedLeg and FloatingLeg as eqx.Module pytrees. Schedule generation takes a calendar + conventions and produces arrays of (accrual_start, accrual_end, payment_date, notional). Cashflow projection is a pure function over these arrays.

Tier 2: Models¶

New stochastic models that unlock entire product categories.

2.1 Short-Rate Models¶

[ ] Hull-White (one-factor) — mean-reverting short rate; analytic bond prices and swaption prices
[ ] G2++ (two-factor) — two correlated Hull-White factors; richer term structure dynamics
[ ] CIR — square-root diffusion, ensures positive rates
[ ] Vasicek — Ornstein-Uhlenbeck for rates (allows negative rates)
[ ] Calibration to swaption surface for Hull-White / G2++

Why: Short-rate models are the backbone of rates desks for Bermudan swaptions, callable bonds, and path-dependent IR exotics. LMM alone is not enough.

Approach: All as eqx.Module with drift/diffusion for diffrax. Hull-White has closed-form bond prices (Jamshidian) — implement both analytic and MC pricing. Calibrate to ATM swaption vols via optimistix.

2.2 Heston Semi-Analytic Pricing¶

[ ] Characteristic function for Heston model
[ ] COS method (Fang-Oosterlee) for option pricing from characteristic function
[ ] Fourier inversion (Carr-Madan / Lewis) as alternative
[ ] Calibration to vol surface using semi-analytic pricing (fast enough for optimizer loop)

Why: MC-only Heston is too slow for calibration and real-time pricing. Semi-analytic methods give prices in microseconds.

Approach: Implement the Heston characteristic function as a pure JAX function. COS method is matrix operations — naturally JAX-friendly. vmap over strikes for the full smile in one call.

2.3 Local Volatility¶

[ ] Dupire local vol extraction from implied vol surface
[ ] Local vol MC simulation via diffrax
[ ] Local vol PDE pricing (Fokker-Planck or backward Kolmogorov)

Why: Local vol is the standard model for exotic equity derivatives. It matches the entire vol surface by construction.

Approach: Dupire formula involves derivatives of the implied vol surface — autodiff through the surface pytree. Simulation via diffrax with state-dependent diffusion.

2.4 Stochastic-Local Volatility (SLV)¶

[ ] Leverage function calibration (ratio of local vol to conditional expectation of stochastic vol)
[ ] SLV MC simulation — Heston dynamics with local vol overlay
[ ] Particle method or kernel regression for leverage function estimation

Why: SLV is the industry standard for exotic equity pricing. It combines the smile-matching of local vol with realistic dynamics of stochastic vol.

Approach: Two-pass calibration: (1) calibrate Heston to vanillas, (2) compute leverage function via MC particle method. Leverage function stored as a 2D grid pytree.

2.5 Jump-Diffusion Models¶

[ ] Merton jump-diffusion — log-normal jumps added to GBM
[ ] Kou double-exponential — asymmetric jump sizes
[ ] Bates — Heston + Merton jumps (stochastic vol with jumps)
[ ] Semi-analytic pricing via characteristic functions for all three

Why: Jumps explain short-dated smile steepness that diffusion models can't capture. Critical for short-dated FX and equity options.

Approach: Characteristic functions are straightforward extensions. MC simulation via diffrax with compound Poisson jump component.

Tier 3: Products and Asset Classes¶

New instrument types and entire asset classes.

3.1 Bermudan Swaptions¶

[ ] Longstaff-Schwartz (LSM) regression for early exercise on LMM paths
[ ] American Monte Carlo with basis function selection (polynomials, neural network regressors)
[ ] Lower/upper bound estimation (Andersen-Broadie)

Why: Bermudan swaptions are among the most traded IR derivatives. Every rates desk prices them daily.

Approach: Generate LMM paths (already have this). At each exercise date, regress continuation value on state variables. Use jnp.polyval or a small neural network for regression. The exercise boundary is differentiable for Greeks.

3.2 Callable and Puttable Bonds¶

[ ] Callable bond pricing via backward induction on Hull-White tree/PDE
[ ] OAS (option-adjusted spread) calculation
[ ] Effective duration and convexity via autodiff on OAS

Why: Callable bonds are a massive market (most corporate bonds are callable). OAS is the standard risk metric.

Approach: Requires Hull-White (Tier 2.1). Build a trinomial tree or use PDE with early exercise boundary. OAS is a shift to the discount curve — autodiff gives sensitivities.

3.3 FX Derivatives¶

[x] FX forward pricing with domestic/foreign discount curves
[x] FX vanilla options — Garman-Kohlhagen (modified Black-Scholes)
[x] FX smile conventions — delta-based quoting (spot delta, forward delta, premium-adjusted delta), strike_to_delta and delta_to_strike conversion
[ ] FX barrier options — continuous and discrete monitoring (instrument defined, analytical pricing TBD)
[ ] Quanto options — correlation between FX and underlying
[ ] TARFs (Target Accrual Range Forwards) — path-dependent FX exotics via MC

Why: FX is one of the largest derivatives markets. FX options have unique smile conventions (delta-space, not strike-space).

Approach: Garman-Kohlhagen is a minor extension of Black-Scholes. FX smile needs delta-strike conversion utilities. TARFs via MC with diffrax.

Status: Core FX pricing implemented in valax/pricing/analytic/fx.py and instruments in valax/instruments/fx.py. Garman-Kohlhagen pricing, FX forward valuation, implied vol inversion, and all three delta conventions (spot, forward, premium-adjusted) with strike↔delta conversion. See the Analytical Pricing guide.

3.4 Credit Derivatives¶

[ ] Survival curve construction from CDS spreads
[ ] CDS pricing — protection and premium leg valuation
[ ] Hazard rate bootstrapping from CDS term structure
[ ] CDO tranche pricing (Gaussian copula, base correlation)

Why: Credit derivatives are essential for bank trading books and CVA computation.

Approach: Survival curves as eqx.Module pytrees (analogous to discount curves). CDS pricing is cashflow discounting with survival probabilities. CDO requires copula simulation — JAX's PRNG system handles this well.

3.5 Inflation Derivatives¶

[ ] Zero-coupon inflation swap pricing
[ ] Year-on-year inflation swap pricing
[ ] Inflation cap/floor — Black-76 on forward CPI ratio
[ ] Seasonality adjustment for monthly CPI

Why: Inflation markets have grown significantly. Real-money investors use inflation swaps for liability hedging.

Approach: Inflation curve as a pytree mapping dates to forward CPI levels. Pricing is standard cashflow discounting with CPI ratios.

3.6 Equity Exotics¶

[ ] Autocallable / phoenix notes — path-dependent with early redemption barriers, coupon barriers, knock-in puts
[ ] Worst-of basket options — multi-asset with correlation
[ ] Lookback options — floating and fixed strike
[ ] Touch / no-touch / one-touch — digital barriers
[ ] Range accruals — accrue coupon while spot is in range
[ ] Compound options — option on an option
[ ] Variance / volatility swaps — realized vol payoffs

Why: Structured products desks sell these daily. Autocallables alone are a multi-hundred-billion dollar market.

Approach: All priced via MC with appropriate payoff functions. Multi-asset requires correlated path generation (Cholesky on correlation matrix). Autocallables need path-wise barrier monitoring. SLV model (Tier 2.4) is the standard for pricing.

3.7 CMS and Spread Options¶

[ ] CMS rate convexity adjustment (replication or SABR-based)
[ ] CMS cap/floor pricing
[ ] CMS spread options — option on spread between two CMS rates
[ ] Range accrual on CMS — structured coupon products

Why: CMS products are actively traded in rates markets. The convexity adjustment is non-trivial and a classic quant problem.

Approach: CMS convexity adjustment via static replication (Hagan) or SABR integration. Spread options via 2D copula or Margrabe-like extensions.

3.8 Mortgage-Backed Securities and Convertible Bonds¶

[ ] MBS — prepayment models (PSA, CPR), OAS, effective duration
[ ] Convertible bonds — equity-credit hybrid with call/put features, PDE or tree pricing

Why: Large markets but specialized. Lower priority unless targeting specific desks.

Approach: MBS requires a prepayment model (empirical) and MC simulation on interest rate paths. Convertibles need a 1D PDE with credit and equity components.

Tier 4: Risk and XVA¶

Portfolio-level risk management and valuation adjustments.

4.1 VaR and Expected Shortfall¶

[x] Historical VaR — P&L distribution from historical scenarios
[x] Parametric VaR — delta-normal using autodiff sensitivities and covariance matrix
[x] Monte Carlo VaR — full revaluation under simulated scenarios (parametric + t-distribution)
[x] Expected Shortfall (CVaR) — tail risk measure
[ ] Marginal / component / incremental VaR

Why: Regulatory requirement (Basel III/IV). Every bank risk system computes these daily.

Approach: Scenario generation + batch repricing via vmap. Autodiff gives portfolio Greeks for parametric VaR. Full reval VaR benefits from JIT compilation and GPU acceleration — this is where JAX shines.

Status: Core framework implemented in valax/risk/. Parametric (normal/t) and historical scenario generation, curve shocks (parallel, steepener, flattener, butterfly, key-rate), full-revaluation VaR/ES via vmapped repricing. Parametric VaR via delta-normal with autodiff gradients. See the Risk guide.

4.2 Stress Testing and Scenario Analysis¶

[x] Scenario definition framework — shifts to curves, vols, spots, correlations
[ ] Historical stress scenarios — replay historical crises (2008, COVID, SVB)
[ ] Reverse stress testing — find scenarios that cause a target loss (optimization problem)
[x] P&L attribution — second-order Taylor decomposition into delta (spot, vol, rate, div), gamma, and unexplained via autodiff

Why: Regulatory requirement and core risk management practice.

Approach: Scenarios as pytree diffs applied to MarketData. Batch repricing via vmap. P&L attribution via Taylor expansion using autodiff Greeks. Reverse stress testing via optimistix.minimize.

Status: Scenario framework implemented. MarketScenario and ScenarioSet pytrees, apply_scenario for full market state shocks, named stress builders (steepener, flattener, butterfly). P&L attribution via pnl_attribution() with second-order Taylor expansion. Historical crisis replay and reverse stress testing are next.

4.3 XVA Suite¶

[ ] CVA (Credit Valuation Adjustment) — expected loss from counterparty default
[ ] DVA (Debit Valuation Adjustment) — symmetric credit charge
[ ] FVA (Funding Valuation Adjustment) — cost of funding uncollateralized exposure
[ ] MVA (Margin Valuation Adjustment) — cost of posting initial margin
[ ] KVA (Capital Valuation Adjustment) — cost of regulatory capital
[ ] Exposure simulation — expected exposure (EE), potential future exposure (PFE), exposure at default (EAD)
[ ] Netting and collateral — netting set aggregation, CSA modeling, margin period of risk

Why: XVA is now a first-class P&L item at every bank. XVA desks are among the most compute-intensive in banking.

Approach: Exposure simulation via MC (reuse existing path generators). At each simulation date, reprice the netting set (this is where GPU acceleration via JAX gives massive speedup). CVA = integral of discounted expected exposure * default probability. Autodiff gives XVA sensitivities.

Tier 5: ML and Performance¶

Machine learning integration and computational scaling.

5.1 Neural Surrogate Pricers¶

[ ] Train neural networks to approximate slow pricing functions (e.g., Bermudan swaption price as function of market state)
[ ] Differential ML — use autodiff Greeks as training targets alongside prices
[ ] Online learning — update surrogate as market moves

Why: XVA requires millions of nested pricings. Neural surrogates reduce compute by 100-1000x while preserving Greeks via autodiff through the network.

Approach: Standard neural network in equinox (already a JAX neural network library). Train on (market_state, price, greeks) triples. The surrogate is a pytree — jax.grad gives Greeks automatically.

5.2 Learned Volatility Surfaces¶

[ ] Neural SVI — neural network parameterization of the vol surface that is arbitrage-free by construction
[ ] Variational autoencoder for vol surface dynamics (generate realistic vol surface moves for risk simulation)

Why: Vol surface fitting is a daily challenge. Neural approaches can enforce arbitrage constraints more naturally than traditional parametric methods.

5.3 Reinforcement Learning for Hedging¶

[ ] Deep hedging — RL agent learns hedging strategy that minimizes a risk measure (CVaR of P&L)
[ ] Transaction cost-aware hedging
[ ] Model-free — learns from historical data, no assumed dynamics

Why: Traditional delta hedging assumes continuous rebalancing and no transaction costs. Deep hedging handles realistic frictions.

Approach: Environment = simulated market paths. Agent = neural network policy. Train with JAX + optax. The entire training loop is differentiable.

5.4 Multi-Dimensional PDE Solvers¶

[ ] ADI (Alternating Direction Implicit) for 2D PDEs (e.g., Heston PDE in (S, v) space)
[ ] Sparse grid methods for higher dimensions
[ ] Neural PDE solvers (PINNs) for high-dimensional problems

Why: Current PDE solver is 1D only. Many important models (Heston, local-stochastic vol, multi-asset) require 2D+ PDE solvers.

Approach: ADI scheme decomposes 2D operator into 1D sweeps — reuse existing tridiagonal solver via lineax. Sparse grids reduce curse of dimensionality.

Tier 6: Operations and Integration¶

Production deployment concerns.

6.1 Market Data Integration¶

[ ] Market data adapters — Bloomberg, Refinitiv, ICE, exchange feeds
[ ] Real-time curve and surface building from streaming quotes
[ ] Market data snapping — end-of-day snapshots for risk

6.2 Trade Lifecycle¶

[ ] Trade booking — create, amend, cancel trades
[ ] Event processing — fixings, exercises, expirations, settlements
[ ] Position management — aggregation, netting

6.3 Real-Time Risk¶

[ ] Incremental risk — update portfolio risk when a single trade changes (avoid full recomputation)
[ ] Streaming Greeks — real-time sensitivity updates as market data ticks
[ ] Risk limits and alerts

Why: These are necessary for production deployment but are more about systems engineering than quantitative finance. They become relevant once the pricing and risk engine is mature.

VALAX Advantages to Leverage¶

Throughout this roadmap, VALAX's JAX-native architecture provides structural advantages:

Capability	Traditional Libraries	VALAX
Greeks	Finite differences (bump-and-reprice)	Exact via `jax.grad` — faster, no numerical noise
Calibration	Numerical Jacobians	Analytic Jacobians via autodiff — faster convergence
Batch pricing	Serial loops or manual parallelism	`vmap` — one line, automatic vectorization
GPU/TPU	Requires rewrite (CUDA kernels)	Free via JAX backend swap
XVA nested MC	Cluster computing, days of runtime	GPU-accelerated, potentially real-time
Neural surrogates	Separate ML stack (PyTorch/TF)	Same framework — train and deploy in JAX
Risk sensitivities	Separate Greek engine	Any pricing function is automatically differentiable

These advantages compound as the library grows. Each new pricing function automatically supports Greeks, GPU acceleration, and batch evaluation with zero additional code.