Module repack_sim 

The repack gap by Monte Carlo: crises, the valuation trigger and its lag.

The closed forms of repack_gap stop where a diffusion stops. A valuation trigger catches an issuer that deteriorates slowly, so with a diffusive intensity alone the gap is priced close to zero. The exposure is a crisis: a spread jump that gaps the collateral through the trigger, or straight into default. This module simulates it, in f64 only. Risk is a central difference on common random numbers, never AD.

• Factors. The Hull-White factor x, the intensity factor y and both their time integrals are stepped exactly from their joint Gaussian law over each step, under the piecewise volatility term.
• Default. Weighted by survival rather than drawn: each path carries exp(−∫ψ − ∫y), ψ matching the issuer’s risky discount factors in closed form including the covariance and the compound-Poisson jump term Λ_J.
• Crises. A path’s first crisis is drawn exactly. At it, the share p of the weight defaults at once; the rest continues with the intensity raised by an exponential jump of mean m. Later crises enter through the exact factor exp(−Λ_J(θ, t)), which keeps the default mass unbiased (the process is independent of the diffusion and memoryless). With repeat_crises every crisis is simulated instead.
• Trigger. On each monitoring date, and right after a crisis, the collateral is priced in closed form on the path’s state. Below level·N the note terminates and the collateral is sold liquidation_lag_days later.

Structs

Claim 🔒

A default claim: its note-currency flows, affine in x, and its collateral-currency flows, affine in x_f and worth S each.

CrisisDraw 🔒

CrossStep 🔒

One step of a cross-currency note: the Cholesky factor of the innovation covariance of (x, y, ∫x, ∫y, x_f, ∫x_f, σ_S·W), the collateral factor’s carries, and the quanto drift’s means.

GapLegs

The simulated charge split by what ended the note.

GapProfileRow

One default date’s profile.

Model 🔒

Everything deterministic a simulation reads, resolved from one view.

Monitor 🔒

A monitoring date and the sale its breach would lead to, with every bond and drift read on them.

PathOutcome 🔒

What one path contributes.

Prepared 🔒

The simulation’s prepared dates and the bonds read on them. The grid — every date a path is read on but a crisis — depends on the note alone.

SimulatedGap

The simulated repack gap.

SimulationSettings

How a simulation runs.

State 🔒

A path’s state: the factors, their integrals, and its time.

StepLaw 🔒

One step’s exact law: the Cholesky factor of its innovation covariance and the carries of the state it starts from.

Stream 🔒

A path’s own stream: SplitMix64 seeded from (seed, stream), normals by Box–Muller. The second member of an antithetic pair negates the normals and reflects the uniforms of the first.

Tally 🔒

One scenario’s running sums over the paths.

Trajectory 🔒

A path’s draws read on the grid: the diffusive states, and its crises — each with the state at it and, under a trigger, at its sale.

Xccy 🔒

What a cross-currency note adds to the model: the collateral currency’s Hull-White factor, the correlations, and the FX rate’s spot and volatility (note units per collateral unit). Under the note currency’s measure the collateral currency’s factor drifts by −ρ_fS·σ_f·σ_S and S_t = S_0·exp(∫r_d − ∫r_f − ½σ_S²t + σ_S·W_t), so E[D_d(t)·S_t] = S_0·P_f(0,t).

Enums

Off 🔒

A point a path is read on off the grid: crisis k, or its sale.

Constants

CRISIS_SALT 🔒

The salt that keeps a path’s crisis uniforms off its normals’ stream, so the normals never move with the crisis rate.

Functions

cholesky 🔒

The lower Cholesky factor of a covariance, a zero row where a variance is exhausted (a zero volatility) rather than a NaN.

cholesky_n 🔒

The lower Cholesky factor of an N×N covariance, as cholesky.

cross_covariance 🔒

The covariance of (x, y, ∫x, ∫y, x_f, ∫x_f, σ_S·W) over [s, t] given the state at s, with the means the collateral factor’s quanto drift −ρ_fS·σ_f·σ_S adds to x_f and ∫x_f.

e_int 🔒

∫_{v1}^{v2} e^{−k·v} dv.

evaluate 🔒

repack_gap_risk_sweep 🔒

simulate_repack_gap_risk, with the inputs whose bumps stepped paths of their own.

run_scenarios 🔒

Runs every scenario on the same paths. Scenarios that share their dynamics share each path’s trajectory: it is stepped once per path per dynamics, and read under each scenario’s market. Returns the tallies and, per scenario, whether its trajectory was its own rather than the first scenario’s.

simulate_repack_gap

The repack gap of note by Monte Carlo against view — resolved for RepackNote::simulation_factors — under settings, valuation trigger and crises included.

simulate_repack_gap_risk

The simulated gap’s sensitivity to every lifted market input of market, by a central difference of ±1e-6 through the lift, every leg on the same paths. An input the simulation does not read is reported as zero without a run; one pinned at the edge of its admissible range is differenced one-sided.

step_covariance 🔒

The 4×4 covariance of (x_t, y_t, ∫_s^t x, ∫_s^t y) given the state at s.

weighted_quantile 🔒

The weighted q-quantile of (weight, value) samples.

Type Aliases

Affine 🔒

A claim or collateral bond at one date: (amount, A, B_x, B_y) per flow, worth Σ amount·A·e^{−B_x·x − B_y·y}.

Sensitivities 🔒

Each lifted input with the simulated gap’s sensitivity to it.