FinanceModels.ShortRate API Reference

simulate(model::AbstractStochasticModel;
         n_scenarios=1000, timestep=1/12, horizon=30.0,
         rng=Random.default_rng())

Generate n_scenarios interest-rate paths. Each path is returned as a RatePath (an AbstractYieldModel) so it plugs directly into present_value, discount, etc.

Discretisation schemes:

• Vasicek / Hull-White: the exact Gaussian transition density, so the simulated short rate has no discretisation bias at any timestep.
• Cox-Ingersoll-Ross: full truncation (Lord, Koekkoek & Van Dijk, 2010) — an auxiliary process may go negative while the observed rate is max(x, 0). Weak bias vanishes as timestep → 0, but is material for coarse steps when the Feller condition is strongly violated.

In all cases the cumulative discount integral $∫₀ᵗ r(s)\,ds$ is accumulated with the trapezoidal rule between grid points, so pathwise discount factors (and hence pv_mc) retain an integration error that grows with timestep even when the short-rate transition itself is exact.

pv_mc(model, contract;
      n_scenarios=1000, timestep=1/12, horizon=nothing,
      rng=Random.default_rng())

Estimate the expected present value of contract under the stochastic model by averaging present_value across simulated scenarios.

The horizon should cover the contract's maturity. The default (maturity + 1) ensures this.

short_rate(path::RatePath, t)

The instantaneous short rate r(t) for a simulated scenario.

RatePath stores the cumulative integral ∫₀ᵗ r(s) ds as a LinearInterpolation. The short rate is the derivative of this cumulative integral.

Because the cumulative integral is built from trapezoidal steps, the returned rate is piecewise-constant within each timestep — an approximation to the continuous short-rate process, not the exact value.

CoxIngersollRoss(a, b, σ, initial)

Cox-Ingersoll-Ross (1985) mean-reverting short-rate model:

dr = a(b - r) dt + σ √r dW

Arguments

• a: speed of mean reversion
• b: long-term mean rate (continuous compounding). Can be passed as a Real or Continuous(b).
• σ: volatility
• initial: initial short rate r₀ (a Rate object or Real)

HullWhite(a, σ, curve)

Hull-White (1990) one-factor model:

dr = (θ(t) - a r) dt + σ dW

where θ(t) is calibrated to fit the initial term structure curve.

Arguments

• a: speed of mean reversion
• σ: volatility
• curve: an existing yield model providing the initial term structure

Vasicek(a, b, σ, initial)

Vasicek (1977) mean-reverting short-rate model:

dr = a(b - r) dt + σ dW

Arguments

• a: speed of mean reversion
• b: long-term mean rate (continuous compounding). Can be passed as a Real or Continuous(b).
• σ: volatility
• initial: initial short rate r₀ (a Rate object or Real)