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FinanceModels.ShortRate API Reference

Exported API

Simulation and Monte Carlo

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

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

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FinanceModels.pv_mc — Function
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.

Note

pv_mc is designed for fixed-cashflow instruments where each RatePath scenario provides the discount factors. For floating-rate instruments whose cashflows depend on the rate path, project cashflows per scenario using Projection instead.

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

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FinanceModels.short_rate — Function
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 Euler-Maruyama trapezoidal steps, the returned rate is piecewise-constant within each timestep — an approximation to the continuous short-rate process, not the exact value.

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Unexported API

FinanceModels.ShortRate.CoxIngersollRoss — Type
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)
Feller condition

The condition 2ab > σ² is required for the variance process to stay strictly positive. When violated, the short rate can reach zero; simulation uses absorption at zero (full truncation scheme) in that case.

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FinanceModels.ShortRate.HullWhite — Type
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
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FinanceModels.ShortRate.Vasicek — Type
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)
Note

The Vasicek model allows negative rates. For very negative rates or long horizons, discount factors may exceed 1.

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Please open an issue if you encounter any issues or confusion with the package.