Namespace NanoQL.Processes
Classes
- BatesProcess
The Bates process: the Heston square-root stochastic-volatility process with log-normal jumps, dS = (r − q − λm)S dt + √v S dW₁ + (e^J − 1)S dN, dv = κ(θ − v) dt + σ√v dW₂, dW₁dW₂ = ρ dt, N a Poisson process of intensity λ and J normal with mean ν and standard deviation δ, m = e^{ν + δ²/2} − 1.
- BlackProcess
Black's (1976) process for a forward or futures contract, d ln S(t) = −σ(t, S)²/2 dt + σ dW_t: the generalized process with its risk-free curve as the dividend curve too.
- BlackScholesMertonProcess
Merton's (1973) extension of the Black-Scholes process to a stock or stock index paying a continuous dividend yield, d ln S(t) = (r(t) − q(t) − σ(t, S)²/2) dt + σ dW_t.
- BlackScholesProcess
The Black-Scholes (1973) stochastic process, d ln S(t) = (r(t) − σ(t, S)²/2) dt + σ dW_t: the generalized process with no dividend yield. The interface is expressed in S; the internal calculations work on ln S.
- CoxIngersollRossProcess
The Cox-Ingersoll-Ross process, governed by dx(t) = k(θ − x(t))dt + σ√x(t) dW(t), discretized by Leif Andersen's quadratic-exponential scheme ("Efficient Simulation of the Heston Stochastic Volatility Model").
- EndEulerDiscretization
Euler end-point discretization for stochastic processes: over a time interval Δt, the drift μ(t0 + Δt, x0) Δt, the diffusion σ(t0 + Δt, x0) √Δt and the covariance σ(t0 + Δt, x0) σ(t0 + Δt, x0)ᵀ Δt.
- EulerDiscretization
Euler discretization for stochastic processes: over a time interval Δt, the drift μ(t0, x0) Δt, the diffusion σ(t0, x0) √Δt and the covariance σ(t0, x0) σ(t0, x0)ᵀ Δt.
- ForwardMeasureProcess
A stochastic process whose dynamics are expressed in the forward measure of a time T.
- ForwardMeasureProcess1D
A one-dimensional stochastic process whose dynamics are expressed in the forward measure of a time T.
- G2ForwardProcess
The forward G2 stochastic process: G2Process's in the forward measure of a time T, its state again shifted so that z₁ + z₂ = r(t), with the T-forward corrections to the drift and the conditional expectation.
- G2Process
The G2 stochastic process: the two-factor G2++ process with its state shifted so that the two components sum to the short rate, (z₁, z₂) = (x + φ(t), y), x and y the zero-mean Ornstein-Uhlenbeck factors and φ the deterministic offset that fits the initial curve; without a curve, the two zero-mean processes (φ ≡ 0).
- GJRGARCHProcess
The GJR-GARCH(1,1) process in its continuous-time limit: dS = μS dt + √v S dW₁ and dv = (ω + (β + αq₂ + γq₃ − 1)v) dt + (ασ₁₂ + γσ₁₃)v dW₁ + √(α²(σ₂² − σ₁₂²) + γ²(σ₃² − σ₁₃²) + 2αγ(σ₂₃ − σ₁₂σ₁₃)) v dW₂, with the moments of the news shocks at the market price of risk λ, the daily parameters scaled by the days per year. Its state is the underlying and the annualized variance.
- GarmanKohlagenProcess
The Garman-Kohlhagen (1983) process for an exchange rate, d ln S(t) = (r(t) − r_f(t) − σ(t, S)²/2) dt + σ dW_t: the generalized process with the foreign risk-free curve as the dividend curve. QuantLib's spelling of the class name is kept.
- GeneralizedBlackScholesProcess
The generalized Black-Scholes stochastic process, d ln S(t) = (r(t) − q(t) − σ(t, S)²/2) dt + σ dW_t, on a risk-free curve, a dividend curve and a Black volatility, with its local volatility σ(t, S) derived from the Black one. The interface is expressed in S; the internal calculations work on ln S.
- GeometricBrownianMotionProcess
The geometric Brownian-motion process, governed by dS(t, S) = μS dt + σS dW_t.
- GsrProcess
The GSR model's state process, with piecewise constant volatilities and reversions, its dynamics expressed in the forward measure of a time T. For a derivation of the formulas, see http://ssrn.com/abstract=2246013.
- HestonProcess
The Heston square-root stochastic-volatility process: dS = μS dt + √v S dW₁, dv = κ(θ − v) dt + σ√v dW₂, with dW₁dW₂ = ρ dt. Its state is the underlying and the variance.
- HestonSLVProcess
The Heston stochastic-local volatility process: the Heston process's spot with its volatility √v scaled by a leverage function L(t, S), and its variance's volatility scaled by a mixing factor.
- HullWhiteForwardProcess
The forward Hull-White stochastic process: HullWhiteProcess's dynamics in the forward measure of a time T, the drift less B(t, T)σ² and the expectation less M_T(t₀, t₀ + Δt, T).
- HullWhiteProcess
The Hull-White stochastic process: the short rate r = x + α(t), x an Ornstein-Uhlenbeck process of speed a and volatility σ from the curve's instantaneous forward at 0, and α(t) = f(t) + ½(σ(1 − e^(−at))/a)², f the curve's instantaneous forward.
- HybridHestonHullWhiteProcess
The three-factor hybrid of a Heston equity and a Hull-White short rate in its forward measure: its state is the underlying, its variance and the short rate, the equity correlated with the short rate.
- JointStochasticProcess
A multi-model process for hybrid products: its constituents' states stacked, their factors correlated across models by a derived class's cross-model correlation.
- Merton76Process
The Merton-76 jump-diffusion process: a Black-Scholes-Merton diffusion with lognormal jumps at a Poisson intensity.
- MfStateProcess
The Markov-functional model's state process, dx = σ(t) e^{at} dW(t), with a piecewise constant volatility σ and a constant reversion a.
- OrnsteinUhlenbeckProcess
The Ornstein-Uhlenbeck process, governed by dx = a (r − x_t) dt + σ dW_t.
- SquareRootProcess
The square-root process, governed by dx = a(b − x_t) dt + σ√x_t dW_t.
- StochasticProcessArray
An array of correlated one-dimensional stochastic processes.
Enums
- GJRGARCHProcessDiscretization
The schemes GJRGARCHProcess steps by: QuantLib's
GJRGARCHProcess::Discretization.
- HestonProcessDiscretization
The schemes Evolve(double, Vector, double, Vector) steps by: QuantLib's
HestonProcess::Discretization.
- HybridHestonHullWhiteProcessDiscretization
The schemes HybridHestonHullWhiteProcess steps by: QuantLib's
HybridHestonHullWhiteProcess::Discretization.