Stochastic Processes

Stochastic processes for use in various models and pricing engines

Heston Processes

HestonProcess

Square-root stochastic-volatility Heston process

type HestonProcess <: AbstractHestonProcess
  s0::Quote
  riskFreeRate::YieldTermStructure
  dividendYield::YieldTermStructure
  v0::Float64
  kappa::Float64
  theta::Float64
  sigma::Float64
  rho::Float64
  disc::AbstractDiscretization
  hestonDisc::AbstractHestonDiscretization
end

HestonProcess(riskFreeRate::YieldTermStructure, dividendYield::YieldTermStructure, s0::Quote, v0::Float64, kappa::Float64, theta::Float64, sigma::Float64, rho::Float64, d::AbstractHestonDiscretization = QuadraticExponentialMartingale())

Default constructor for the Heston Process

BatesProcess

Square-root stochastic-volatility Bates process

type BatesProcess<: AbstractHestonProcess
  hestonProcess::HestonProcess
  lambda::Float64
  nu::Float64
  delta::Float64
  m::Float64
end

BatesProcess(riskFreeRate::YieldTermStructure, dividendYield::YieldTermStructure, s0::Quote, v0::Float64, kappa::Float64, theta::Float64, sigma::Float64, rho::Float64, lambda::Float64, nu::Float64, delta::Float64, d::AbstractHestonDiscretization = FullTruncation())

Constructor for the Bates Process. Builds underlying Heston process as well

Black Scholes Processes

Various types of Black-Scholes stochastic processes

Black Scholes types are based off of a GeneralizedBlackScholesProcess, with a structure seen here:

type GeneralizedBlackScholesProcess <: AbstractBlackScholesProcess
  x0::Quote
  riskFreeRate::YieldTermStructure
  dividendYield::YieldTermStructure
  blackVolatility::BlackVolTermStructure
  localVolatility::LocalConstantVol
  disc::AbstractDiscretization
  isStrikeDependent::Bool
  blackScholesType::BlackScholesType
end

BlackScholesMertonProcess

Merton (1973) extension to the Black-Scholes stochastic process

BlackScholesMertonProcess(x0::Quote, riskFreeRate::YieldTermStructure, dividendYield::YieldTermStructure, blackVolatility::BlackConstantVol, disc::AbstractDiscretization = EulerDiscretization())

Constructs a Black Scholes Merton Process, based off the GeneralizedBlackScholesProcess structure above.

Other Stochastic Processes

OrnsteinUhlenbeckProcess

type OrnsteinUhlenbeckProcess <: StochasticProcess1D
  speed::Float64
  vol::Float64
  x0::Float64
  level::Float64
end

OrnsteinUhlenbeckProcess(speed::Float64, vol::Float64, x0::Float64 = 0.0, level::Float64 = 0.0) = new(speed, vol, x0, level)

Constructor for the OrnsteinUhlenbeckProcess

GsrProcess

Gaussian short rate stochastic process

type GsrProcess <: StochasticProcess1D
  times::Vector{Float64}
  vols::Vector{Float64}
  reversions::Vector{Float64}
  T::Float64
  revZero::Vector{Bool}
  cache1::Dict{Pair{Float64, Float64}, Float64}
  cache2::Dict{Pair{Float64, Float64}, Float64}
  cache3::Dict{Pair{Float64, Float64}, Float64}
  cache4::Dict{Float64, Float64}
  cache5::Dict{Pair{Float64, Float64}, Float64}
end

GsrProcess(times::Vector{Float64}, vols::Vector{Float64}, reversions::Vector{Float64}, T::Float64 = 60.0)

Constructor for the GsrProcess