Financial Models

Financial Models

The financial models functionality is provided by DiffEqFinancial.jl and helps the user build and solve the differential equation based financial models.

SDE Model Library

The following constructors create SDEProblem types which can be solved using the stochastic differential equation solvers.

HestonProblem

\[dS = μSdt + \sqrt{v}SdW_1 \\ dv = κ(Θ-v)dt + σ\sqrt{v}dW_2 \\ dW_1 dW_2 = ρ dt\]

Constructor:

HestonProblem(μ,κ,Θ,σ,ρ,u0,tspan)

GeneralizedBlackScholesProblem

\[d \ln S(t) = (r(t) - q(t) - \frac{Θ(t,S)^2}{2})dt + σ dW_t\]

Solves for $log S(t)$. Constructor:

GeneralizedBlackScholesProblem(r,q,Θ,σ,u0,tspan)

BlackScholesProblem

\[d \ln S(t) = (r(t) - \frac{Θ(t,S)^2}{2})dt + σ dW_t\]

Solves for $log S(t)$. Constructor:

BlackScholesProblem(r,Θ,σ,u0,tspan)

ExtendedOrnsteinUhlenbeckProblem

\[dx = a(b(t)-x)dt + σ dW_t\]

Constructor:

ExtendedOrnsteinUhlenbeckProblem(a,b,σ,u0,tspan)

OrnsteinUhlenbeckProblem

\[dx = a(r-x)dt + σ dW_t\]

Constructor:

OrnsteinUhlenbeckProblem(a,r,σ,u0,tspan)