# 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

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

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

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

### BlackScholesProblem

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

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)