cW[ρ_]:=ItoProcess[{{0,0},IdentityMatrix[2]},{{w1,w2},{0,0}},t,{{1,ρ},{ρ,1}}];

hm=ItoProcess[{
\[DifferentialD]s[t]==μ s[t]\[DifferentialD]t+(Sqrt[r[t]])s[t]\[DifferentialD](Subscript[w, s])[t],
\[DifferentialD]r[t]==κ (θ-r[t])\[DifferentialD]t+ξ (Sqrt[r[t]])\[DifferentialD](Subscript[w, ν])[t]},
{s[t],r[t]},{{s,r},{(Subscript[s, 0]),(Subscript[r, 0])}},t,{(Subscript[w, s]),(Subscript[w, ν])}\[Distributed]cW[ρ]];

td=BlockRandom[SeedRandom[1988];RandomFunction[hm/.{μ->0,κ->2,θ->1,ξ->1/2,ρ->-1/3,(Subscript[s, 0])->25,(Subscript[r, 0])->1.25},{0,1,0.005},6,Method->"StochasticRungeKutta"]];

Row[{ListLinePlot[td["PathComponent",1],PlotLabel->"Price of the asset"],ListLinePlot[td["PathComponent",2],PlotLabel->"Volatility of the asset"]},Spacer[20]]