I have the following input data:
Remove["Global`*"] x = 5/30 // N; y = 0.8; μ = 0.2; T = 5; ρ = 0.8; σ (*to be determined*)
And this is the given equation:
Solve[CDF[ NormalDistribution, ((1/ Sqrt[ρ])*(((Sqrt[1 - ρ])*(InverseCDF[ NormalDistribution, (x)]) + (InverseCDF[ NormalDistribution, (CDF[ NormalDistribution, -(Log[y] + (μ - 0.5*σ^2)* T)/(σ*Sqrt[T])])]))))] == 0.0158854, σ, InverseFunctions -> True]
If I want to Solve for "ρ" it works, but whenever I try to Solve for σ i get the following error message:
"Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >>"
Is here the problem that sigma is simultanously in both an inverseCDF and a CDF?
is there a formula which can be applied in order to get rid of the CDF and inverseCDF?
Or should it be done by splitting up the given equation?
Can anybody help me?
thanks in advance