Suppose I want to get the implied volatility for a given option, whose process does not generate a closed-form formula. In that framework, how is the IV calculated, given the fact that bisection method does not work due to error in simulated value of the call?
My initial thought was:
2) Suppose that I want to price a Call Option with given parameters, whose market price is $C_{mkt}=11$.
1)Simulate N theoretical prices with different values of volatility. Fit a polynomial on the series $\{Theoretical_{j_1},Theoretical_{j_2},...,Theoretical_{j_N}\}$,
where: $Theoretical_i=\text{Theoretical price for option with IV}=j_i $
$\text{and } \{j_1,j_2,...,j_N\} \text{is a set of IVs}$
3) Find the $IV^*$,
that gives:
$C_{mkt}= f({IV*}), \text{where: f(x) is a polynomial with the pseudo-theoretical value for IV=x, }$