# Implied volatility in Monte Carlo models

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:

$$C_{mkt}= f({IV*}), \text{where: f(x) is a polynomial with the pseudo-theoretical value for IV=x, }$$

• The implied volatility of an option is a specific level of volatility that will give the option price if you put it in the standard Black Scholes formula. So you have the other parameters, like interest rate and time to maturity, then you can easily solve for the IV for a given price...... Or have misunderstood you? – Sanjay Apr 8 '19 at 21:20
• If I do not use the BS formula, but something more complex that requires simulation of the Option price, then how can I solve for IV if I do not know the exact function. My initial thought was an interpolation between points – alexbougias Apr 8 '19 at 21:23
• Two points of what? (strike,IV)-points? From the phrasing of the question it is not clear to me how your data look like? To me, your question is unclear as it is stated. Please consider editing and adding more information – Sanjay Apr 8 '19 at 21:45
• That makes much more sense. Downvote removed! – Sanjay Apr 9 '19 at 9:27