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I have a python script set up to run a loop to plug in different values for IV into the binomial model to get an option price as close as possible to the market price. My issue is that at the moment my script is painfully slow. My question is what should be my starting value for sigma? The historical annualized vol? And what method is the most efficient to get a precise IV in as few loops as possible?

My current method looks something like this: Sigma = sigma/Vega/100 I saw an alternative online that looked like this: Sigma =sigma+(price-price1)/Vega

Not sure which one is better or what other alternatives there are

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