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I am trying to derive a Stock Price Distribution for a particular time frame. Meaning thereby, let's say Market is about to close in 30 minutes and I want to calculate Stock Price Distribution for the opening of the next day. I have read some of the research paper(s), in which they have said that by double differentiating the call prices we can infer the Stock Price Distribution. Reference: https://medium.com/engineer-quant/inferring-stock-price-distribution-from-option-quotes-85b2f1ed16ff

The Problem with above approach is that if the options is about to get expire in 7 days, then the stock distribution can be derive for the 7 days only. But If I want to derive for some custom time frame, I am getting stuck. What should be the solution for this?

Should I be deriving the Probability Density through Monte Carlo, and if yes, how to set the parameters for gap up and gap down in the stock in the Monte Carlo approach? Or some other efficient method can be used for this?

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