I am new to Quantitiative Finance. Coming from Computer Science domain, I wanted to clear the key distinguishing factor between analytical, numerical and ML based models for option pricing.
As far as I have learned, following are the differences between these three.
1- Given the required parameters, we can say that the price calculated for a call or put option using Black-Scholes Formula is an analytical approach as it gives a closed form answer while the underlying asset is operating with Black-Scholes asssumption.
2- If we use Monte-Carlo method to get the price for an option, it will be considered as a numerical approach because to get an answer for a given data point, the algorithm will have to extrapolate
n paths for the under lying asset using geometric Brownian Motion formula hence making it numerical in nature.
3- If we use any Machine Learning or Deep Learning model given the input parameters from the data, it will be considered as a machine learning based approach as it will use machine learning or deep learning parameteric approach to learn the underlying pattern of the option price and hence predict the value.
Please let me know if I am missing something or am mistaken in any of the above concepts.