The Black Scholes equation is named after researchers Fisher Black and Myron Scholes [1], although R. Merton is also credited with contributing to it), and is a second-order parabolic partial differential equation that can be used to determine the theoretical price of a European-style call or put option. The main objective of using financial options is to hedge underlying assets, which may be currencies, stocks, indices, commodities, among others, against adverse movements in market prices. This contribution was a seminal work that gave rise to an entire field of knowledge in the area of risk and derivatives.

The original model assumes the existence of a risk-free rate, no transaction costs, no dividend payments, and no commission payments, in addition to the possibility of lending and borrowing in the market and no arbitrage opportunities. An important assumption is that the pricing model follows a geometric Brownian motion.

The model has been generalized in several directions and has had a major influence on markets and risk control. However, in recent years, some discrepancies have emerged between the theoretical and empirical models, such as those arising from the issue of volatility smile and skew.

On the other hand, in recent years, the exponential growth of data has been unprecedented throughout history. According to the International Data Corporation (ICD), 181 ZB will be reached by 2025.

Machine learning (ML) is an advanced big data technique for managing, analyzing, and processing large volumes of data that has generated new applications in various fields of basic sciences, image processing, medicine, social sciences, and business, among other areas.

ML focuses on solving practical problems by gathering a set of data and, based on statistical models, building algorithms to find solutions. Strictly speaking, machines do not learn in the same way as humans, but rather through mathematical algorithms that are applied to a collection of data called training data, producing a desired output. There are three main types of machine learning: supervised learning, unsupervised learning, and reinforcement learning.

ML learning follows a process of minimizing a loss function that compares target values with predicted outputs and also measures how well the model is representing the training data during training. In other words, the goal is to minimize the loss between the model's predictions and the target values. This minimization process is carried out through optimization, the most common being gradient descent.

In the supervised learning model, we also have classification, which is a process that predicts which category, class, or label the data belongs to. The prediction process consists of approximating a mapping function from the input variables to the discrete output variables. Another type of model is regression, which refers to the problem of forecasting numerical values given a set of inputs. Its purpose is to construct a mathematical equation that defines the output as a function of the input.

Deep learning is a category within neural networks that are modeled on the learning that occurs in the human brain and consists of an artificial network of neurons that allow a model to adjust itself by analyzing new data. With this model, each unit known as a node or neuron is the basic unit (also known as a perceptron) that applies an activation function to the inputs it receives and produces an output. These outputs pass to the next layer of neurons, which are used as inputs for their own activation functions and generate more outputs. The process is repeated until it reaches the final stage of neurons, which produces the model's result.

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