Machine Learning Python

Using PyTorch for Neural Networks to Create Black- Scholes Model Option Pricer In this exercise, our aim is to learn the Black-Scholes European call option price formula via a deep neural network. Recall the Black-Scholes European call option price formula We first create a sample dataset of model parameters by using moneynees S/K instead of S and K separately. Thus, we create input features as 1. Moneyness: S/K with a narrow range: [0.5, 1.5] and a wide range: [0.4, 1.6] 2. Time to maturity: τ with a narrow range: [0.3, 0.95] and a wide range: [0.2, 1.1] 3. Risk free rate: r with a narrow range: [0.03, 0.08] and a wide range: [0.02, 0.1] 4. Volatility: σ with a narrow range: [0.02, 0.9] and a wide range: [0.01, 1.0] 1.1 Create the dataset Create the dataset using the narrow and wide ranges via Latin Hypercube Sampling (LHS). 1.2 Read the dataset If you cannot create the dataset, you can read it from the files [login to view URL] and [login to view URL] available at: [login to view URL] The first column is V/K, second column is S/K, third column is τ, fourth column is r and the fifth column is σ. 1.3 Divide the data into training, validation and test sets Split the data into 80% training, 10% validation and 10% test sets, which are used for training, validation and testing purposes, respectively. 1.4 Create a neural network Ceate a neural network with 4 hidden layers, with 400 neurons in each hidden layer. Use the Adam optimizer with a batch size of 1024. Initialize the first layer weights using Glorot_uniform initialization. The recommended activation function is ReLu but you are free to choose any other activation function which gives a better performance. 1