In this exercise set you familiarise yourself with the inner working of
keras for deep neural networks. Make sure you followed the technical prerequisits described in Absalon on how to install the required software on your machine before you start working on the exercises.
You will apply well-known methods such as random forests and neural networks to a simple application in option pricing. More specifically, we are going to create an artificial dataset of option prices for different values based on the Black-Scholes pricing equation for call options. Then, we train different models to learn how to price call options without prior knowledge of the theoretical underpinnings of the famous option pricing equation.
- Simulate prices for Call options based on a grid of different combinations of times to maturity (
T), risk-free rates (
r), volatilities (
sigma), strike prices (
K), and current stock prices (
S). Compute the Black-Scholes option price for each combination of your grid.
- Add an idiosyncratic error term to each observation such that the prices considered do not exactly reflect the values implied by the Black-Scholes equation.
- Split the data into a training set (which contains some of the observed option prices) and a test set that will only be used for the final evaluation
- Create a
recipewhich normalizes all predictors to have zero mean and unit standard deviation.
tidymodelsto fit a neural network with one hidden layer (
mlp) on the training data.
tidymodelsto fit a random forest (
rand_forest) on the training data.
- Figure out how you can use
kerasto create a deep neural network which predicts option prices from the set of input parameters. Figure out how to set the activation function, the number of perceptrons per layer and compile the model.
- Fit the deep neural network with the pre-processed training data (hint, this is a bit tricky, you may want to consult the function
- Evaluate the predictive performance of your competing model. Which model performed best in the test sample to predict option prices?
All solutions are provided in the book chapter Option pricing via machine learning and the lecture slides