# Deep Learning Equity Derivatives

We are very happy to host in this blog the theses of some undergraduates students of the Master’s Degree Course in Quantitative Finance at University of Bologna.

These theses are all about Deep Learning applied to financial markets, showing very interesting aspects. The students used a high performance computing infrastructure provided by E4, to make their analysis.

The first thesis we host is entitled Deep Learning Equity Derivatives and was written by Alessio Peroni and Giovanni Amici.

**Deep Learning Equity Derivatives** is a research thesis consisting in evaluating the application of Deep
Learning (a branch of Machine Learning) to financial derivatives valuation, with the Heston’s stochastic volatility model. The project is focused on derivatives of shares (i.e. taking shares as financial instruments underlying), but the method can easily be generalized and used for FX or interest rate derivatives.

The idea of using Deep Learning in pricing comes from the fact that derivatives valuation can require a huge amount of computational time, especially if these derivatives are ‘exotic’ and if they are priced with a high accuracy. An exotic derivative is a financial instrument with quite a complex structure, It usually meaning that there is not a closed form mathematical formula to solve it, but instead one needs to apply some numerical methods as for example a Monte Carlo simulation. Monte Carlo simulation is a technique which, in this case, permits to generate a certain number of random paths of the underlying stock price, according to some pre-defined dynamics, and then to derive the derivative price taking into consideration all of these paths.

As regards the methodology used, there are two most innovative aspects. First, to train neural networks, data from synthetic market have been used. In fact, to build a dataset of reasonable size to train a network, the entire history of financial markets wouldn’t be enough. Another fundamental point is that of the calibration of the parameters of the model used for the dynamics of the underlyings (Heston). The innovative idea was to use surfaces as input from the neural network of volatility, which are easily observable parameters on the market. In this way, to price an option, it is sufficient to have a volatility surface and the specific parameters of the contract that we want to price, i.e. maturity e strike.

To know more, download the PDF.

Or, please, contact the authors Alessio Peroni and Giovanni Amici.