Hi, my name is Maxime and I had the pleasure to do an internship at the Scuola Normale Superiore in Pisa on the modelization of decentralised exchanges based on stochastic processes. I am French and for two months I lived in Pisa to have a foreign experience in research.

My academic background is mainly fundamental physics, but after learning how stochastic processes could be applied to other fields of research than physics, I wanted to learn more on creating models for financial exchanges. 
The main objective of my study was to create a model (numerical or/and theoretical) for decentralised exchanges of cryptocurrencies by considering that the events were following a Poissonian rate evolution.

During my study, I first analysed data of Limit Order Book (LOB) markets and I tried to create a numerical model with stochastic processes, with the help of what has already been done in its theoretical analysis. My goal was to understand how stochastic processes can be used to create a model for financial exchanges by learning how to do it theoretically, to then apply this to create a numerical model with Python coding. 
After verifying that my numerical model was efficient, I modified it to correspond to a decentralised exchange, where 2 volumes of offers for selling/buying cryptocurrencies interact with each other.

The model I created had several issues, but after they have been solved, some instability persisted. I identified some that it comes from the interaction between 2 classical events (which also happen for LOB markets) and one event which is specific to the exchange we study (the SWAP event where the cryptocurrencies are exchanged). I also found a theoretical model in the case when the price of one of the currencies is really high (>100) that corresponds very well to the results of the numerical model. In this case, the model actually behaves like a model for LOB markets.

Throughout my experience in Pisa, I had the support of my host institution (the Scuola Normale Superiore) and I received a very helpful assistance on how to set up in my new internship thanks to the TNA program.

The diploma of my home institution requires an international experience in research labs, and the TNA program is a great way of having support when travelling to a foreign country and settling in. Overall my experience at the Scuola Normale Superiore has been really great, with nice people ready to help when needed and a beautiful historical building. 

I really enjoyed living in Pisa, while of course there is the Pisa tower and the cathedral, many events are planned in June and July and there is always something happening in the city centre. This time of the year is especially nice for the weather and the beautiful walks along the Arno river with breathtaking sunsets. 

To students still wondering about it, I strongly recommend having a foreign experience. Interacting with people in a foreign country with a different language, learning a new culture and meeting new people is becoming more and more important as globalisation has never been so important. 

It broadens your ideas and perspective on the world and the people who contribute to make it better. In the end, this has been a great journey. I could learn a lot about mathematical finance and how to use physics to analyse financial exchanges, and I improved my skills in Python coding and modelisation, and on top of that, thanks to my interactions with students in Pisa, I practised my knowledge of Italian to finally speak Italian!