**22nd January - 11:30 (****Link: https://videoconf-colibri.zoom.us/j/87292833142****) **

A Call option is a financial contract that gives his holder the right, but not the obligation, to buy some underlying asset at some specified price in a specific moment in time. In this lecture we will talk about the Black-Scholes model and the well known pricing formula for European Call Options. We will look at the mathematics behind this formula and how we can use it to define the prices for several other financial products.

The general equilibrium theory aims to explain the relations between demand and supply and how they determine prices and allocations in several markets that are simultaneously active in an economy. The goal in general equilibrium theory is to achieve models that are closer to the economic and financial reality, but in an abstract framework, where formalization and the introduction of mathematical techniques is possible. The general equilibrium analysis include the study of the conditions that guarantee its existence, uniqueness, stability and efficiency. This thesis aims to contribute to the literature on general equilibrium with bankruptcy and trading constraints , by presenting a proof of equilibrium existence in an economy with exogenous trading constraints that lead to market exclusion and that induce endogenous credit segmentation. To prove equilibrium existence in this economy, we use an impatience property on agents' preferences, that allows us to find upper bounds to securities and debt contract prices. Moreover, with the obligation to constitute colateral when trading debt contracts, we avoid return rates equal to zero, which ensures that equilibrium is not trivial due to pessimistic expectations.

**__________________________________________________**

Pedro Mota has a MSc in Statistics and Optimization and a PhD in Mathematics with a specialization in Statistics (FCT NOVA). He is currently an Assistant Professor at Departamento de Matemática of FCT NOVA and a researcher at CMA - Centro de Matemática e Aplicações, FCT NOVA. His main research areas include Statistics of Stochastic Processes and Financial Mathematics with several papers published in this areas. In more recent years, he has been involved in several Mathematics outreach initiatives among younger and pre-university students, being a member of ClubeMath.

I’m Carolina and I’m 23 years old. I started studying at FCT in 2015, where I made a bachelor in Mathematics. In 2018 I started a master in Mathematics and Applications, with a specialization in Financial Mathematics, a course I had been aiming for since my arrival at FCT.