FX modelling under collateralization

We present the market practice for interest rate yield curves construction and pricing interest rate derivatives. Then we give a brief description of the Vasicek and the Hull-White models, with an example of calibration to market data. We generalize the classical Black-Scholes-Merton pricing formulas, considering more general cases such as perfect or partial collateral, derivatives on a dividend paying asset subject to repo funding, and multiple currencies. Finally we derive generic pricing formulae for different combinations of cash flow and collateral currencies, and we apply the results to the pricing of FX swaps and CCS, and we discuss curve bootstrapping.

Planning Processes for Transport Solutions An Application To the City of Bologna

Mathematical models and the involved methods applied to real contexts are essential tools for designing and evaluating solutions concerning physical elements and/or organizational components of transportation systems. To deal with this, the systems engineering approach is used, which considers the relationships among the transportation system elements and their performances. This approach allows quantifying the effects of transportation projects by taking into account the intrinsic complexity of the transportation system and then assessing the effects of solutions to solve – or mitigate – transportation problems. This thesis focuses on the application of the transport system engineering approach to a real city – Bologna, in northern Italy – in order to: 1. simulate the current transportation system conditions (status quo); 2. compare and assess the results obtained by two different approaches for simulating the link traffic flows on the road transportation network and their related impacts (externalities) 3. identify potential solutions to solve critical aspects, particularly in terms of traffic flow congestion and related environmental impacts (findings)