Validation of an intermediate-complexity flood risk model for climate change adaptation

In questo lavoro di tesi viene presentato e validato un modello di rischio di alluvione a complessità intermedia per scenari climatici futuri. Questo modello appartiene a quella categoria di strumenti che mirano a soddisfare le esigenze identificate dal World Climate Research Program (WRCP) per affrontare gli effetti del cambiamento climatico. L'obiettivo perseguito è quello di sviluppare, seguendo un approccio ``bottom-up" al rischio climatico regionale, strumenti che possano aiutare i decisori a realizzare l'adattamento ai cambiamenti climatici. Il modello qui presentato è interamente basato su dati open-source forniti dai servizi Copernicus. Il contributo di questo lavoro di tesi riguarda lo sviluppo di un modello, formulato da (Ruggieri et al.), per stimare i danni di eventi alluvionali fluviali per specifici i livelli di riscaldamento globale (GWL). Il modello è stato testato su tre bacini idrografici di medie dimensioni in Emilia-Romagna, Panaro, Reno e Secchia. In questo lavoro, il modello viene sottoposto a test di sensibilità rispetto a un'ipotesi enunciata nella formulazione del modello, poi vengono effettuate analisi relative all'ensemble multi-modello utilizzato per le proiezioni. Il modello viene quindi validato, confrontando i danni stimati nel clima attuale per i tre fiumi con i danni osservati e confrontando le portate simulate con quelle osservate. Infine, vengono stimati i danni associati agli eventi alluvionali in tre scenari climatici futuri caratterizzati da GWL di 1.5° C, 2.0° C e 3.0°C.

Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.