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and analysis that had been inexorably accumulating during the evolution of the Eurozone crisis.

      A big, big thank you goes to Rosario Strazzullo, coordinator of the tertiary and services national department of the CGIL. This book would not be what it is without the endless exchange of ideas, opinions, impressions between us and the always constructive interventions during the finishing and rewording of complex concepts.

      I would like to thank the President of Centro Studi NENS, Vincenzo Visco, whose clever insights and intellectual provocations have allowed me to add whole new chapters to the book.

      Finally, thanks to everyone who encouraged and supported me in recent years (and still does).

      About the Author

      Marcello Minenna, acknowledged by Risk Magazine as the “quant enforcer” and the “quant regulator”, is the head of the quantitative analysis unit at CONSOB (Commissione Nazionale per le Società e la Borsa, the Italian Securities and Exchange Commission), where he develops quantitative models for surveillance and supports the enforcement and regulatory units in their activities. Marcello teaches at several universities and holds courses for practitioners in the field of financial mathematics around the world. He graduated in economics from Bocconi University and received his MA and PhD in mathematics for finance from Columbia University and from the State University of Brescia. He is the author of several publications, including the bestselling Risk Book A Guide to Quantitative Finance.

      About the Website

      Please visit this book's companion website at www.wiley.com/go/incompletecurrency to access learning tools that provide additional coverage of the material presented in this book.

      The password for downloading the files is: eurosol123

      The list of Excel files available on the website:

      ● Implementing formulae to determine Medium-term Budgetary Objective (MTO) for selected Eurozone countries

      ● Implementing the Debt Brake Rule formulae for selected Eurozone Countries

      ● Debt/GDP ratio simulator for selected Eurozone countries

      ● Net Balance and Debt of Eurozone countries: dynamic histograms

      ● GDP and Balance of Payments of Eurozone countries: dynamic histograms

      ● Inflation in the Eurozone countries: dynamic histograms

      ● Total Asset of Eurozone Banking Systems: dynamic histograms

Chapter 1

      The Building Blocks of the Single European Currency

      This first chapter will introduce the reader to some basic economic and financial concepts that are necessary to fully understand how the Eurozone works and the fundamental determinants of the Euro monetary system. In § 1.1, with simple words the reader will learn the way a financial product is designed and evaluated, by exploiting the intuitive concepts of uncertainty, probability and risk. Then the most widespread and popular financial products (bonds, swaps, CDS), broadly publicised by the media coverage, are presented and explained with examples and charts.

      These tools do not remain in the abstract world but they are immediately put to work in the real world to describe the elementary working mechanisms of the Euro currency area. In § 1.2 we will explore the concept of credit risk with specific reference to a sovereign issuer: we will see that the riskiness of a country is closely related to the size of its public debt (especially when measured in terms of GDP) and that the sustainability of the debt depends on some key factors, inflation being surely one of the major ones. In § 1.3 the single interest rate curve is described by giving its rationale and recalling the history of its birth. In § 1.4 the reader is introduced to the functioning of the monetary policy and discovers the real mandate of the ECB and the striking differences it has with the other central banks. Finally, § 1.5 gives a tutorial overview on a theme–credit risk–that is central in the analysis of the root causes of the Eurozone crisis.

1.1 The Basic Concepts: Financial Flows, Risks and Probability Distribution

      Every financial transaction which involves the exchange of amounts of money over time (let's call them flows) is subject to some form of uncertainty. It is not possible to know for sure how much (and if) you will gain from an investment, or how much will have to be paid for a loan at a variable rate: the randomness in the occurrence and amount of flows is somehow inevitable and structural, and represents the risk of financial transactions.

      What is the value, in monetary terms today, of an investment in bonds or a fixed-rate mortgage? If I wanted to transfer the bond of my investment to someone else, how much would I get in return? If I wanted to pay off my mortgage early, how much would I have to pay? These are the main questions which professionals must answer every day to enable the smooth functioning of the financial system. Since these are financial transactions characterised by unavoidable uncertainty, and therefore a certain degree of risk, the only way to deal with them is to try to measure this uncertainty, in some way, through the use of probabilities. All financial products are valued, in the most objective way possible, looking to estimate the probability they have of producing gains or losses for the investor.

      Let's try and understand how.

      1.1.1 The Risk of Interest Rates

Imagine we are holders of a bond of Bank A, at a variable rate, with a duration of only 6 months. In this experiment, the bank cannot fail. At maturity, therefore, we have the assurance that the bank will return the invested capital (€100) plus a coupon that pays a variable interest rate. The value of the coupon will be uncertain, and will depend on the level reached by the interest rate in 6 months. With many rates possible, many coupon values are possible. For example, in Figure 1.1, nine possible values are considered for the coupon paid: only once does it reach a very low value of around €0.20, once it has a value of €1, three times the coupon pays €1.50, twice there is a coupon of €2 and on two other occasions the coupon exceeds €2.

Figure 1.1 Possible realisations of the random coupon depending on the possible values of the interest rate

What is happening is that not all levels of the rate can be reached with the same probability. This is fairly intuitive: if we observe a rate of 1.6 % today, it is more probable that in 6 months the rate will be 1.7 % as opposed to 5 % and therefore that you will get a coupon of just €1.70 instead of €5. Now imagine studying the market data today and being able to assign each possible future interest rate a precise probability: the value of the coupon in 6 months is still uncertain, but we have developed an accurate estimation of the probability of gain, which is graphically represented by a bell-shaped curve defined in technical jargon of distribution probability (see Figure 1.2).

Figure 1.2 Probability distribution of the values at the maturity of a floating rate bond issued by Bank A

      The bell-shaped curves which represent the probability distribution contain a wealth of information on the bond that we purchased from Bank A: studying this, we can now say that it is very probable (90 % represented by the central and lower areas) that the coupon that will be cashed will not be greater than €2 (total investment of €102); at the same time there is reasonable certainty, more than 90 % (central and upper areas) that my coupon will not be less than €1 (total investment of €101). It's

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