Finance and insurance

1] Analysis of the financial return and risk profiles of financial investments: 1.1 The process of governance and operational management of investments and financial risks: - analysis of business models (HTC, HTCS, HFT): characteristics, functioning, and regulatory constraints - analysis of the accounting treatment of financial instruments/portfolios (amortized cost, fair value through other comprehensive income, fair value through profit or loss) and objectives/characteristics of the SPPI Test/Benchmark Test; - From the concept of business model to that of business/risk management centers; - definition of the structure of financial portfolios: drivers for their definition (accounting approach, prudential supervision approach, and management approach) and operational implications; - system of market risk limits Finance and operational ceilings/sub-ceilings; 1.2 Analysis of the financial return and risk profile of bond investments: - IRR: calculation, scope and related limits - Analysis of the price function and the variability of returns on fixed-rate bonds, variable-rate bonds and callable bonds; - Deterministic risk measures: - duration, convexity, basis point value, reformulation of duration based on the forward structure of rates, scenario analysis; - the use of risk indicators in operational strategic investment ; Probabilistic risk measures: - VaR methodology: • Parametric model; • Historical simulation model; • Monte Carlo model; - Expected shortfall 1.3 Analysis of the return and financial risk profile of equity investments: modern portfolio theory: - Markowitz diversification: the role of correlation; - definition of the investment opportunity region and construction of the efficient portfolio frontier: the case of risky assets only, the case of both risky and risk-free assets, the case of no short selling, and the case of the possibility of short selling; - selection of efficient portfolios through indifference curves and identification of the portfolio with minimum variance; - the Capital Asset Pricing Model: the security market line and the beta coefficient 1.4 Analysis of the return profile and financial risks relating to operations in derivative products and forward exchange transactions: - sensitivity analysis by class/category and risk factors underlying derivative products and forward forex transactions 1.5 Operational risk management using ALMO: - static and dynamic hedging (delta hedging) - hedge accounting (micro and macro fair value hedge and cash flow hedge) 2] Valuation of financial instruments: 2.1 Multi-curve valuation framework - Reminders on the term structure of interest rates: from IRR to ZC rates, FW rates - Deposits, FRAs and interest rate futures, interest rate swaps - Bootstrapping of ZC rates - market rate interpolation methods (linear, cubic splines) - Alternative method based on reducing the number of unknowns - ZC rate interpolation - comparison of different methodologies - Need for a multi-curve valuation framework, CSA, BMR reform - Overnight Indexed Swap - Multi-curve bootstrapping: methodologies, applications, and examples - Extension to risky yield curves - Asset Swap: definitions, types, examples - Valuation of IRS and Asset Swap - Extension of the multi-curve paradigm to multi-currency instruments: valuation of FX Swap/Outright and Cross-Currency Swap 2.2 Standard market models for the valuation of interest rate derivatives - Standard market models: choice of cash flow - Normal and Lognormal Forward Model - Interest rate Cap and Floor: pricing via flat volatilities and forward volatilities - Negative rates: Shifted Lognormal Forward Model vs Normal Forward Model - Digital Cap/Floor: replication via call/put spread and inconsistency of the analytical formula - European Swaptions: pricing, sensitivities, Swaption Volatility Cube - European Bond Options, Callable Bonds: relationship between Swaptions and Bond Options, valuation, sensitivities, yield vol/price vol - Asset Swap Option: pricing and sensitivities (overview) 2.2 Standard Market Models for the Valuation of Inflation-Indexed Instruments - Zero Coupon Inflation-Indexed Swap: market conventions, bootstrapping of the CPI Forward curve, Seasonality - ZC Seasonal Swap, alternative bootstrapping of the CPI forward curve - Zero Coupon Inflation-Indexed Cap/Floor: pricing, sensitivities - Year on Year Inflation-Indexed Swap and Cap/Floor: calculation of convexity adjustment using Put-Call Parity (overview) - Inflation-linked bonds: BTP€I, BTP-Italia and related Asset Swaps - Pricing and sensitivities of Asset Swaps on BTP€i - Approximate formulas for pricing Asset Swaps on BTP-Italia (overview) 2.3 Valuation of instruments with non-standard indexation (overview) - Instruments with non-standard time lags, cash exchange and timing adjustment: valuation of Swaps with fixing in Arrears, unnatural tenor/reset Swaps, etc. - Constant Maturity Swaps, convexity adjustment: pricing using analytical approximation and the replication portfolio method - Foreign markets, Quanto correction: applications and examples

Knowledge of Microsoft Office, particularly Excel and its functions useful for financial mathematics and statistics applications.

Material (slides and Excel files) distributed by the lecturer, available on the classroom dedicated to the Financial Optimisation course. This material constitutes the main and substantial reference for learning the topics covered in class, as this is a course in which the practical component is predominant. To supplement the above material, the following texts can be referred to for further information: 1] Options, Futures and Other Derivatives – J. Hull (2022) Publisher: Pearson. With reference to this text, the main parts and chapters of reference are respectively: PART II (Markets and Forward Instruments) including Chapter 4 (Interest Rates) / Chapter 5 (Determination of Forward and Futures Contract Prices) / Chapter 7 (swaps) - PART III, specifically Chapter 11 (fundamental properties of stock options) / Chapter 14 (Wiener processes and Ito's lemma) / Chapter 15 (the Black & Merton model) / Chapter 19 (Greek letters) / Chapter 20 (volatility surfaces) - PART VII (Interest Rate Derivatives) including Chapter 29 (Interest Rate Derivatives: Standard Market Models) / Chapter 30 (Convexity, Timing and Quanto Adjustments) 2] Risk Management and Financial Institutions - J-Hull (2023) - Publisher: Pearson. With reference to this text, the relevant main chapters are: Chapter 11 (Value at Risk and Expected Shortfall), Chapter 12 (Historical Simulation and Extreme Value Theory), Chapter 14 (Interest Rate Risk), Chapter 16 (Scenario Analysis and Stress Testing) 3] Interest Rate Modelling in the Multi-Curve Framework Marc Henrard - Springer. Optional reading of the text in question to supplement the material distributed during lessons and available in the relevant classroom.

Class attendance is not mandatory but is recommended for the effectiveness of the learning process, given the practical nature of the Financial Optimization course. Classes are held every Monday and Friday from 8:00 a.m. to 10:00 a.m. and every Tuesday from 4:00 p.m. to 6:00 p.m. The classroom is 6B.

Assessment of knowledge acquired mainly in the classroom on the topics of pricing and operational management of financial investments through various practical exercises based on real cases.

Classroom lessons featuring various practical exercises based on real cases drawn from the financial operations of banks.