Advanced Laboratory in Financial Risk Management
A.Y. 2024/2025
Learning objectives
There are 3 primary objectives for this course:
(1) help students understand the basics of financial derivatives like options, forwards, futures, and swap contracts.
(2) how to use the Binomial Model as the basic framework to obtain arbitrage-free prices of Call and Put options, Forwards and Futures contracts. The emphasis is on intuitive understanding of the pricing models rather than mathematical derivations.
And
(3) understand various investment strategies that combine Call and Put options with the underlying stock, or Exchange Traded Funds (ETFs).
(1) help students understand the basics of financial derivatives like options, forwards, futures, and swap contracts.
(2) how to use the Binomial Model as the basic framework to obtain arbitrage-free prices of Call and Put options, Forwards and Futures contracts. The emphasis is on intuitive understanding of the pricing models rather than mathematical derivations.
And
(3) understand various investment strategies that combine Call and Put options with the underlying stock, or Exchange Traded Funds (ETFs).
Expected learning outcomes
At the end of the Laboratorio, students will 1) Know how to compute gains/losses from going long or short futures contracts; 2) how to create synthetic securities using stocks and bonds; 3) understand how to trade (speculate with) Futures contracts, and Call and Put options in bullish and bearish markets.
Lesson period: Third trimester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Third trimester
Course syllabus
This course lays the foundation for a deep understanding of financial derivatives, risk management and structuring of financial investment instruments. The emphasis is on intuitive understanding rather than mathematical derivations.
Below is a breakdown of the key topics:
1. Financial Options: Fundamentals and Pricing
Definition of call and put option contract - Reasons for buying calls and puts - Other typical European payoffs - Definition of arbitrage opportunity - Definition of Forward Price - Put Call parity - How to build a binomial tree and how to use it to price an option - Relationship between volatility and option value - Definition of time value - Binomial Tree multistep - Call Option Pricing Example in Excel and Python - Black Scholes Closed Formula - Montecarlo Method
2. Hedging and Sensitivity Analysis
Mission of an options trader - Description of the main sensitivities: Delta, Gamma, Vega, Theta, Rho - Trader and Risk Manager's point of view regarding the use of sensitivities
3. Risk Management
Mission of a Risk Manager - Profit and Loss Explained - Historic bootstrap - Computing VaR and Expected Shortfall - Model Risk - Other Risk Management measures
4. Certificates and Structuring
Goal of the issuer, subscriber, and structurer - Static replication - Structuring using options - Mission of a structurer in defining the certificate features - Certificate classification - Examples of certificate structuring: Bons Cap, Autocallable and Leverage certificate
5. Fixed Income Instruments
Description of a fixed rate bond - Yield to Maturity - Commonly used Risk Measures : Duration, PVBP, convexity - Spread analysis: Z-spread, ASW-Spread I-Spread - Floating Rate Note - Interest Rate Swap - Cap and Floor - Swaption - Futures - Risk analysis of the main fixed income structured bond: Collared Bond, Reverse Floater, Callable, Puttable, CMS bond.
Key Skills Developed
1. Option Pricing: Using binomial models, Black-Scholes, and Monte Carlo simulations.
2. Risk Metrics: Quantifying and managing financial risk.
3. Product Structuring: Designing and analyzing structured products and certificates.
4. Interest Rate Instruments: plain vanilla and structured bonds, spread analysis and interest rate derivatives.
Below is a breakdown of the key topics:
1. Financial Options: Fundamentals and Pricing
Definition of call and put option contract - Reasons for buying calls and puts - Other typical European payoffs - Definition of arbitrage opportunity - Definition of Forward Price - Put Call parity - How to build a binomial tree and how to use it to price an option - Relationship between volatility and option value - Definition of time value - Binomial Tree multistep - Call Option Pricing Example in Excel and Python - Black Scholes Closed Formula - Montecarlo Method
2. Hedging and Sensitivity Analysis
Mission of an options trader - Description of the main sensitivities: Delta, Gamma, Vega, Theta, Rho - Trader and Risk Manager's point of view regarding the use of sensitivities
3. Risk Management
Mission of a Risk Manager - Profit and Loss Explained - Historic bootstrap - Computing VaR and Expected Shortfall - Model Risk - Other Risk Management measures
4. Certificates and Structuring
Goal of the issuer, subscriber, and structurer - Static replication - Structuring using options - Mission of a structurer in defining the certificate features - Certificate classification - Examples of certificate structuring: Bons Cap, Autocallable and Leverage certificate
5. Fixed Income Instruments
Description of a fixed rate bond - Yield to Maturity - Commonly used Risk Measures : Duration, PVBP, convexity - Spread analysis: Z-spread, ASW-Spread I-Spread - Floating Rate Note - Interest Rate Swap - Cap and Floor - Swaption - Futures - Risk analysis of the main fixed income structured bond: Collared Bond, Reverse Floater, Callable, Puttable, CMS bond.
Key Skills Developed
1. Option Pricing: Using binomial models, Black-Scholes, and Monte Carlo simulations.
2. Risk Metrics: Quantifying and managing financial risk.
3. Product Structuring: Designing and analyzing structured products and certificates.
4. Interest Rate Instruments: plain vanilla and structured bonds, spread analysis and interest rate derivatives.
Prerequisites for admission
A basic course in finance, mathematical analysis and statistics
Teaching methods
In presence classes only. Projection of presentations and spreadsheets
Teaching Resources
Hull, J., Options, futures, and other derivatives. Global edition, Pearson, (June 17, 2021).
(N.B. If you follow the lectures carefully and study the Power Point slides, the textbook is not really necessary)
(N.B. If you follow the lectures carefully and study the Power Point slides, the textbook is not really necessary)
Assessment methods and Criteria
Assignment to be submitted individually by each student (no group projects)
SECS-P/05 - ECONOMETRICS - University credits: 3
Laboratory activity: 20 hours
Professor:
Bugin Andrea
Professor(s)