20189 - QUANTITATIVE FINANCE AND DERIVATIVES - MODULE 2
Department of Finance
Course taught in English
Course Director:
FRANCESCO SAITA
FRANCESCO SAITA
Instructors:
Class 44: FRANCESCO SAITA, Class 45: FRANCESCO SAITA, Class 46: FRANCESCO SAITA, Class 47: FRANCESCO SAITA
Class 44: FRANCESCO SAITA, Class 45: FRANCESCO SAITA, Class 46: FRANCESCO SAITA, Class 47: FRANCESCO SAITA
Suggested background knowledge
The course assumes students have already a basic knowledge of futures, options and swaps – at the level of a basic undergraduate course such as a course in Financial Markets and Institutions – and the theoretical foundations of non-arbitrage evaluation of derivatives acquired from the first-term course Quantitative Finance and Derivatives 1 (QF&D 1). Knowledge of the contents of the first-term course Quantitative Finance and Derivatives 1 is taken for granted. Exchange students who want to take the exam should carefully check whether they possess at least a sufficient understanding of (a) equilibrium forward prices for stocks, (b) the derivation and use of the binomial model to price European options, (c) the derivation and use of the Black-Scholes to price European options. In fact, these topics are developed in the QF&D 1 course. Most exchange students without prior knowledge on these topics have historically found it hard to perform decently in the QF&D 2 exam.
Mission & Content Summary
MISSION
The goal of the course, building on the competencies already acquired in the Quantitative Finance and Derivatives 1 course, is (1) to explain the usage (for hedging, but especially for trading purposes) of forward, stock index and Treasury Bond future and option contracts, (2) to explain how the risk of option portfolios is managed through options' Greeks and (3) to present an introduction to the pricing of interest rate swaps and credit derivatives. A greater attention is devoted to equity derivatives considering their relevance in a wide set of professions in the finance industry (apart from trading and sales, they can be relevant for instance in complex M&A deals, in hedging or return-enhancing strategies in asset management or private banking).
CONTENT SUMMARY
- Forwards and futures (Pricing of forward and futures contracts. Arbitrage with transaction costs. Arbitrage strategies for stock index futures. Using stock index futures for hedging and trading. Government bond futures pricing and the identification of the cheapest to deliver bond).
- Options (American options’ pricing with the binomial model. Extensions of the Black-Scholes formula to options on futures and stock indexes. Sensitivity coefficients (greeks) and their use in directional and volatility trading strategies. Volatility smile and skew and volatility term structure. Volatility spread trading strategies).
- Interest rate swaps (Pricing and valuation of fixed to floating interest rate swaps. Pricing swaps with single curve pricing and double curve pricing)
- Exotic options (Main exotic options contracts. Use of exotic options for hedging and risk management. An introduction to Monte Carlo valuation of single-asset exotic options. Structuring equity-linked bonds).
- Introduction to credit derivatives (Credit default swaps and their valuation).
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
- Describe the most relevant derivatives contracts (forward, futures, plain vanilla options, interest rate swaps, credit default swaps and exotic options such as Asian, barrier, digital and basket options).
- Explain the meaning of the main sensitivity coefficients ("greeks") that can be used to measure risks for an option portfolio.
- Identify the key risk factors that drive the price of an option, of a forward or future contract, of an interest rate swap or a credit default swap).
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
- Apply arbitrage techniques to check the existence of possible arbitrage opportunities between spot and forward prices of a stock/stock index, or between European call and put options prices.
- Derive the optimal number of stock index future contracts to be traded in order to partially or to fully hedge an equity portfolio.
- Determine the change in the value of an option portfolio as a consequence of shocks in its risk factors conditional on the value of the sensitivity coefficients of the option portfolio.
- Calculate under some simplyfing assumptions the pricing of an interest rate swap and of a credit default swap.
Teaching methods
- Lectures
- Practical Exercises
DETAILS
The course also includes one trading simulation in which teams of students simulate buying and selling options among each other, while having to keep under control overall risk exposure.
Exercises are used during face-to-face lectures, in which students are frequently asked to solve small problems that represent applications of the theory that has just been explained
Assessment methods
| Continuous assessment | Partial exams | General exam | |
|---|---|---|---|
|
x |
ATTENDING AND NOT ATTENDING STUDENTS
The final exam is composed by open-ended questions and exercises, aiming at assessing the student's ability to identify equilibrium prices and possible arbitrage opportunities emerging from actual prices differing from equilibrium prices; to understand and explain the risk profile of simple and complex options' positions through its sensitivity coefficients ("greeks") and to evaluate and when possible quantify the effects of possible shocks on the factors that drive option prices; to price, according to the simplified methodologies presented in detail in the course, interest rate and credit default swaps.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
- J. Hull, Options, Futures and Other Derivatives, Prentice Hall, selected chapters (important: since the book has had over time many revisions and different editions, the precise edition and the corresponding list of relevant chapters and paragraphs will be indicated at the beginning of the course)
- Readings and slides prepared by the instructors and available on the course website
Last change 12/05/2025 16:27