METHODS AND MODELS IN FINANCE

Course objectives

This course intends to provide mathematical tools used to define and investigate continuous-time models devoted to the evaluation of the fair value of derivative securities within the main financial markets. Specific goals: - At the end of the lectures, students will be able to apply standard stochastic calculus tools to financial problems. Furthermore, they can understand and explain the main models that describe the dynamics of stochastic processes involved in characterizing specific financial variables, such as interest rate term structure and equity derivatives. Students will also learn how to apply theoretical rules to practical experiences. - Students who pass the exam can identify the suitable model to describe the financial structure, and also establish the most efficient methodologies to solve the related financial issues. - By using the information inferred from the lectures, students may autonomously inspect the financial context, take into account the whole range of methods to use, and interpret the obtained results. - After passing the exam (that consists of a written text with open-ended questions and/or exercises), students will be able to adequately outline the main topics covered by the lectures, either verbally or through written documents. - Standard lectures and self study allow students to develop a method to autonomously acquire new financial knowledge and theoretical\practical skills.

Channel 1
IMMACOLATA OLIVA Lecturers' profile

Program - Frequency - Exams

Course program
The "Methods and Models for Finance" course aims to provide the mathematical tools to describe and analyze some of the most important mathematical models of continuous-time finance used for the valuation of derivative securities in major financial markets, while also providing appropriate numerical applications. Upon completion of the course, students will have the skills to move from theory to the implementation of continuous-time financial models to obtain the fair value of a large number of derivative securities. After passing the examination, students will be able to recognize the most suitable model to describe a given financial context and determine the most efficient methodologies for dealing with problems in that context. After analyzing the main methods and models, students will be able to independently analyze the financial context, evaluate possible resolution methodologies, and interpret the results obtained. Furthermore, students will be able to adequately describe the topics learned during the course, both orally and in written documents. Both lectures and individual activities ensure that students develop a method for autonomously acquiring new knowledge and skills in economics and finance, both theoretical and practical. PART 1: Stochastic calculus Continous-time martingales Girsanov theorem PART 2: Investment strategies and self-financing portfolios First and second fundamental theorems of the Asset Pricing Theory and non-arbitrage principle The Black-Scholes-Merton model Stochastic volatility models PART 3: Term structure of interest rates Interest rates derivatives Heath-Jarrow-Morton theorem Exponential affine models PART 4: Credit risk Credit derivatives Risky bonds evaluation
Prerequisites
Students are required to know basic probability and mathematical concepts
Books
I. Oliva e R. Renò (2021) Principi di Finanza Quantitativa, Maggioli Editore F.D. Rouah (2013) The Heston model and its extensions in Matlab and C#, Wiley. A.J. McNeil, R. Frey e P. Embrechts (2005) Quantitative Risk Management: Concepts, Techniques, Tools, Princeton University Press.
Teaching mode
The course is based on standard classroom lectures
Frequency
The course is delivered in in-person mode: the teacher has her class in person from Faculty classrooms, using the computer equipment available. Students must attend lectures in person. Lessons are also recorded and shared with students.
Exam mode
The assessment procedure is based on a written test with open-ended questions and\or exercises. In particular, the exam will consist of three questions related to some topics covered during the lectures. In case of open-ended questions, students will be required to provide an exhaustive answer, attempting to contextualize both the techniques and the modelling used. As for the exercises, students are required to show the whole mathematical procedure that leads to the final result, also providing appropriate comments.
Bibliography
A. Pascucci (2011) PDE and martingale methods in option pricing, Springer. M. Avellaneda e P. Laurence (2000) Quantitative modeling of derivative securities, Chapman&Hall/CRC. J. Hull (2000) Opzioni, futures e altri derivati, Pearson Ed. S. J. Shreeve (2000) Stochastic calculus for finance II -- continuous-time models, Springer.
Lesson mode
The course is based on standard classroom lectures
  • Lesson code1055921
  • Academic year2024/2025
  • CourseFinance and insurance
  • CurriculumFinanza
  • Year2nd year
  • Semester1st semester
  • SSDSECS-S/06
  • CFU9
  • Subject areaAttività formative affini o integrative