QUANTITATIVE FINANCIAL MODELLING

Course objectives

The goal of this course is to describe the mathematical models defining the dynamics of the interest rate term structure, as well as to show the main option pricing techniques, when the underlying evolves according to either a discrete-time or a continuous time model. It also deals with credit risk and interest rates derivatives. Specific goals: - At the end of lectures students will be able to recognize, define and analyze models and pricing methods for derivatives traded in the main financial markets (interest rates, credit and equity derivatives). Moreover, they will manage to apply the theoretical framework to practical experiences. -The 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 autonomously may 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 enable students to develop a method to autonomously acquire new financial knowledge and theoretical\practical skills.

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SERGIO BIANCHI Lecturers' profile

Program - Frequency - Exams

Course program
Stochastic models for financial markets. Sample space, events, probability, algebras, sigma-algebras, filtrations. Partitions and information structure. Stochastic Processes: definitions, properties, examples. Binomial trees. Martingales (in discrete and continuous time). Brownian motion. Stochastic calculus and Itô-Doeblin formula. Assumptions and modelling principles for financial markets. Financial markets: bonds, stocks and derivatives. Efficient Market Hypothesis. Law of one price. No arbitrage conditions. Market completeness. Fundamental theorems of asset pricing. Option pricing and hedging. Cox-Ross-Rubinstein and Black-Scholes models. Risk neutral valuation: European, American, and exotic option pricing (mention). Dynamic hedging. Market premium and change of numeraire. Affine models in continuous time and valuation formulas. Interest rate models. Forward rates, Zero Coupon Bonds. Term structures. Affine models. HJM models. Numerical methods for parameter estimation. Estimation of stochastic differential equation coefficients. Pricing by Monte Carlo method.
Prerequisites
Students should know and master the undergraduate notions of mathematics and probability
Books
Steven E. Shreve (2005), Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer Finance Steven E. Shreve (2004), Stochastic Calculus for Finance II: Continuous-Time Models, 2nd edition, Springer Finance John C. Hull (2008), Options, Futures and Other Derivatives, 7th edition, Prentice Hall Paul Glasserman (2004), Monte Carlo Methods in Financial Engineering, Springer. Additional materiale distributed on the course webpage
Teaching mode
The course includes classroom lectures and laboratory activities in Matlab environment
Frequency
Classes are scheduled to be attended in presence
Exam mode
The exam includes a written or practical test in form of an open questions and/or exercises and/or computer test
Lesson mode
The course includes classroom lectures and laboratory activities in Matlab environment
  • Lesson code10592803
  • Academic year2024/2025
  • CourseFinance and insurance
  • CurriculumFinancial risk and data analysis - in lingua inglese
  • Year1st year
  • Semester2nd semester
  • SSDSECS-S/06
  • CFU9
  • Subject areaAttività formative affini o integrative