Numerical Methods for Finance
A.Y. 2022/2023
Learning objectives
The first part of the course aims to provide a good knowledge of stochastic calculus and no arbitrage principles that constitute the foundations in the pricing of financial derivatives. We first discuss the Wiener process, then we move to the construction of stochastic integrals. We also introduce the concept of a martingale measure and its connection with the Fundamental Theorem of Asset Pricing.
The second part of the course aims to introduce students to the main numerical methods for the estimation of stochastic processes and to the numerical evaluation of contingent claims. The main topics presented are: Monte Carlo simulation, parameter estimation of stochastic processes, model selection and calibration.
The second part of the course aims to introduce students to the main numerical methods for the estimation of stochastic processes and to the numerical evaluation of contingent claims. The main topics presented are: Monte Carlo simulation, parameter estimation of stochastic processes, model selection and calibration.
Expected learning outcomes
At the end of the course, students should have acquired the fundamentals of stochastic calculus and the main numerical methods for the evaluation of contingent claims. Students should be able to produce scripts in the R programming language for the estimation of a stochastic process that describes the asset price dynamics and evaluate numerically contingent claims based on no arbitrage principles.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
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
Second trimester
Course syllabus
Binomial tree model for option pricing
Introduction to continuous time stochastic processes
Wiener process
Stochastic differential equations
Ito stochastic integral and Ito formula
Black and Scholes Model
Simulation of stochastic differential equations
Monte Carlo approach to option pricing
Parameter estimation from discretely observed stochastic differential equations
Historical and implied volatility
Calibration Methods.
Introduction to continuous time stochastic processes
Wiener process
Stochastic differential equations
Ito stochastic integral and Ito formula
Black and Scholes Model
Simulation of stochastic differential equations
Monte Carlo approach to option pricing
Parameter estimation from discretely observed stochastic differential equations
Historical and implied volatility
Calibration Methods.
Prerequisites for admission
The students must have some preliminary knowledge of calculus, standard financial mathematics, linear algebra and optimization.
Elementary Probability and Integration
Elementary Probability and Integration
Teaching methods
classroom and laboratories
Teaching Resources
Bjork, T. (2009) Arbitrage Theory in Continuous Time. Oxford University press, 2009
Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd., Chichester, 472 page, ISBN: 978-0-470-74584-7
Iacus, S.M. (2008) Simulation and Inference for Stochastic Differential Equations: with R examples, Springer Series in Statistics, Springer NY, 300 pages, ISBN: 978-0-387-75838-1
Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd., Chichester, 472 page, ISBN: 978-0-470-74584-7
Iacus, S.M. (2008) Simulation and Inference for Stochastic Differential Equations: with R examples, Springer Series in Statistics, Springer NY, 300 pages, ISBN: 978-0-387-75838-1
Assessment methods and Criteria
Module NMFF: Written exam composed of practical exercises and theoretical questions + assignments (or alternatively an oral exam based on the numerical implementation of the proposed algorithms)
Professor(s)
Reception:
Tuesday 1.00 - 4.00 pm. Send me an email to schedule a meeting (Suspended Tuesday 12 November 2024).
room 33 III floor and Teams