97438 - Stochastic Models for Finance

Course Unit Page

  • Teacher Giacomo Bormetti

  • Credits 6

  • SSD SECS-S/06

  • Teaching Mode Traditional lectures

  • Language English

  • Campus of Bologna

  • Degree Programme Second cycle degree programme (LM) in Mathematics (cod. 5827)


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Decent work and economic growth

Academic Year 2022/2023

Learning outcomes

The course aims at providing students with an introduction to affine modeling in finance. Thanks to their analytical tractability, affine models are largely used to parametrically describe the evolution of financial time series (returns, volatilities, jumps) and model the dynamics of interest rate term structures, survival probabilities, and, more recently, contagious markets. Affine modeling in continuous time represents a powerful tool to price and hedge options, interest rate derivatives, credit instruments and to capture the spreading of financial distress. In recent years, an affine approach in discrete time has been proven to be extremely successful to link time series econometrics (e.g. GARCH and Gamma (Realised) volatility modeling) to asset pricing. At the end of the course, the student is familiar with a flexible approach to modeling in finance and economics and with several applications of relevant interest for both regulators and the financial industry.

Course contents

Introduction to securities markets: Model specifications, arbitrage and other economic considerations, risk neutral probability measures, valuation of contingent claims, complete and incomplete markets, risk and return, options, futures, and other derivatives.

Econometric Asset Pricing: Financial volatility and jumps: non parametric realised measures. Observation driven and parameter driven models. Stochastic discount factors: absolute and relative asset pricing. Esscher transform. GARCH and Gamma models. Moment generating functions and recursive option pricing formulas.


Pliska, Stanley R. Introduction to mathematical finance. Oxford: Blackwell publishers, 1997.

Gatheral, Jim. The volatility surface: a practitioner's guide. Vol. 357. John Wiley & Sons, 2011.

Christoffersen, P., Jacobs, K., Ornthanalai, C., & Wang, Y. (2008). Option valuation with long-run and short-run volatility components. Journal of Financial Economics, 90(3), 272-297.

Corsi, F., Fusari, N., & La Vecchia, D. (2013). Realizing smiles: Options pricing with realized volatility. Journal of Financial Economics, 107(2), 284-304.

Teaching methods

Lectures at the blackboard.

Assessment methods

Final oral exam.

Evaluation of learning

  • <18 insufficient
  • 18-23 sufficient
  • 24-27 good
  • 28-30 very good
  • 30 cum laude excellent

Important: the final will take place either at the Department of Mathematics or remotely via Microsoft Teams depending on the prevailing sanitary conditions.

Teaching tools

Classroom lectures.

Office hours

See the website of Giacomo Bormetti