91958 - Stochastic Models for Finance

Academic Year 2021/2022

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)

    Also valid for Second cycle degree programme (LM) in Mathematics (cod. 5827)

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.

Readings/Bibliography

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