Derivative Modelling and Risk Management

Recommended Prerequisites

Basic courses in (Differential and Integral) Calculus, Linear Algebra, Differential Equations and Probability and Statistics (in particular Stochastic Processes and Calculus).

Teaching Methods

The classes are essentially of expository style and include examples and exercises to apply the material being taught.

 

Learning Outcomes

The main goal is teaching the basic principles of financial derivatives modeling and the underlying mathematical tools. One aims also at showing how to collect, to process and to analyze financial data and how to use numerical techniques to solve problems within the scope of this modeling.

 

The course aims at developing the following skills: knowledge of mathematical results; ability to formulate and solve problems; building and using mathematical models for real world situations. On the personal level it also allows to develop self-learning skills and independent thinking.

Work Placement(s)

No

Syllabus

(1st Part – Basics)
Stochastic and stochastic differential equations modeling of financial assets. Arbitrage.

The Black-Scholes equation and formula for European options. Risk neutrality. Implied volatility and implied density. Hedging (put-call parity and dynamical hedging). The binomial method.

(2nd Part – Extensions)
Extensions of the Black-Scholes model (options on assets paying dividends, options on futures). Exotic options. American options. Options dependent on the asset trajectory. Bonds and term structure models. Options on bonds and other interest rate products. Volatility estimation

Head Lecturer(s)

Ercília Cristina da Costa e Sousa

Assessment Methods

Assessment
Final Exame or During the Semester: 2 midterm exam(50 a 75%) + a set of homework assignments (50 a 25%): 100.0%

Bibliography

L.N. Vicente, Introdução à Matemática Financeira, Departamento de Matemática da FCTUC, 2006/2007.

L.D. Abreu, Modelação de Preços de Derivados Financeiros, Departamento de Matemática da FCTUC, 2011.

T. Björk, Arbitrage Theory in Continuous Time, Oxford University Press, 1998.

D.J. Higham, An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.

J.C. Hull, Options, Futures, and Other Derivatives, Prentice-Hall, 2003.

B. Øksendal, Stochastic Differential Equations - An Introduction with Applications, quinta edição, Springer-Verlag, 2000.

P. Wilmott, S. Howison, J. Dewynne, The Mathematics of Financial Derivatives, Cambridge University Press, 1995