Mathematical Finance UCL

Overview

The Mathematical Finance course from UCL Summer School discusses what constitutes a fair price for a contract and explains why fair prices are rarely used in everyday transactions. You will then investigate financial markets in a discrete-time setting, with some revision of basic probability theory. The concept of risk-neutral asset pricing will be discussed with reference to pricing stocks and options in the exchange.

The final part of the module introduces key concepts of stochastic calculus and focuses on continuous-time finance through the widely used Black–Scholes model.

Learning outcomes

By the end of the module, students will have:

• Described and classified financial derivative instruments, supported by knowledge of basic financial concepts.

• Explained the fundamental concept of no-arbitrage principle and illustrated with practical examples.

• Applied basic probability theory to formulate option pricing in discrete time in the context of simple financial models.

• Demonstrated familiarity with the fundamental knowledge and calculation of Stochastic analysis and the Black-Scholes formula.

• Constructed basic risk-free portfolio and developed a fundamental understanding of hedging options.