Financial derivatives are widely used as instruments to modify exposures to various types of financial risk. Examples include call options on a stock index, interest rate derivatives such as swaptions, and credit derivatives. The theory of financial derivatives, as it has been developed in recent decades, is based on a mix of economic ideas and concepts from mathematics.
The material in this Open Press textbook originates from notes for a course that the author has taught at Tilburg University for more than ten years, as part of the MSc program in Quantitative Finance and Actuarial Science. The text aims to provide students with an introduction to continuous-time models that are used to analyze derivative contracts in finance and insurance. Users are expected to have a solid background in standard calculus, linear algebra, and probability; prior experience with stochastic calculus, however, is not a prerequisite.