This book is discussing the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The contents will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance.

Stochastic processes, and stochastic differential equations of increasing complexity, are discussed for the various asset classes, reaching to the models that are in use at financial institutions. Only in exceptional cases, solutions to these stochastic differential equations are available in closed form.

The typical models in use at financial institutions have changed over time.
Basically, each time when the behaviour of participants in financial markets changes, the corresponding stochastic mathematical models describing the prices may change as well. Also financial regulation may play its role in such changes. In the book we therefore discuss a variety of models for stock prices, interest rates as well as foreign-exchange rates. A basic notion in such a diverse and varying field is:

“don’t fall in love with your favorite model!”