The course Quantitative Finance provides an introduction to financial engineering. Financial engineering is a multidisciplinary field that uses techniques and theories from (mathematical) finance, computational finance, operations research, probability theory, statistics & data science, and economics. Practitioners working on financial engineering problems are often called “quants”. Quants typically work at banks, insurance companies and pension funds, and at traders.

Important topics in Financial Engineering include:

• The modelling of asset prices (how will the price of, for example, a commodity as gold, or the stock Royal Dutch Shell evolve over time)?
• The valuation of financial derivatives (contracts whose cashflows are related to the price evolution of other financial assets).
• Measurement of risk (in, for example, a trading portfolio or a balance sheet).
• The use of financial instruments to reduce (hedge) risk.
• Optimal allocation of assets.

The course Quantitative Finance will provide you with the mathematical tools (continuous-time stochastic processes, martingales, stochastic integrals and differential equations, and Itô calculus) in order to be able to formulate continuous-time models for asset prices. Using the no free lunch principle and replication portfolios, you will learn two methods for the valuation of financial derivatives: the Partial Differential Equation method and the method of “risk-neutral pricing” also known as the “equivalent martingale measure approach”. In particular cases it is possible to obtain “closed-form formulas” for the solution to a stochastic differential equation (SDE) or the price of a financial derivative. An important example is the famous Black-Scholes formula, for which Robert C. Merton and Myron Scholes received the 1997 Nobel Memorial Prize in Economic Sciences. As it is not always possible to derive closed-form formulas, we will also discuss numerical techniques, most prominently Monte Carlo methods, in order to obtain numerical approximations.

• Students are able to formulate the main results of Itô calculus, provide proofs of these results, and to apply this calculus.
• Students are able to develop continuous-time models for the evolution of equity prices; are able to derive the value and hedge for financial derivatives (given a continuous-time model for the underlying asset).
• Students can simulate financial models with Monte Carlo methods and know how to make these simulations more efficient through variance reduction and importance sampling.