Advanced Course on Numerical Methods in Finance (IRP in Quantitative Finance)
10 videos • 2,057 views • by Centre de Recerca Matemàtica https://www.crm.cat/numerical-methods... In this course we will focus on the pricing of options and quantitative risk management from the numerical standpoint. These problems entail an ambitious task in terms of computational complexity and they therefore require sophisticated algorithms. Efficient numerical methods are required to rapidly price complex contracts and calibrate complex financial models to market data. In option pricing, it is the famous Feynman-Kac theorem that relates the conditional expectation of the value of a contract payoff function under the risk-neutral measure to the solution of a partial differential equation. In the research areas covered by this theorem, various numerical pricing techniques can be developed. In brief, existing numerical methods can be classified into three major groups: partial (integro) differential equation (PIDE) methods, Monte Carlo simulation and numerical integration methods. Each of them has its merits and demerits for specific applications in finance, but the methods from the latter class are often used for calibration purposes. Advanced numerical methods are needed within the risk management field as well. The computation of risk measures in either market or credit portfolios is a real problem that financial companies have to deal with. The size of this type of portfolios along with the continually evolving regulatory changes make necessary to look at the new academic developments.