Continuous Time Finance 2: (FinKont2)

Competencies

1. Confidence in using continuous-time finance models to analyze problems and models that go (well) beyond the basic “call-option in Black/Scholes”-case. The confidence is obtained by working through (fairly) specific specific examples (see also 2. below) rather than “abstract nonsense”.
2. Producing “sensible numbers” from the continuous-time models; the numbers may arise from implementation of specific numerical algorithms, from well-designed experiments, or from empirical analysis.
3. Ability to read original research papers in finance journals, both broad academic journals such as Journal of Finance, technical journals such as Mathematical Finance, or applied quantitative journals such as Journal of Derivatives.

Skills

• Design, conduct and analyze simulation-based hedge experiments
• Derive no-arbitrage conditions models with dividends, multiple currencies, stochastic interest rates, or a non-traded underlying asset.  
• Use change-of-numeraire techniques to price  interest rate options

These are the skills acquired in first, part of the course (3 weeks). The second part the course (whose topics will vary slightly from year to year depending on lecturer and student interests)  will hone these skills further as well as teach some other ones (e.g. how an how not to read an academic paper).

 
Knowledge

• Dynamic hedging, model risk and "the fundamental theorem of derivative trading"
• Dividends and foreign exchange models
• Arbitrage-free term structure models; the Heath-Jarrow-Morton formalism;  1-dim. affine models; Vasicek and Cox-Ingersoll-Ross; LIBOR market models
• Pricing of interest rate derivatives (caps, swaptions)
• Selected topics such as advanced models for option pricing (stochastic volatility, jumps) or multi-dimensional affine term structure models.