NMAK13033U Continuous Time Finance 2: Beyond Black-Scholes (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, “fixed curriculum” part of the course. The yearly varying “selected topics” parts (the xxx in the course name) will hone these skills further as well as teach some other ones.

 
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" varying from year to year. Examples include: multi-dimensional affine term structure models, Markovian representation and unspanned stochastic volatility,  transform methods and option pricing (the Heston model), numerical solution of partial differential equations. term structure and derivative modelling post-2007 (multi-curve frameworks, funding and collateral, CVA-adjustments)