Module 3: Extensions of the Black-Scholes Framework

23 - 27 April 2018

PDF icon M3 18_timetable_v6.pdf

Course Materials




  • Derivative pricing: equivalent measures, risk-neutral pricing, fundamental theorems of asset pricing in discrete time;
  • American options: early exercise, linear complementarity problem, perpetual put, free boundary formulation, smooth pasting;
  • Finite differences for American options: explicit methods, projected iterations, a penalty method; workshop;
  • Variance swaps and the log contract, replication, the VIX index;
  • Implied and local volatility; Breeden-Litzenberger formula, Dupire's formula; hedging and pricing under stochastic volatility models;
  • Change of measure: Girsanov's theorem, exponential martingales, change of numeraire;
  • Overview of instruments in rates markets, mechanisms and conventions; interpolation of yield curves and volatility term structures, bootstrapping, funding instruments and discount curves for banks; basic derivatives, sensitivities;
  • Yield curve modelling; short rate models, use and calibration: Vasicek, CIR, Hull-White, market models (HJM, LMM), and
  • Value at risk and expected shortfall; Convex and coherent risk measures, Euler principle and capital allocation.



Assignment due: 12 noon UK time, 29 May 2018

The Module 3 assignment is available under Course Materials during, or shortly after, the week you are in Oxford. Although not a compulsory assignment, it is highly recommended that you do submit an assignment to give an indication of how you are progressing on the course, ready for the examinations. If you do not plan to submit the assignment then please let the Course Administrator know.

Submit assignment here

Keep a record of the submission ID for future reference. If you encounter any problems please contact the Course Administrator as soon as possible.

Please remember to put your candidate number, rather than your name, on the assignment. You can find your candidate number on the Student Self Service System.