Module 4: Exotic Options and Advanced Modelling Techniques

11 - 15 June 2018

Timetable for Module 4 

Course Materials



    • The dual approach to optimal investment: application to portfolio selection under drift uncertainty (to include an introduction to linear filtering);
    • Stochastic optimization: dynamis programming, continuous time stochastic control, HJB equations, martingale optimality principle, verification theorems, Merton problem with terminal wealth and consumption;
    • Basic exotic options: general payoffs, options on futures, pay-later options; multi-stage options, forward-start options, compound options, choosers; multi-factor problems, FX and basket options;
    • Exotic options: down-and-out and other barrier contracts, relfection principle, Asians options, lookbacks , similarity reductions;
    • Practicalities of exotics pricing: model ambiguitym calibration, robustness, arbitrage and no good deals;
    • Jump diffusion and L\'{e}vy processes: Poisson and Cox process, Ito with jumps, Merton's model; L\'{e}vy processes; hedging and pricing, jump-risk, characteristic functions;
    • SABR model, Markov approach to pricing with short rate models, practical risk management of vanilla fixed income derivatives;
    • Monte Carlo for SDEs,  Euler-Maruyama method, weak and strong convergence; exotic options: continuity corrections for discretely sampled paths for barriers and lookbacks; workshop, and
    • Introduction to econometrics: AR(I)MA, (G)ARCH, model fitting, regression, back-testing.


    Assignment due: 12 noon UK time, 16 July 2017

    The Module 4 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.