MATH 515/STAT 540. Final Project. Spring 2009.

• You will be asked to develop a topic on quantitive finance. The project must have a computational component where you will implement or illustrate the proposed method(s).
• A list of tentative topics is given below, but you are encourage to propose your own topic or look for other references related to the below topics.
• Your team (all of you) will present the project in class (about 40 min per presentation):
  • Imagine your team was asked to give a presentation to the ``research development board" of you company, which will determine if your project should be developed or not.
  • You cannot assume that the board (me and classmates) are already familiar with the problem and with the technical details about it.
  • You presentation should include the following points:
    • CLEAR description of the problem(s)
    • Motivations of the problem
    • Proposed solution methodology. This should be outlined in a understandable way (LEAVING ASIDE technicalities, but giving the key points).
    • The advantages and drawbacks of your method. The expected results (either based on theoretical justifications, based on the results described in your references, or your own results if already available).
    • Creative extensions that you can envision will receive a bonus score.
  • Both each member and the team as a whole will be evaluated.
  • Any member of the team that takes significantly more time than his/her assigned time will be penalized.
  • Keep in mind that good COMMUNICATION skills at a technical and non-technical level are essential for successfully finding a job in the financial industry.
• Attendance to the presentations of other teams is mandatory.
• A report with a more detailed exposition of what you presented in class, your results, conclusions, and recommendations will be due by the last day of semester. This must also include the numerical code properly documented.

• Portfolio optimization.
  Team's presentation slides
• An Effective Decision-Based Genetic Algorithm Approach to Multiobjective Portfolio Optimization Problem. Chi-Ming Lin and Mitsuo Gen. Applied Mathematical Sciences, Vol. 1, no. 5, 201-210. 2007.
• Monte Carlo computation of optimal portfolios in complete markets. J. of Economic Dynamics and Control 27, 971-986, 2003. Available at http://www.hss.caltech.edu/~cvitanic/papers.html.
• A Monte Carlo Method for Optimal Portfolios. Detemple, Garcia, and Rindisbacher. Journal of Finance, 2003, vol. 58, issue 1, pages 401-446.

• Low complexity Monte-Carlo Simulation for Hedging.
  Team's presentation slides
• Cvitanic-Goukasian-Zapatero (2002) "Hedging with Monte Carlo Simulation". In E. Kontoghiorghes, B. Rustem and S. Siokos (eds.), "Computational Methods in Decision-Making, Economics and Finance".

• Hedging under transaction cost.
  Team's presentation slides: Part 2
• Wilmott on Quantitative Finance and references therein. Chapter 48.
• Option pricing with transaction costs using a Markov chain approximation. Monoyios, Michael. Journal of Economic Dynamics and Control, 28. pp. 889-913. 2004. Available at http://eprints.maths.ox.ac.uk/232/

• Covariance estimation of the stock returns and portfolio optimzation.
  Team's presentation slides
• Improved estimation of the covariance matrix of stock returns with an application to portfolio selection by Ledoit and Wolf.
• A well-conditioned estimator for large-dimensional covariance matrices ny Ledoit and Wolf.

• ``Technical Analysis" and ``Forecasting the market".
  Team's presentation slides
• Wilmott on Quantitative Finance and references therein. Chapter 20. Preview: p1., p2., p3.
• Technical analysis compared to mathematical models based methods under parameters mis-speciÞcation. Blanchet-Scalliet et. al. Journal of Banking & Finance 31 (2007) 1351-1373.
• Other references that students need to find.

• Energy derivatives.
  Team's presentation slides
• Wilmott on Quantitative Finance and references therein. Chapter 72. Preview: p1., p2., p3.
• Other references that students need to find.