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The goal of this project is to gain a deeper understanding of the theory of quantitative finance by implementing mathematical models. The programming language being used is C++.

I am going to implement the following models and to utilize the following techniques.

price and calculate greeks for all products

• European, American, Bermudan, Asian,
• Call, Put, Cash-or-Nothing, Asset-or-Nothing,
• Knock-in, Knock-out barrier
  • Up-and-Out
  • Down-and-Out
  • Up-and-In
  • Down-and-In
• Lookback
  • Floating Strike Lookback
• Credit Product: Corpula
• Interest Rate Product

with all frameworks

• Black-Scholes

• Interest Rate Models

  • HJM
  • Libor Market Model(BGM)
  • Short rate:
    • Hull-White
    • Vasicek,
    • Cox-Ingersoll-Ross,
    • Black-Derman-Toy,
    • Black-Karsinski

• Volatility Model:

  • local volatility,
  • Stochastic volatility
  • implied constant volatility,
  • implied volatility surface

• Pricing techniques:

  • Monte Carlo:Simple, Exotic
    Variance Reductions:AntiThetic,moment matching
  • Tree: Binomial, Trinomial, different u and d
  • PDE
    • FDM
      • explicit
      • implicit
      • crank-nicolson
  • Analytic solution

• with all C++ technologies:

  • design pattern
  • generic programming
  • STL
  • boost
  • numerical library:
    • blas
    • lapack
    • GNU Scientific Library
    • Numerical Recipes
  • multi-threaded: boost thread, MPI, CUDA