Readme

Introduction

NLA is a project designed to implement the numerical linear algebra techniques taught by Baruch Pre-MFE program. It is organized according to the course sequence.

• LU decomposition
• Computation of discount factors by solving linear system
• Multiple period model by using cubic spline interpolationlation
• One price model implementation in option pricing
• Eigenvalue and Eigenvector
• Symmetric matrix

The techniques implemented is only a implementation practice of NLA in financial field. Only used for study purpose.

How to use

Unblock the run_script.py according to the Question * to test different functions.

Files

• Decomposition.py

  Including the following contents:

  • Class LU

    Mainly related functions based on or using LU decomposition.

    Offers the following functions:

    • Forward substitution

    • Backward substitution

    • LU decomposition (without / with row pivoting)

    • Computation of discount factors by solving linear system

    • Solving a multiple linear system shared the same matrix

  • Class EquationSimulation

    Inherit from class LU, mainly implement the cubic spline interpolation model.

    Offers the following function:

    • Simulation of the bond pricing equation

  • Class OnePeriodMarketModel

    Inherit from class LU, mainly implement the Arrow-Debreu one period market model for option pricing.

    Offers the following functions:

    • Check complete market
    • Check arbitrage free
    • Generate one period pricing model (parameters)
    • Option pricing
    • Error computation (average absolute value / root mean squared error)
    • Graph of the errors for all the securities in the market

• OLRRegression.py

  • Class OLR

    Inherit from the class Cholesky, mainly responsible for the Least squares computation by using NLA techniques.

    Offers the following functions:

    • OLR equation estimates
    • Compute errors
    • A special function provided according to the paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2908494
    • Implied volatility computation according to the BSM

  • Class PortfolioOptimize

    Inherit from the class Cholesky, mainly responsible for portfolio optimization based on mean-variance theory.

    Offers the following functions:

    • Tangency portfolio weighting computation
    • Min variance weighting computation
    • Min variance portfolio standard variance computation
    • Max return weighting computation
    • Max return portfolio return computation
    • Min variance portfolio without cash position computation
    • Min variance portfolio without cash position standard variance computation

• OtherFunctions.py

  Functions that support for the lectures.

• Verifications.py

  Mainly contains functions for matrix checking during the previous functions.

• run_script.py

  Offer some samples for the implementation of the above functions.

TODO

Write test script