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Maths Refresher for Finance

Day One

Numbers, Algebra and Functions

  • Linear, quadratic and other polynomial functions
  • Numerical methods and the Taylor series
  • Role of the exponential function in Finance


  • Bonds and Bond Yields
  • Modelling Yield Curves with polynomials and splines
  • Price optimisation using quadratics

Differentials and Calculus

  • Gradients, rates of change and differential calculus
  • Partial Differentials and PDEs
  • Definite and indefinite integrals


  • Techniques in calculus
  • Bond Prices, Interest Rates and Duration
  • Role of the Diffusion Equation PDE in Finance

Matrix Algebra

  • Matrix rules and operations
  • Cofactors and Determinants
  • The Portfolio Matrix


  • Simultaneous equations and solutions
  • Payoff Matrices
  • Portfolio risk & return and the Variance-Covariance matrix

Day Two

Probability and Sets

  • Sets, diagrams, notation and probability laws
  • Probability Trees and Discrete Probability Distributions
  • Hypothesis or Significance Testing


  • Probability Calculations
  • Expected Monetary Value
  • Significance Testing with Trading Data

Distributions and Stochastic Processes

  • Real-world Distributions and Descriptive Statistics
  • Theoretical probability distributions – Binomial, Normal and others
  • Stochastic approaches to Financial Data
  • Random walks and the Wiener Process


  • Descriptive Statistics and the FTSE
  • Random variables and Random walks
  • Stochastic Equity Returns Modelling

Forecasting and Regression

  • Time-series Approaches
  • Correlation, Variance and Covariance
  • Linear and multiple regression
  • Real data and cautions in forecasting


  • Simple linear regression
  • Multiple regression forecasting models

Further Advanced Workshop Excel Examples:

  • Simple and Log returns, Volatility and VaR
  • Log returns, Alpha, Beta and the Security Characteristic Line
  • Modern Portfolio Theory and CAPM
  • Modelling Bond Default with Probability Transition Matrices

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