Module Overview

The Fundamentals of Matrix Algebra

• The role of matrix algebra
• Addition and subtraction of Matrices
• Scalar and Vector Multiplication
• Commutative, associative and distributive laws in matrix algebra
• Identity and Null matrices
• Methods for solving linear equations
• Matrix Inversion (determinants and non-singularity)
• Solving Matrix Equation s with the inverse
• Cramer’s rule for Matrix solutions
• Application to Macroeconomic models and input-output analysis.

 

Calculus of Multivariate Functions

• Partial derivatives, Second order partial derivatives.
• Implicit and Total Differentiation.
• Elasticity .Utilities. Marginal product of capital and labour.
• Indifference curves and Isoquants. M.R.C.S and M.R.T.S.
• Constrained Optimisation, Lagrange multipliers.
• Rules of Integral Calculus
• Initial Conditions and boundary conditions
• Integration by substitution and parts
• Financial and economic applications
• Area under a curve
• The definite integral
• Present value of Cash flows
• Consumer and producer surplus

 

Derivatives Introduced.

• Futures, Options, Types of Traders.
• Interest rates, conversion from discrete time to continuous time.
• Calculating forward rates and derivation of formula.
• Forward pricing, value of a Forward contract.
• Calculating zero interest rates from fixed income instruments
• Bond pricing, Bond yield, Bond duration
• Using calculus to derive Duration and Convexity formulae
• Mechanics of interest rate swaps.
• Valuation of Interest Rate and Currency Swaps

Regression and Correlation

• Multiple regression.
• Confidence intervals for regression coefficients, hypothesis tests.
• Prediction intervals.
• Regression packages.

The module will be taught using a combination of lectures, tutorials and laboratory sessions.

Module Content & Assessment
Assessment Breakdown	%
Formal Examination	60
Other Assessment(s)	40