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Algorithmic Homework

Mathematical Techniques in Finance Edition 2

Mathematical Techniques in Finance Algorithmic Homework

Thoroughly explores the advanced mathematical techniques used in modern finance. Requiring comprehensive knowledge of the underlying principles and utilising methods from calculus, this e-workbook facilitates mastery of the theory of interest and stimulates rigorous analysis of the techniques used in pricing, financing, investing, trading and managing risks and returns. The e-workbook combines academic thought, proof, theory and the application of formulas.

Measuring interest involved in single payment transactions

  • Interest accumulation
  • Nominal and effective rates of interest and discount
  • The force of interest
  • Future value at simple, compound and continuous rates
  • Present value at simple, compound and continuous rates
  • Equations of value
  • Adjusting for inflation

Annuity valuation

  • Future value of an ordinary annuity
  • Future value of an annuity-due
  • Present value of an ordinary annuity and an annuity-due
  • Solving for the term, payment and yield of an annuity
  • Valuation of deferred annuities
  • Present value of a perpetuity as the limit of an annuity
  • Valuing annuities with varying interest and periodic payments
  • Continuous annuities
  • Valuing annuities with inconsistent compounding and payment frequencies
  • Valuing annuities that form a geometric progression
  • Valuing annuities that form an arithmetic progression
  • Applications to reinvestment risk, depreciation and other real world problems


  • Amortisation method of loan repayment
  • Developing an amortisation schedule
  • Retrospective and prospective methods of loan outstanding
  • Adjusting the repayment and/or term in response to changes in the loan interest rate
  • Sinking-fund method of loan repayment
  • Applications to valuing loans and other real world problems

Valuation of bonds

  • Pricing a bond on a coupon date
  • Pricing a bond between coupon dates
  • Solving for the yield to maturity implied in a bond purchase
  • Holding period return allowing for reinvestment rates
  • Amortisation of a bond
  • Allowing for income and capital gains tax on bonds
  • Applications to callable and serial bonds

Probability and random variables

  • Introduction to the theory of probability
  • Rules of probability and enumeration
  • Random variables
  • Probability distributions
  • Expected value and variance
  • Applications to portfolio theory

The rate of return on an investment

  • Internal rate of return and net present value
  • Payback period
  • Profitability index
  • Dollar-weighted rate of return
  • Time-weighted rate of return
  • Applications to investment decisions and fund management with continuous transactions

The term structure of interest rates

  • Spot and forward rates
  • Yield curves
  • The relationship between spot rates and bond yields
  • Applications to arbitrage and interest rate swaps
  • Duration and immunisation
  • Duration of a series of cash flows and bond duration
  • Convexity of a series of cash flows
  • Asset-liability matching and immunisation
  • Applications to interest rate risk management

Valuing securities and financial instruments

  • Pricing using the arbitrage principle
  • Forward and futures contracts
  • Modelling shares using the CAPM approach
  • Modelling using the binomial and Black-Scholes approaches
  • Fixed income investments and bond default risk
  • Foreign exchange rates and the interest rate parity theorem