Singapore University of Social Sciences

Applied Financial Mathematics I

Applied Financial Mathematics I (MTH359)


MTH359 Applied Financial Mathematics I gives an introduction to basic option theory and pricing formula for the Black-Scholes model. The alternating phases of economic growth and decline cause fluctuations in financial assets which is a major pain point. Hence, mathematics is applied to finance to better understand and manage the risks associated with trading options. Mathematical rigor will be emphasized in the course.

Level: 3
Credit Units: 5
Presentation Pattern: EVERY JULY


  • Basic concepts financial markets
  • Type of options: Puts & Calls, European & American
  • Interest rates
  • Binomial tree model for modelling price processes
  • Hedging strategies and risk-neutral option valuation
  • Normal distributions
  • Wiener processes (Brownian motion)
  • Stochastic differential equations
  • Itô’s lemma
  • Black-Scholes analysis and formula
  • Boundary and final conditions
  • Implied volatility

Learning Outcome

  • Differentiate between the types of options: Puts & Calls, European & American.
  • Compute the expected value of a financial contract using binomial tree model.
  • Construct the Itô’s integral.
  • Set up hedging strategies to minimise risks.
  • Solve pricing problems with the application of Black-Scholes formula.
  • Calculate the implied volatility for an option contract.
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