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Unit of study_

MATH3975: Financial Derivatives (Advanced)

This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: the notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and hedging of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Students enrolled in this unit at advanced level will have to undertake more challenging assessment tasks, but lectures in the advanced level are held concurrently with those of the corresponding mainstream unit.

Code MATH3975
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02)
MATH3933 or MATH3015 or MATH3075

At the completion of this unit, you should be able to:

  • LO1. Demonstrate familiarity with fundamental concepts in the area of financial markets with application to existing securities related to equities and interest rates.
  • LO2. Develop stochastic models and solve qualitative and quantitative problems associated with the valuation and hedging of options.
  • LO3. Understand, explain and apply the principles of stochastic modelling in the context of financial markets.
  • LO4. Understand, explain and apply the principles of optimal stopping in the context of American-style options.
  • LO5. Understand, explain and apply the principles of Dynkin games in the context of game options.
  • LO6. Understand and apply the Black-Scholes continuous-time model for European-style options.
  • LO7. Apply mathematical expertise to solve practical problems using various approaches in discrete and continuous time.‚Äč