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ST401: Stochastic Methods in Finance

Lecturer(s): Dr Wei Wu

Important: This module is only available to final year (4) integrated Masters students in the Department of Statistics.

Commitment: 3 x 1-hour lectures per week, 1 tutorial class per fortnight. This module runs in Term 1.

Prerequisite(s): ST318 Probability Theory and ST339 Introduction to Mathematical Finance.

Leads to: ST909 Continuous Time Finance for Interest Rate Models.

Aims: To provide an introduction to continuous time stochastic models as applied in mathematical finance. To cover, in conjunction with ST339 Introduction to Mathematical Finance, the CT8 Actuarial syllabus. To gain an understanding of Brownian Motion and Stochastic Calculus. To be able to use this to model the evolution of financial markets in continuous time and price a variety of financial instruments.

Content:

  • Introduction to Brownian Motion and Stochastic Calculus.
  • Continuous-time models of security prices.
  • Introduction to SDE and Markov processes.
  • Black-Scholes theory: PDE and SDE approaches.
  • Risk-neutral evaluation and equivalent martingale measures, Girsanov and martingale representation theorems.
  • Basic Greeks, delta-hedging.
  • Put-Call parity and Put-Call symmetry.
  • Introduction to optimal stopping and American Options.
  • Bond prices and term structure of interest rates: Hull-White, Vasicek and CIR models.

Books: S.E. Shreve. Stochastic Calculus for Finance, v. 1 and 2. Springer Finance, Springer

T. Bjork, Arbitrage theory in continous time, Third Edition, Oxford University Press, 2009. J.M.Steele, Stochastic calculus and financial applications, Springer 2011.

Subject CT8, Financial Economics, Core Technical, The Faculty of Actuaries and Institute of Actuaries, available at Student Support Office.

Assessment: 100% by 2-hour April examination

You may also wish to see:

ST401: Resources for Current Students (restricted access)