STOCHASTIC CALCULUS AND BLACK SCHOLES THEORY MTH772P

Semester B in 2012-13

The lectures are Thursday 9am and 10am M203
The tutorials are Thursday 12pm Eng216

  • Final exam (3 hours) is 2/05/2013 10am

    This module enables you to acquire a deeper knowledge about the Ito stochastic calculus as applied to mathematical finance. You will learn about the role of the Ito integral in solving stochastic differential equations, and its role in developing the Black-Scholes theory for option pricing. You will also obtain a clear understanding of the simplifying assumptions in the Black-Scholes model. The course will develop pricing methologies for both vanilla options (European call and put options) as well as exotic options such as barrier options.

    Recommended literature (used for the notes):

    S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models: v. 2 (Springer Finance Textbooks)

    J.M. Steele, Stochastic Calculus and Financial Applications (Springer)

  • Section1: Brownian motion

  • Section2: Stochastic integration

  • Section3: Ito formula and processes

  • Section4: Risk-neutral pricing

  • Section5: Stochastic differential equations

  • Section6: Stopping times and the first passage

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  • Exercises Sheet 1
  • Solutions Exercises Sheet 1
  • Exercises Sheet 2
  • Solutions Exercises Sheet 2
  • Exercises Sheet 3
  • Solutions Exercises Sheet 3
  • Exercises Sheet 4
  • Solutions Exercises Sheet 4

    A brief account of sigma-algebras is found here

  • Practitioner Seminar Series: Mikhail Soloveitchik (HSBC) will speak on Concept of a random stopping time in the modern financial engineering Thursday 24th January, 17.30, room 103 (Maths)

  • Practitioner Seminar Series: Alex Lipton (Bank of America Merrill Lynch) will speak on volatility models in his talk Filling the Gaps Thursday 7th February, 17.30, room 103 (Maths)