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Lectures on Financial Mathematics

 

We are developing a series of publicly available lectures that will lead in a very gentle way to the Black-Scholes Option Pricing Formula, and perhaps beyond. We hope you enjoy them.

NOTE: These lectures have audio.

Comments? Write to mfmath@umn.edu.


Lectures Currently Available


Errata:

1. In Lecture 4, what is called the "error function" is not. The function appearing in the lecture (the integral from -\infty to x of e^{-t^2/2}/\sqrt{2\pi} dt) seems to have no simpler name than "the cumulative distribution function of a standard normal distribution". The error function is related, but not quite the same, see http://en.wikipedia.org/wiki/Error_function.

2. In Lecture 4, what is called the "moment generating function" is not. The function appearing in the lecture (the expected value of z^X) is a kind of generating function, which is a term of art for a mathematical object whose Taylor expansion (typically at 0 or 1) has interesting coefficients. The moment genenerating function is related, but not quite the same, see http://en.wikipedia.org/wiki/Moment-generating_function.


The future outlined lectures below are postponed at least until Summer 2011.

However, we are now developing a series of class recordings which are open to the public. The lectures that most closely follow this online lecture series are linked from http://www.math.umn.edu/~adams/FM5011/diary5011.html. Simply point to that website and search for the word "recording". This lecture series will be completed by Thursday 10 December 2009.

We are also making public recordings of our preparatory courses, FM 5001/5002. Recording for FM 5001 are linked from http://www.math.umn.edu/~adams/FM5001/diary5001.html. Again, point to that website and search for the word "recording". This lecture series will be completed by Wednesday 16 December 2009.

Recorded lectures for FM 5002 will start appearing at http://www.math.umn.edu/~adams/FM5002/diary5002.html by Wednesday 20 January 2010 and will be completed by Wednesday 5 May 2010.

Future Lectures

  • Random Variables
    • piecewise constant random variables
    • independence
    • expectation
    • variance and standard deviation
    • change of measure
    • σ-algebras
    • general random variables
  • The Central Limit Theorem Redux
  • Girsanov's Theorem
    • risk-neutral volatility is real-world volatility
  • First Derivation of Black-Scholes
  • Stochastic Processes
    • Stochastic Calculus
    • Stochastic Differential Equations
  • Itô's Lemma (a.k.a.~the Stochastic Chain Rule)
  • Black-Scholes Redux

 

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