Department of Mathematics 203 Avery Hall University of Nebraska Lincoln Lincoln, NE 68588-0323 402-472-3731 (voice) 402-472-8466 (fax)

Course Information

Office Hours: 308 Avery
Monday-Wednesday-Friday: 10:30 AM - 11:20 AM.
Other times by appointment, please email me to arrange a time.

Tests, Quizzes, Projects, Homework Assignments

1. Interest is assumed to be compounded contiuously.
2. The mathematical function log(x) means the natural logarithm, that is, logarithms to the base e.

Lessons

Note: In all tests, quizzes and homewrk assignments, unless specifically noted otherwise

1. Interest is assumed to be compounded contiuously.
2. The mathematical function log(x) means the natural logarithm, that is, logarithms to the base e.

History, Background, and Fundamentals

Brief History of Mathematical Models in Finance Theory
Updated Wednesday, 01-Sep-2010 06:19:02 CDT
Brief History of Mathematical Models in Finance Theory
Updated Wednesday, 01-Sep-2010 06:18:59 CDT
Covered on August 25, 2003, August 22, 2005, August 27, 2007; August 24, 26, 28, 2009; August 23, 25, 27, 2010.

Options
Updated Tuesday, 07-Sep-2010 05:42:47 CDT
Options
Updated Tuesday, 07-Sep-2010 05:42:45 CDT
Covered on August 25, 2003, August 24-26, 2005, August 29,31, 2007; August 28, 31, 2009; August 30, 2010.

Speculation and Hedging with Options
Updated Tuesday, 07-Sep-2010 05:43:43 CDT
Speculation and Hedging with Options
Updated Tuesday, 07-Sep-2010 05:43:42 CDT
Covered on August 29, 2003, August 26,30, 2005; September 5, 2007; September 2, 2009; September 1, 2010.

Arbitrage
Updated Tuesday, 07-Sep-2010 05:44:51 CDT
Arbitrage
Updated Tuesday, 07-Sep-2010 05:44:39 CDT
Covered on September 3, 2003; August 30, 2005; September 7, 2007; September 4, 2009; September 3, 2010.

Brief Remarks on Mathematical Models
Updated Wednesday, 28-Dec-2011 07:33:53 CST
Brief Remarks on Mathematical Models
Updated Wednesday, 28-Dec-2011 07:34:01 CST
Covered on September 3, 2003; September 2, 2005; September 7, 10, 2007; September 9, 2009; September 8, 2010.

Randomness
Updated Saturday, 21-Jan-2012 20:27:22 CST
Randomness
Updated Saturday, 21-Jan-2012 20:27:35 CST
Covered on September 12, 2007; September 11, 2009; September 10, 2010.

Stochastic Processes
Updated Wednesday, 15-Sep-2010 05:48:56 CDT
Stochastic Processes
Updated Wednesday, 15-Sep-2010 05:48:53 CDT
Covered September 14, 2009; September 13, 2010.

A Binomial Model of CDOs
Updated Wednesday, 22-Sep-2010 12:42:15 CDT
A Binomial Model of CDOs
Updated Wednesday, 22-Sep-2010 06:04:27 CDT
Covered September 15,17 2010.

Simple Binomial Models for Financial Derivatives

Single Period Binomial Models for Financial Derivatives
Updated Tuesday, 28-Sep-2010 05:41:19 CDT
Single Period Binomial Models for Financial Derivatives
Updated Tuesday, 28-Sep-2010 05:41:16 CDT
Covered on September 8, 2003; September 8, 2005; Covered on September 14, 2007; September 16, 2009; September 20, 2010.

Multiple Period Binomial Models for Financial Derivatives
Updated Tuesday, 28-Sep-2010 05:42:05 CDT
Multiple Period Binomial Models for Financial Derivatives
Updated Tuesday, 28-Sep-2010 05:42:03 CDT
Covered on September 10, 2003; September 10, 2005; September 17, 2007; September 18, 2009; September 22, 2010.

First Step Analysis of Coin-Tossing Games

A Coin Tossing Experiment
Updated Tuesday, 28-Sep-2010 05:43:04 CDT
A Coin Tossing Experiment
Updated Tuesday, 28-Sep-2010 05:43:00 CDT
Covered on September 12, 2003; September 12, 2005; September 19, 2007; September 21, 2009.

Ruin Probabilities
Updated Tuesday, 28-Sep-2010 05:44:44 CDT
Ruin Probabilities
Updated Tuesday, 28-Sep-2010 05:44:30 CDT
Covered on September 15, 2003, September 14, 16, 19 2005; September 24, 26, 2007; September 21, 23, 25 2009; September 24, 27, 2010.

Duration of the Game till Ruin
Updated Thursday, 30-Sep-2010 07:47:29 CDT Re-
Duration of the Game till Ruin
Updated Thursday, 30-Sep-2010 07:47:27 CDT Re-
Covered on September 17, 22, 2003; September 21, 2005; September 26, 28, 2007; September 28, 2009; September 29, 2010.

A Stochastic Process Model of Cash Management
Updated Monday, 14-Jun-2010 06:13:40 CDT
A Stochastic Process Model of Cash Management
Updated Monday, 14-Jun-2010 06:13:29 CDT
Covered on September 30, October 2,5 2009; October 4,6,2010.

Limit Theorems for Coin-Tossing Games

Laws of Large Numbers
Updated Thursday, 22-Jul-2010 05:32:24 CDT
Laws of Large Numbers
Updated Thursday, 22-Jul-2010 05:32:24 CDT
Covered on September 24,26,29, 2003; September 23, 2005; October 1, 3, 2007; October 7, 2009; October 8, 2010.

Moment Generating Functions
Updated Friday, 22-Oct-2010 08:02:16 CDT
Moment Generating Functions
Updated Friday, 22-Oct-2010 08:02:13 CDT
Covered on September 26, 2005; October 3,5, 2007; October 9, 2009; October 11, 2010.

The Central Limit Theorem
Updated Wednesday, 29-Sep-2010 06:21:05 CDT
The Central Limit Theorem
Updated Thursday, 21-Oct-2010 14:17:30 CDT
Covered on September 28, 30 2005; October 10, 12, 15, 2007; October 12, 14, 2009; October 13, 15, 2010.

The Excess of Heads over Tails
Updated Tuesday, 02-Nov-2010 06:30:58 CDT
The Excess of Heads over Tails
Updated Tuesday, 02-Nov-2010 06:30:55 CDT
Covered on September 29, October 1, 3, 2003, October 3,5, 7, 10, 2005; October 17, 19, 2007; October 16, 22, 24 2009; October 20, 22, 2010.

Brownian Motion

Intuitive Introduction to Diffusions
Updated Monday, 01-Nov-2010 05:59:55 CDT
Intuitive Introduction to Diffusions
Updated Monday, 01-Nov-2010 05:59:53 CDT
Covered on October 24, 2007; October 28, 2009; October 25, 2010.

The Definition of Brownian Motion
Updated Tuesday, 09-Nov-2010 05:38:46 CST
The Definition of Brownian Motion
Updated Tuesday, 09-Nov-2010 05:38:41 CST
Covered on October 8, 10, 13, 2003; October 24, 2005; October 29, 27, 2007; October 30, 2009; October 27, 2010.

Approximation of Brownian Motion
Updated Monday, 13-Jun-2011 07:49:47 CDT
Approximation of Brownian Motion
Updated Monday, 13-Jun-2011 07:49:43 CDT
Covered on October 15, 2003, October 26, 2005; November 2, 2007; November 1, 2010.

Transformations of Brownian Motion
Updated Tuesday, 09-Nov-2010 07:41:46 CST
Transformations of Brownian Motion
Updated Tuesday, 09-Nov-2010 07:41:54 CST
Covered on October 17, 2003, October 28, 31, 2005; November 5, 2007; November 4, 2009; November 3, 2010.

Hitting Times and Gambler's Ruin
Updated Monday, 08-Nov-2010 07:44:30 CST
Hitting Times and Gambler's Ruin
Updated Friday, 12-Nov-2010 06:01:31 CST
Covered on October 22, 2003, October 31, 2005; November 7, 2007; November 6, 2009; November 8, 2010.

Path Properties
Updated Friday, 12-Nov-2010 06:02:22 CST
Path Properties
Updated Friday, 12-Nov-2010 06:02:14 CST
Covered on October 22, 2003, October 31, 2005; November 9, 2007; November 9, 2009; November 10, 2010.

Quadratic Variation of Brownian Motion
Updated Tuesday, 16-Nov-2010 06:01:42 CST
Quadratic Variation of Brownian Motion
Updated Tuesday, 16-Nov-2010 06:01:39 CST
Covered on October 24,27, 2003, November 4, 2005, November 11, 2009; November 15,2010.

Stochastic Calculus

Stochastic Calculus

Stochastic Differential Equations and Euler-Maruyama Method
Updated Tuesday, 28-Jun-2011 07:34:10 CDT
Stochastic Differential Equations and Euler-Maruyama Method
Updated Tuesday, 28-Jun-2011 07:34:17 CDT
Covered on October 31, 2003; November 9, 2005; November 13, 2009; November 17, 2010.

Ito's formula and Stochastic Calculus
Updated Wednesday, 29-Jun-2011 07:39:41 CDT
Ito's formula and Stochastic Calculus
Updated Wednesday, 29-Jun-2011 07:39:53 CDT
Covered on November 3, 2003; November 11, 2005; November 16,18, 2009; November 19, 2010.

Geometric Brownian Motion
Updated Wednesday, 29-Jun-2011 07:40:22 CDT
Geometric Brownian Motion
Updated Wednesday, 29-Jun-2011 07:40:34 CDT
Covered on November 5, 2003, November 14, 2005; November 20, 2009, November 22, 2010.

Black-Scholes: Derivations, Solutions, Modeling

Derivation of the Black-Scholes Equation
Updated Thursday, 25-Nov-2010 06:14:15 CST
Derivation of the Black-Scholes Equation
Updated Thursday, 25-Nov-2010 06:13:59 CST
Covered on November 10,12, 2003, November 16, 18, 2005; November 23, 30, 2009; November 29, December 1, 2010.

Solution of the Black-Scholes Equation
Updated Saturday, 04-Dec-2010 07:17:29 CST
Solution of the Black-Scholes Equation
Updated Saturday, 04-Dec-2010 07:17:09 CST
Covered on November 14, 17, 19, 24 2003; November 21, 28, 2005; December 2,4 2009; December 3,6, 2010.

Put-Call Parity Principle
Updated Saturday, 04-Dec-2010 07:20:04 CST
Put-Call Parity Principle
Updated Saturday, 04-Dec-2010 07:19:57 CST
Covered on December 1, 2003, November 30, December 2, 2005; December 7, 2009; December 8, 2010.

Implied Volatility
Updated Wednesday, 15-Dec-2010 06:15:28 CST
Implied Volatility
Updated Wednesday, 15-Dec-2010 06:15:17 CST
Covered on December 1, 2003; December 7, 2009.

Sensitivity, Hedging, and the "Greeks"
Updated Wednesday, 15-Dec-2010 05:41:17 CST
Sensitivity, Hedging, and the "Greeks"
Updated Wednesday, 15-Dec-2010 05:41:03 CST
Covered on December 8,10, 2003; December 2, 2005.

Limitations of the Black-Scholes model
Updated Saturday, 21-Jan-2012 20:28:15 CST
Limitations of the Black-Scholes model
Updated Saturday, 21-Jan-2012 20:28:21 CST
Covered on December 12, 2003; December 5, 2005, December 11, 2009; December 10, 2010.

Online Tables for Probability and Cumulative Distributions

1. Statsoft This site has several different distributions in a nice back-of-the-book-looking HTML format.
2. David Lane, Rice University, Hyperstat This links to a Java applet that will compute the percentages for the normal distribution when given the Z values.
3. StatTrek Statistical Tables Binomial Calculator An easy-to-use applet that calculates binomial probabilities along with cumulative distribution functions and complementary cumulative distribution functions. Tabs/links at the top of the page connect to similar calculators for the chi-square, f-distribution, hypergeometric, multinomial, negative binomial, normal, Poisson, and t-distribution PDF and CDFs as well. Finally on each page, there are short descriptions and explanations in the form of Frequently Asked Questions.

Annotated Bibliography

A personal, eclectic and biased annotated bibliography of books and articles about probability, stochastic processes and mathematical finance.

Outside Readings/Links:

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Steve Dunbar's Home Page, http://www.math.unl.edu/~sdunbar
Email to Steve Dunbar, sdunbar@unl.edu