Financial Mathematics for Actuaries (M339W=M389W)

Important external links

On R and RStudio

I will be using R to demonstrate in class. Graduate homework will also (partially) be required to be completed in R. I created some resources for Applied Statistics. They are linked here in case anyone is interested.

R (main website)

RStudio (main website)

The instructions slideshow

The basic R slideshow

The basic R “cheatsheet”

If … else

A tutorial on functions in R

Extra-credit homework

The purpose of these six assignments is for you to review prerequisite material.

Each assignment will contribute up to 1 percentage point to your final score in this course.

Extra-Credit Homework #1 – due on Thursday, September 1st

Extra-Credit Homework #2 – due on Thursday, September 8th

Extra-Credit Homework #3 – due on Thursday, September 15th

Extra-Credit Homework #4 – due on Thursday, September 22nd

Extra-Credit Homework #5 – due on Thursday, September 29th

Extra-Credit Homework #6 – due on Thursday, October 13th

Class 1: August 22nd
Orientation. The binomial asset pricing model [review].

A role model

First-Day Handout

M339D Class Notes on dividend-paying-stocks for review

Lecture Sixteen: The binomial asset-pricing model.

Class notes: Basic prerequisite material. Review of the binomial asset pricing model.

Quiz #1 – due on Wednesday, August 24th

Homework #1 – due on Monday, August 29th

Class 2: August 24th
Random number generation. The inverse transform method.

Wikipedia: Random number generation

Wikipedia: Mersenne twister

An atmospheric RNG

Class notes: The inverse transform method.

Problem set #1: Problems

Problem set #1: Solutions

Quiz #1 – solutions

Quiz #2 – due on Friday, August 26th

Class 3: August 26th
SLLN. Monte Carlo simulation.

Class notes: SLLN. Monte Carlo.

Problem set #2: Problems

Problem set #2: Solutions

Quiz #2 – solutions

Quiz #3 – due on Wednesday, August 31st

Class 4: August 29th
Binomial option pricing [review].

Class notes: Binomial option pricing.

Lecture Seventeen: Binomial option pricing.

Problem set #3: Problems

Problem set #3: Solutions

Homework #1 – solutions

Extra class notes: More on binomial option pricing.

Binomial pricing of currency options. (review)

Class notes: Currency options (the binomial model). (review)

Binomial pricing of futures options. (review)

Class notes: Futures options (the binomial model). (review)

Homework #2 – due on Tuesday, September 6th

Class 5: August 31st
Binomial pricing of American options [review].

Class notes: Binomial pricing of American options.

Old class notes: Binomial pricing of American options [problems].

Extra-Credit Homework #1 – solutions

Quiz #3 – solutions

Quiz #4 – due on Friday, September 2nd

Class 6: September 2nd
Real options.

Investopedia: Real options.

Problem

Class notes: Real options.

Quiz #4 – solutions

Quiz #5 – due on Wednesday, September 7th

Class 7: September 7th
Subjective expectations and forward contracts.

Class notes: Subjective probabilities.

Problem set #4: Problems

Problem set #4: Solutions

Graduate Homework #1 – due on Wednesday, October 5th

Homework #2 – solutions

Homework #3 – due on Monday, September 12th

Open Intro Stats Video: The normal approximation to the binomial.

Quiz #6 – due on Friday, September 9th

Class 8: September 9th
Binomial trees proceeding to the limit. The normal approximation to the binomial. Realized returns.

Class notes: Binomial trees proceeding to the limit. The normal approximation to the binomial. Realized returns.

Mathematica Code: One Random Walk

YouTube: One Random Walk

Mathematica Code: Binomial model limit

Quiz #5 – solutions

Extra-Credit Homework #2 – solutions

Class 9: September 12th
More on realized returns.

Class notes: Realized returns.

Quiz #6 – solutions

Class 10: September 14th
Moment generating functions. The log-normal distribution. Jensen’s inequality.

Lecture notes: The lognormal distribution

Class notes: mgf. The log-normal distribution. Jensen’s inequality.

The Log Normal Distribution from the Wolfram Demonstrations Project by Chris Boucher

Mathematica demonstration: Modeling return distributions

Homework #3 – solutions

Quiz #7 – not to be handed in

Class 11: September 16th
Log-normal stock prices: Parameter interpretation.

Class notes: Lognormal stock prices: Mean. Median.

Problem set #5: Problems

Problem set #5: Solutions

Lecture notes: On pricing in the Black-Scholes model.

Extra-Credit Homework #3 – solutions

Quiz #7 – solutions

Quiz #8 – not to be handed in

Homework #4 – not to be handed in

Class 12: September 19th
Measures of risk: variance, semi-variance, VaR.

Wikipedia: Variance. Semi-variance.

Wikipedia: Value at Risk (VaR).

Problem

Class notes: VaR.

Quiz #8 – solutions

Class 13: September 21st
Log-normal stock prices: Tail probabilities.

Class notes: Tail probabilities.

Quiz #9 – not to be handed in

Homework #4 – solutions

Homework #5 – not to be handed in

Lognormal “confidence” intervals.(optional material)

Class notes: Lognormal “confidence” intervals (optional).

Class 14: September 23rd
Tail probabilities and VaR.

Class notes: Tail probabilities and VaR.

Quiz #9 – solutions

Quiz #10 – not to be handed in

TVaR. Coherent risk measures.

Class notes: Tail Value-at-Risk (TVaR). Coherent risk measures.

Wikipedia: Tail Value at Risk (TVaR).

Wikipedia: Coherent risk measures.

Extra-Credit Homework #4 – Solutions

Class 15: September 26th
Partial expectation. Conditional expectation.

Class notes: Partial expectation. Conditional expectation.

Quiz #10 – solutions

Quiz #11 – not to be handed in

In-Term One: Topics

Practice for In-Term One – problems

Practice for In-Term One – solutions

Class 16: September 28th
The Black-Scholes pricing formula.

Problem packet

Class notes: Black-Scholes.

Wikipedia: Black-Scholes

The original article by Black and Scholes

Mathematica Code: Black-Scholes price

Homework #5 – solutions

Homework #6 – due on Monday, October 10th

Graduate Homework #2 – due on November 4th

Class 17: September 30th
Black-Scholes pricing: Puts. Forward start options.

Problem packet

Class notes: Black-Scholes pricing: Puts. Forward start options.

Extra-Credit Homework #5 – solutions

Quiz #11 – solutions

Quiz #12 – due on Wednesday, October 12th

In-Term One – problems

Class 18: October 3rd
Black-Scholes pricing: The rolling insurance strategy. Gap options.

Lecture Twelve: Gap options (prerequisite material)

Class notes: The rolling insurance strategy. Gap options.

The “master” Black-Scholes pricing formula (optional) Black-Scholes prices: Currency options. Futures options (optional)

Class notes: Black-Scholes pricing: Currency options (optional). Futures options (optional).

Black-Scholes prices: Discrete-dividend-paying stocks. (optional)

Class notes: Black-Scholes pricing: Discrete-dividend-paying stocks (optional).

Class 19: October 5th
Option Greeks in the Black-Scholes model.

Class notes: Option Greeks.

Wikipedia: Greeks

Old Slides: Option Greeks.

Class 20: October 7th
Focus on the delta.

Problem

Class notes: Focus on the Delta.

Quiz #13 – due on Friday, October 14th

Class 21: October 10th
Option elasticity and volatility.

Problem packet

Class notes: Option elasticity.

Suggested Problem: MFE Exam Spring 2007: Problem #5 (option volatility)

Quiz #12 – solutions

Quiz #14 – due on Wednesday, October 19th

In-Term One – solutions

Class 22: October 12th
More on option elasticity. Focus on the gamma.

Class notes: Option elasticity [cont’d]. Gamma.

Homework #6 – solutions

Class 23: October 14th
Other Greeks.

Mathematica Code: Black-Scholes Greeks

YouTube Video

Homework #7 – due on Monday, October 17th, 2022

Implied volatility.

Problem

Class notes: Implied volatility.

Extra-Credit Homework #6 – solutions

Quiz #13 – solutions

Class 24: October 17th
Implied-volatility practice. The delta-gamma-theta approximation.

Problem packet

Class notes: The delta-gamma-theta approximation.

Quiz #14 – solutions

Quiz #15 – due on Friday, October 21st

Class 25: October 19th
Delta-hedging.

Wikipedia: Market maker.

Problem

Class notes: Delta-hedging.

Homework #7 – solutions

Quiz #16 – due on Wednesday, October 26th

Homework #8 – due on Monday, October 24th

Class 26: October 21st
Delta-hedger’s profit. Delta-gamma hedging.

Class notes: Delta-hedger’s profit. Delta-gamma hedging.

Quiz #15 – solutions

Quiz #17 – due on Friday, October 28th, 2022

Graduate Homework #3 – due on Monday, December 5th

In-Term Two: Topics

Class 27: October 24th
Exchange options.

Lecture Thirteen: Exchange options (for review from M339D)

Class notes: Exchange options.

Quiz #16 – solutions

Homework #9 – due on Friday, October 31st

Class 28: October 26th
My favorite problem.

Problem

Class notes: My favorite IFM problem.

Homework #8 – solutions

Class 29: October 28th
Analyzing the project. Break-even analysis.

Wikipedia: Cost of capital.

Wikipedia: Equity cost of capital.

Wikipedia: Capital budgeting.

Planet money: Spreadsheets!

Information, competition, and stock prices. The efficient market hypothesis. Historical returns of stocks and bonds.

Investopedia: Historical returns.

Wikipedia: Efficient-market hypothesis.

Problem packet

Class notes: Break-even analysis. Expected return of a portfolio.

Extra class notes: Expected return of a portfolio.

Quiz #17 – solutions

Quiz #18 – due on Wednesday, November 2nd

In-Term Two – due on Friday, November 4th

Class 30: October 31st
The volatility of a two-stock portfolio.

Problem packet

Class notes: The volatility of a portfolio.

Quiz #19 – due on Wednesday, November 9th

Class 31: November 2nd
The volatility of a large portfolio. Diversification.

Class notes: Diversification.

Class 32: November 4th
Feasible sets. Efficient portfolios. Effect of correlation.

Mathematica demonstration: A Two-Asset Markowitz Feasible Set

Mathematica demonstration: A Three-Asset Feasible Set and Efficient Frontier

Class notes: Efficient portfolios. Effect of correlation.

Extra class notes: More on the effect of correlation.

Homework #10 – due on Monday, November 7th

In-Term Two – solutions

Class 33: November 7th
Sharpe ratio.

Problem

Class notes: Sharpe ratio.

Quiz #18 – solutions

Quiz #20 – due on Friday, November 11th, 2022

Class 34: November 9th
Required returns. Betas of stocks.

Problem packet

Class notes: Required returns.

Extra class notes: More on required returns.

Homework #9 – solutions

Class 35: November 11th
The Capital Asset Pricing Model (CAPM).

Wikipedia: CAPM

Class notes: CAPM.

Quiz #19 – solutions

Quiz #21 – due on Wednesday, November 16th

Homework #11 – due on Monday, November 14th

Class 36: November 14th
Alphas of stocks.

Wikipedia: Linear regression.

Extra class notes: Alphas of stocks.

Problem

Class notes: Alphas of stocks.

Quiz #20 – solutions

Quiz #22 – due on Friday, November 18th

Quiz #23 – due on Wednesday, November 30th

Behavior of individual investors. Systematic trading biases.

Class notes: Alphas. Behavior of individual investors.

An article on familiarity bias.

Familiarity breeds investment.

Wikipedia: Overconfidence effect.

Wikipedia: Disposition effect.

Investopedia: Herd behavior.

Class 37: November 16th
The efficient market hypothesis.

Wikipedia: Efficient-market hypothesis.

Problem packet

Extra class notes: EMH.

Quiz #24 – due on Friday, December 2nd

Multifactor models.

Problem

Class notes: EMH. Multifactor models.

Extra class notes: More on multifactor models.

Wikipedia: Multifactor models.

Wikipedia: The Fama-French model.

Wikipedia: The Carhart four-factor model.

Homework #10 – solutions

Quiz #25 – due on Monday, December 5th, 2022

Class 38: November 18th
Modigliani-Miller I.

Problem packet

Class notes: Modigliani-Miller I.

Wikipedia: The Modigliani-Miller Theorem

Quiz #21 – solutions

Class 39: November 28th
Modigliani-Miller II.

Problem

Class notes: Modigliani-Miller II.

Quiz #22 – solutions

Class 40: November 30th
The effect of taxes on the capital structure.

Problem packet

Class notes: The effect of taxes.

Homework #11 – solutions

Class 41: December 2nd
The effect of taxes on the capital structure [practice].

Class notes: The effect of taxes (problems).

Quiz #23 – solutions

Class 42: December 5th
Options embedded in insurance products.

Problem packet

Class notes: GMDB.

Class notes: Other variable annuities.

Class notes: Some exotic options.

Homework #12 – will be solved in class

In-Term Three: Topics

Practice for In-Term Three – problems

Practice for In-Term Three – solutions

In-Term Three – problems

Homework #12 – solutions

Quiz #24 – solutions

Quiz #25 – solutions

In-Term Three – solutions