Introduction to Actuarial Financial Mathematics (M339D=M389D)
Important external links
Link to the
Sample SoA problems - Introductory material
Link to the
Sample SoA solutions - Introductory material
Sample MFE problems and solutions - Advanced
MFE Exam, Spring 2007: Problems
MFE Exam, Spring 2007: Solutions
MFE Exam, Spring 2009: Problems
MFE Exam, Spring 2009: Solutions
A MOOC:
Intro to Actuarial Science
Class 1: August 30th
Orientation. Role of financial markets.
A role model
First-Day Handout (12noon)
Lecture One: Background.
Catastrophe Bonds
Funny
Quiz #1
--
due on Friday, September 1st
Class 2: September 1st
Standing assumptions. Conventions.
Lecture Two: Transaction Costs
Lecture Three: Standing Assumptions and Conventions
Quiz #1
--
Solutions
Homework I -
due on Friday, September 8th
Prerequisite in-term topics
Class 3: September 6th
Outright Purchase. Discrete-dividend-paying stocks. Realized returns.
Class notes
Class 4: September 8th
Continuous dividends. Market indices.
Class notes
Homework I - Solutions
Class 5: September 11th
The Prerequisite In-Term Exam
Class 6: September 13th
Short sales.
Class notes
Class 7: September 15th
Financial portfolio. Initial cost. Payoff.
Lecture Four: Initial cost, payoff and profit (the simplest case).
Class notes
From NPR: On effects of changing coffee prices
Class 8: September 18th
Forward contracts.
Lecture Five: Basic risk management. Forwards.
Internet content:
Hedging
Suggested problems: Sample SoA problems (FM exam - Derivatives markets): #25, #28 (rationale for hedging)
Class 9: September 20th
Hedging using forwards.
Problem set #1: Forward contracts. Hedging.
Problem set #1: Forward contracts. Hedging.
-- Solutions
Suggested problems: Sample SoA problems (FM exam - Derivatives markets): #18 (forwards + expected profit); #36(tax considerations)
Class 10: September 22nd
European call options.
Lecture Six: European call options
Class 11: September 25th
Covered option writing. European put options.
Lecture Seven: European put options. Moneyness.
Suggested problems: Sample SoA problems (FM exam - Derivatives markets): #19, #35 (European put options)
Class 12: September 27th
Hedging with puts and calls.
Problem Set #2
-- Solutions
Class 13: September 29th
Collars.
Lecture Eight: Collars.
Class notes
: Hedging with calls, puts, collars.
Class 14: October 2nd
Derivative securities.
Early exercise. American-style options.
Lecture Nine: Derivative securities.
A nice read on derivatives:
From The New York Times
Recommended reading:
Employee stock options
Internet activity:
Option-price quotes (example)
Suggested problems: Sample SoA problems (FM exam - Derivatives markets): #24 (rationale for existence of derivatives)
Class notes
Internet content:
Life Assurance Act (1774)
Internet content:
Fantasy Football Insurance
Class 15: October 4th
All-or-nothing options. Dynamic portfolios.
Class notes
: Digital options.
Warm-up worksheet #1
--
due on Friday, October 6th
Homework II -
due on Wednesday, October 11th
Class 16: October 6th
Arbitrage portfolios. Law of the unique price.
Pricing forwards on stocks.
Class notes
: Law of the unique price
Warm-up worksheet #1
--
Solutions
Lecture Ten: Pricing prepaid forwards and forwards on stocks.
Suggested problems: Sample SoA problems (MFE exam - Intro): #20, #21, #29, #31
Warm-up Worksheet #2 --
due on Monday, October 9th (as a quiz)
Class 17: October 9th
Put-call parity.
Lecture Eleven: Put-call Parity
Suggested problems: Sample SoA MFE (Advanced) problems: #1-#3; Sample MFE (Intro): Problems #2, #5, #14, #40 (put-call parity)
Class notes: Put-call parity (old)
Class notes: Put-call parity (old)
Exam-prep checklist.
Warm-up Worksheet #2 -- Solutions
Sample In-Term Exam I
Class 18: October 11th
More on put-call parity. Equity-linked securities.
Sample In-Term Exam I
- more problems
Class notes
Homework II
--Solutions
Class 19: October 13th
Chooser options.
Class 20: October 16th
In-Term Exam One
Class 21: October 18th
Gap options.
Lecture Twelve: Gap options
Class notes
In-Term Exam I -- Solutions
Class 22: October 20th
Futures.
Options on futures contracts.
Suggested problems: Sample SoA problems (MFE exam - Intro): #30, #32 (futures)
Homework III
-- due on
Monday, October 30th
Class 23: October 23rd
Options on currencies.
Class notes
: Currency options.
Class notes
: Currency options.
Class 24: October 25th
Exchange options.
Lecture Thirteen: Exchange options
Class notes
: Exchange options.
Class notes
: Exchange options.
Class notes
: Currency options. Exchange options.
Class 25: October 27th
No class. Medical emergency.
Class 26: October 30th
Option price bounds. Monotonicity.
Box spreads.
Lecture Fourteen: Call/put-price bounds. Bull spreads.
Class notes
: Bounds. Monotonicity.
Class notes
: Bounds. Monotonicity.
Class notes: Bounds. Monotonicity.
Homework III -
Solutions
Class 27: November 1st
Cord-slope bounds.
Class notes
: Cord-slope bounds.
Class notes
: Cord-slope bounds.
Class notes
: Cord-slope bounds.
Class notes
: Cord-slope bounds.
Class 28: November 3rd
Option-price convexity. Speculating on volatility.
Lecture Fifteen: Call-price convexity.
Class notes
: Option-price convexity. Speculating on volatility.
Homework IV -
due on Friday, November 10th
Class 29: November 6th
Straddles. Strangles.
Class notes
: Speculating on volatility. Collars. Ratio spreads.
Quiz II -
due on Wednesday, November 8th
Class 30: November 8th
Collars(revisited). Ratio spreads.
Problem set: Collars(review). Ratio spreads. Box spreads.
Suggested problem(s): Sample MFE(Intro): Problem #60 (hedging with a collar while minimizing the cost of hedging); Sample MFE (Advanced): Problem #40 (payoff recognition)
Quiz II -
Solutions
The binomial asset-pricing model.
Lecture Sixteen: The binomial asset-pricing model.
Class notes
: Binomial asset pricing.
Class notes
: Binomial asset pricing.
Class notes
: Binomial asset pricing.
Class 31: November 10th
Binomial option pricing (one period).
Lecture Seventeen: Binomial option pricing.
Class notes
: Binomial option pricing (one period).
Class notes
: Binomial option pricing (one period).
Class notes
: Binomial option pricing (one period).
Quiz III -
due on Monday, November 13th
Homework IV -
Solutions
Homework V -
due on Friday, November 17th
Class 32: November 13th
Graphical interpretation of binomial option pricing.
Class notes
: Graphical interpretation of a call's replicating portfolio.
Arbitrage in binomial pricing. Forward binomial trees.
Lecture Eighteen: Forward trees.
Quiz III -
Solutions
Quiz IV -
due on Wednesday, November 15th
Class 33: November 15th
Two-period binomial models.
Class notes
: Binomial option pricing (more periods).
Quiz IV -
Solutions
Class 34: November 17th
Medical emergency.
Class 35: November 20th
Multiple binomial periods.
Problem set #2
--Solutions
Homework V -- Solutions
Quiz V -
due on Monday, November 27th
Homework VI -
due on Monday, November 27th
Class 36: November 27th
More on early exercise.
Binomial pricing of American options.
Class notes
: Binomial option pricing (American options).
Suggested problems: Sample MFE Problem #44 (binomial pricing of American options)
Class 37: November 29th
Properties of American-option prices.
Class notes
: Bounds on American option prices.
Suggested problems: Sample MFE Problem #26 (bounds on European and American option prices)
Homework VI -
Solutions
Quiz V -
Solutions
Quiz VI -
due on Friday, December 1st
Homework VII -
due on Monday, December 4th
Class 38: December 1st
Asian options and their binomial pricing.
Slides: Intro to Exotic options. Asian options. --
ignore the first part about perpetual American options
Class notes
: Asian options. Barrier options.
Quiz VII -
due on Wednesday, December 6th
Quiz VI -- Solutions
Class 39: December 4th
Barrier options.
Slides: Barrier, compound, and gap options.
-- ignore Black-Scholes pricing
Suggested Problem: Sample MFE Problem #42 (barrier options)
Class notes: Barrier options.
Homework VII -
Solutions
Sample In-Term II
Class 40: December 6th
Barrier options [cont'd].
Quiz VII -
Solutions
Class 41: December 8th
Compound options.
Class notes: Compound options.
Binomial pricing of currency options.
Class notes: Currency options (the binomial model).
Binomial pricing of futures options.
Class notes: Futures options (the binomial model).
Class 42: December 11th
In-Term Exam Two