Introduction to Actuarial Financial Mathematics (M339D=M389D)
Important external links
Link to the
Sample SoA problems and solutions
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 28th
Orientation. Role of financial markets.
A role model
First-Day Handout (12noon)
Lecture One: Background.
Funny
Class 2: August 30th
Standing assumptions. Conventions.
Lecture Two: Transaction Costs
Lecture Three: Standing Assumptions and Conventions
Class notes
: Standing assumptions. Conventions.
Problem Set #1
--
Solutions
An old prerequisite exam
-- Problems
An old prerequisite exam
-- Solutions
Quiz #1
--
due on Wednesday, September 4th
Class 3: September 4th
Financial portoflios.
Class notes
: Financial portfolios.
Quiz #1
--
Solutions
Quiz #2
-- due on Friday, September 6th
Class 4: September 6th
Outright purchase. Discrete-dividend-paying stocks. Foreign currencies.
Class notes
: Outright purchase. Discrete-dividend-paying stocks. Foreign currencies.
Problem Set #2
--
Solutions
Quiz #2
-- Solutions
Class 5: September 9th
The Prerequisite In-Term Exam
The prerequisite in-term exam
--
Solutions
Class 6: September 11th
Continuous dividends. Static portfolios. Initial cost. Payoff. Profit.
Class notes
: Continuous dividends. Static portfolios. Initial cost. Payoff. Profit.
Problem Set #3
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Solutions
Quiz #3
--
due on Monday, September 16th
Class 7: September 13th
Payoff and profit curves.
Class notes
: Payoff diagram. Profit diagram.
Class 8: September 16th
Short sales.
Class notes
: Short sales.
Quiz #3
--
Solutions
Quiz #4
--
due on Wednesday, February 13th
Class 9: September 18th
Fully-leveraged purchase.
Lecture Four: Initial cost, payoff and profit (the simplest case).
From NPR: On effects of changing coffee prices
Forward contracts.
Lecture Five: Basic risk management. Forwards.
Internet content:
Hedging
Class notes
: Fully-leveraged purchase. Forward contracts.
Quiz #5
--
just for practice -- not to be handed in
Homework I -
due on Wednesday, September 25th
Class 10: September 20th
Hedging using forwards.
Class notes
: Hedging using forwards.
Problem Set #4
--
Solutions
Quiz #4
--
Solutions
Class 11: September 23rd
European call options.
Lecture Six: European call options
Class notes
: European calls.
Quiz #5
--
Solutions
Class 12: September 25th
Hedging using a call option: Caps. Covered/naked option writing.
Class notes
: Hedging using a call option: Caps. Covered/naked option writing.
Problem Set #5
--
Solutions
Homework I - Solutions
Quiz #6
--
just for practice -- not to be handed in
Class 13: September 27th
European put options. Floors. Covered puts.
Class notes
: European put options.
Lecture Seven: European put options. Moneyness.
Quiz VI -
Solutions
Class 14: September 30th
Moneyness. Collars.
Lecture Eight: Collars.
Class notes
: Moneyness. Collars.
Suggested problems: Sample SoA problems (IFM exam - Derivatives - Intro): #12, #26, #35, #48, #49, #61, #62, #66, #75 (European put options, moneyness)
Homework II -
due on Monday, October 7th
Class 15: October 2nd
Hedging with collars. Derivative securities. Dynamic portfolios.
Class notes
: Hedging with collars. Derivative securities. Dynamic portfolios.
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)
Internet content:
Life Assurance Act (1774)
Internet content:
Fantasy Football Insurance
Class 16: October 4th
Arbitrage portfolios. Law of the unique price.
Class notes
: Arbitrage portfolios. Law of the Unique Price. Replicating portfolios.
Quiz #7
--
due on Wednesday, October 9th
Class 17: October 7th
Pricing forwards on stocks.
Lecture Ten: Pricing prepaid forwards and forwards on stocks.
Suggested problems: Sample SoA problems (MFE exam - Intro): #20, #21, #29
Class notes
: Prepaid forwards. Focus on the forwards and prepaid forwards on stocks.
Sample In-Term Exam I
- Problems
Sample In-Term Exam I
- Solutions
Homework II -
Solutions
Class 18: October 9th
Futures.
Class notes
: Forward prices and arbitrage. Futures.
Internet content:
Planet money
: Delicious cake futures
Suggested problems: Sample SoA problems (IFM exam - Derivatives: Intro): #30, #32, #45, #69 (futures)
Quiz #7 -
Solutions
Quiz #8
--
due on Friday, October 11th
Class 19: October 11th
Put-call parity.
Lecture Eleven: Put-call Parity
Suggested problems: Sample SoA IFM (Advanced) problems: #1-#3; Sample IFM (Intro): Problems #2, #5, #14, #40 (put-call parity, synthetic forward)
Class notes
: Put-call parity.
Quiz #8 -
Solutions
Class 20: October 14th
In-Term Exam One
In-Term Exam I -- Solutions
Class 21: October 16th
Chooser options.
Class notes
: Chooser options. Equity-linked instruments.
Quiz #9 -
due on Friday, October 18th
Homework III
-- due on
Wednesday, October 23rd
Class 22: October 18th
Equity-linked securities. Gap options.
Lecture Twelve: Gap options
Class notes
: Gap options.
Old class notes
Old class notes
Quiz #9 -
Solutions
Class 23: October 21st
Options on currencies.
Class notes
: Futures options. Currency options.
Quiz #10 -
due on Friday, October 25th
Class 24: October 23rd
Exchange options. Maximum options. Generalized put-call parity.
Lecture Thirteen: Exchange options
Class notes
: Exchange options.
Homework III -
Solutions
Class 25: October 25th
Option price bounds. Monotonicity.
Lecture Fourteen: Call/put-price bounds. Bull spreads.
Class notes
: Call/put-price bounds. Monotonicity.
Quiz #10 --
Solutions
Quiz #11 -
due on Monday, October 28th
Homework IV
-
due on Friday, November 1st
Class 26: October 28th
Bull spreads. Cord-slope bounds. Bear Spreads. Box Spreads.
Class notes
: Bull spreads. Cord-slope bounds.
Quiz #11 --
Solutions
Class 27: October 30th
Option-price convexity. Speculating on volatility.
Lecture Fifteen: Call-price convexity.
Class notes
: Call/put-price convexity. Butterfly spreads.
Quiz #12
-
due on Monday, November 4th
Class 28: November 1st
Straddles. Strangles.
Class notes
: Straddles. Strangles.
Suggested problem(s): Sample IFM (Derivatives; Advanced): Problem #40 (payoff recognition)
Homework IV
-
Solutions
Quiz #13
-
due on Wednesday, November 6th
Class 29: November 4th
Collars (revisited). Ratio spreads. Box spreads.
Class notes
: Ratio spreads. Box spreads.
Quiz #12 --
Solutions
Quiz #14
-
due on Friday, November 8th
Class 30: November 6th
The binomial asset-pricing model.
Lecture Sixteen: The binomial asset-pricing model.
Class notes
: The binomial asset pricing model.
Quiz #13
-
Solutions
Quiz #15
-
due on Monday, November 11th
Homework V -
due on Wednesday, November 13th
Class 31: November 8th
Binomial option pricing (one period). Risk-neutral probability.
Lecture Seventeen: Binomial option pricing.
Class notes
: Binomial option pricing (one period).
Quiz #14
-
Solutions
Quiz #16
-
due on Monday, November 18th
Class 32: November 11th
Graphical interpretation of binomial option pricing. Arbitrage in binomial pricing.
Class notes
: Graphical interpretation of a call's replicating portfolio.
Sample In-Term II
-- Problems
Sample In-Term II
-- Solutions
Quiz #15
-
Solutions
Class 33: November 13th
Forward binomial trees.
Lecture Eighteen: Forward trees.
Class notes: Two binomial periods.
Sample In-Term II
-- More True/False Problems
Sample In-Term II
-- More True/False Solutions
Homework V -- Solutions
Class 34: November 15th
In-Term Exam Two
In-Term II
-- Solutions
Class 35: November 18th
Two-period binomial models.
Homework VI
-
due on Monday, November 25th
Quiz #16
-
Solutions
Class 36: November 20th
Multiple binomial periods.
Class notes
: Binomial option pricing (more periods). Early exercise.
Class 37: November 22nd
More on early exercise.
Class 38: November 25th
Binomial pricing of American options.
Class notes
: Binomial pricing of American options.
Suggested problems: Sample IFM (Derivatives: Advanced) Problem #44 (binomial pricing of American options)
Homework VI
-
Solutions
Class 39: December 2nd
Properties of American options prices.
Old class notes
: Bounds on American option prices.
Suggested problems: Sample MFE Problem #26 (bounds on European and American option prices)
Quiz XVII
-
due on Wednesday, December 4th
Homework VII -
due on Monday, December 9th
Class 40: December 4th
Asian options and their binomial pricing.
Class notes: Asian options.
Old class notes
: Asian options. Barrier options.
Quiz XVII
-
Solutions
Quiz XVIII
-
due on Friday, December 6th
Class 41: December 6th
Barrier options.
Slides: Barrier, compound, and gap options.
-- ignore Black-Scholes pricing
Suggested Problem: Sample MFE Problem #42 (barrier options)
Class notes: Barrier options.
Quiz XVIII -
Solutions
Class 42: December 9th
Compound options.
Class notes: Compound options.
Homework #7 -
Solutions
Problem set -
Problems
Problem set -
Solutions
Problem set -
More problems
Problem set -
Solutions to more problems