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 -- 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