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: January 17th
Orientation. Role of financial markets.
A role model
First-Day Handout (12noon)
First-Day Handout (1pm)
Lecture One: Background.
Catastrophe Bonds
Funny
Class 2: January 19th
Standing assumptions. Conventions.
Lecture Two: Transaction Costs
Lecture Three: Standing Assumptions and Conventions
Class notes
: Standing assumptions.
Quiz #1
--
due on Wednesday, January 24th
Homework I -
due on Friday, January 26th
Prerequisite in-term topics
Class 3: January 22nd
Financial portoflios. Outright purchase. Discrete-dividend-paying stocks. Foreign currencies.
Class notes
: Portfolios. Outright purchase. Discrete-dividend-paying stocks.
Old class notes
Class 4: January 24th
Continuous dividends. Initial cost. Payoff. Profit.
Class notes
: Foreign currencies. Continuous-dividend-paying stocks. Initial cost. Payoff. Profit.
Old class notes
Quiz #1
--
Solutions
Class 5: January 26th
Payoff and profit diagrams.
Class notes
: Payoff diagram. Profit diagram.
Homework I - Solutions
Class 6: January 29th
The Prerequisite In-Term Exam
The prerequisite exam
-- Problems
The prerequisite exam
-- Solutions
Class 7: January 31st
Short sales.
Class notes
: Short sales.
Class notes
Class 8: February 2nd
Fully-leveraged purchase.
Lecture Four: Initial cost, payoff and profit (the simplest case).
Class notes
From NPR: On effects of changing coffee prices
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 notes
: Forward contracts.
Class 9: February 5th
Hedging using forwards.
European call options.
Lecture Six: European call options
Class notes
: Hedging a short sale using forward contracts. European calls.
Quiz #2
-- due on Friday, February 9th
Homework II -
due on Monday, February 12th
Class 10: February 7th
Hedging using a call option: Caps. Covered/naked option writing. European put options.
Class notes
: Caps. Covered calls. European put options.
Lecture Seven: European put options. Moneyness.
Suggested problems: Sample SoA problems (MFE exam - Intro): #12, #26, #35, #48, #49, #61, #62, #66, #75 (European put options, moneyness)
Class 11: February 9th
Floors. Covered puts.
Class notes
: Floors. Covered puts.
Quiz II -
Solutions
Class 12: February 12th
Moneyness. Collars.
Lecture Eight: Collars.
Class notes
: Moneyness. Collars.
Old class notes
: Hedging with calls, puts, collars.
Homework II
-- Solutions
Class 13: February 14th
Derivative securities. All-or-nothing 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
: Digital options.
Internet content:
Life Assurance Act (1774)
Internet content:
Fantasy Football Insurance
Quiz III -
due on Friday, February 16th
Class 14: February 16th
Dynamic portfolios.
Class notes
: Derivative securities. Digital options. Replicating portfolio.
Quiz III -
Solutions
Warm-up worksheet #1
--
due on Monday, February 19th
(counts as a double quiz!!!)
Homework III
-- due on
Friday, February 23rd
Class 15: February 19th
Arbitrage portfolios. Law of the unique price.
Class notes
: Dynamic portfolios. Arbitrage. Law of the Unique Price.
Old class notes
: Law of the unique price
Class 16: February 21st
Pricing forwards on stocks.
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, February 26th (as a quiz)
Class 17: February 23rd
Futures.
Suggested problems: Sample SoA problems (MFE exam - Intro): #30, #32 (futures)
Class 18: February 26th
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)
Class 19: February 28th
Chooser options. Equity-linked securities.
Class 20: March 2nd
Gap options.
Lecture Twelve: Gap options
Class notes
Class notes
Class 21: March 5th
In-Term Exam One
Class 22: March 7th
Options on futures contracts.
Class 23: March 9th
Options on currencies.
Class notes
: Currency options.
Class notes
: Currency options.
Class 24: March 19th
Exchange options. Maximum options. Generalized put-call parity.
Lecture Thirteen: Exchange options
Class notes
: Exchange options.
Class notes
: Exchange options.
Class notes
: Currency options. Exchange options.
Class 25: March 21st