Free Tools for Rational Education
The Actuary's Free Study Guide for
Exam 3F / Exam MFE
First Edition Published in February-May 2008
Second Edition Published in July 2014
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Click here to download a free PDF copy of the Second Edition of this study guide.
Table
of Contents
Section |
Page |
Study
Methods for Actuarial Exam 3F / Exam MFE |
4 |
Section 1:
Put-Call Parity |
12 |
Section 2:
Parity of Options on Stocks |
15 |
Section 3:
Conversions and Reverse Conversions |
19 |
Section 4:
Parity of Options on Currencies |
22 |
Section 5:
Parity of Options on Bonds |
25 |
Section 6:
Generalized Put-Call Parity |
28 |
Section 7:
Classification of Calls and Puts |
32 |
Section 8:
Maximum and Minimum Option Prices |
35 |
Section 9:
Early Exercise on American Options |
39 |
Section 10:
Option Prices and Time to Expiration |
43 |
Section 11:
Option Prices for Different Strike Prices |
46 |
Section 12:
Strike-Price Convexity |
49 |
Section 13:
Exam-Style Questions on Put-Call Parity and Arbitrage |
51 |
Section 14:
Exam-Style Questions on Put-Call Parity and Arbitrage – Part 2 |
56 |
Section 15:
One-Period Binomial Option Pricing |
59 |
Section 16:
Risk-Neutral Probability in Binomial Option Pricing |
62 |
Section 17:
Constructing Binomial Trees for Option Prices |
64 |
Section 18:
Multi-Period Binomial Option Pricing with Recombining Trees |
66 |
Section 19:
Binomial Option Pricing with Puts |
70 |
Section 20:
Binomial Option Pricing with American Options |
73 |
Section 21:
Binomial Pricing for Currency Options |
78 |
Section 22:
Binomial Pricing for Options on Futures Contracts |
81 |
Section 23:
Exam-Style Questions on Binomial Option Pricing |
84 |
Section 24:
Exam-Style Questions on Binomial Option Pricing for Actuaries – Part 2 |
87 |
Section 25:
Volatility and Early Exercise of American Options |
91 |
Section 26:
Comparing Risk-Neutral and Real Probabilities in the Binomial Model |
94 |
Section 27:
Option Valuation Using True Probabilities in the Binomial Model |
96 |
Section 28:
The Random-Walk Model |
99 |
Section 29:
Standard Deviation of Returns and Multi-Period Probabilities in the
Binomial Model |
101 |
Section 30:
Alternative Binomial Trees |
103 |
Section 31:
Constructing Binomial Trees with Discrete Dividends |
106 |
Section 32:
Review of Put-Call Parity and Binomial Option Pricing |
109 |
Section 33:
The Black-Scholes Formula |
113 |
Section 34:
The Black-Scholes Formula Using Prepaid Forward Prices |
116 |
Section 35:
The Black-Scholes Formula for Options on Stocks with Discrete Dividends |
119 |
Section 36:
The Garman-Kohlhagen Formula for Pricing Currency Options |
122 |
Section 37:
The Black Formula for Pricing Options on Futures Contracts |
125 |
Section 38:
Exam-Style Questions on the Black-Scholes Formula |
128 |
Section 39:
Option Greeks: Delta |
132 |
Section 40:
Option Greeks: Gamma and Vega |
135 |
Section 41:
Option Greeks: Theta, Rho, Psi, and Greek Measures for Portfolios |
138 |
Section 42:
Option Elasticity and Option Volatility |
141 |
Section 43:
The Risk Premium and Sharpe Ratio of an Option |
143 |
Section 44:
The Elasticity and Risk Premium of an Option Portfolio |
145 |
Section 45:
Calendar Spreads and Implied Volatility |
147 |
Section 46:
Revised Exam-Style Questions on Option Elasticity, Option Volatility,
and the Black-Scholes Formula |
151 |
Section 47:
The Delta-Gamma Approximation |
155 |
Section 48:
The Delta-Gamma-Theta Approximation |
157 |
Section 49:
The Black-Scholes Partial Differential Equation |
160 |
Section 50:
The Return and Variance of the Return to a Delta-Hedged Market-Maker |
162 |
Section 51:
Exam-Style Questions on Market-Making and Delta-Hedging |
164 |
Section 52:
Asian Options |
168 |
Section 53:
Barrier Options |
170 |
Section 54:
Compound Options |
173 |
Section 55:
Pricing Options on Dividend-Paying Stocks |
176 |
Section 56:
Gap Options |
178 |
Section 57:
Exchange Options |
180 |
Section 58:
Exam-Style Questions on Exotic Options |
182 |
Section 59:
The Basics of Brownian Motion |
186 |
Section 60:
The Basics of Geometric Brownian Motion |
189 |
Section 61:
The Basics of Mean-Reversion Processes |
191 |
Section 62:
Basics of Ito's Lemma for Actuaries |
193 |
Section 63:
Probability Problems Using Arithmetic Brownian Motion |
195 |
Section 64:
Probability Problems Using Geometric Brownian Motion |
197 |
Section 65:
Sharpe Ratios of Assets Following Geometric Brownian Motions |
199 |
Section 66:
Another Form of Ito's Lemma for Geometric Brownian Motion |
201 |
Section 67:
Multiplication Rules and Exam-Style Questions for Brownian Motion and
Ito's Lemma |
203 |
Section 68:
Conceptual Questions on Brownian Motion |
207 |
Section 69:
More Exam-Style Questions on Ito's Lemma and Brownian Motion |
210 |
Section 70:
The Vasicek Interest-Rate Model |
214 |
Section 71:
Exam-Style Questions on the Vasicek Interest-Rate Model |
218 |
Section 72:
The Cox-Ingersoll-Ross (CIR) Interest-Rate Model |
225 |
Section 73:
The Black Formula for Pricing Options on Bonds |
229 |
Section 74:
Forward Rate Agreements and Caplets |
233 |
Section 75:
Interest Rate Caps and Pricing Caplets Using the Black Formula |
236 |
Section 76:
Binomial Interest-Rate Models |
238 |
Section 77:
Basics of the Black-Derman-Toy (BDT) Interest-Rate Model |
243 |
Section 78:
Pricing Caplets Using the Black-Derman-Toy (BDT) Interest-Rate Model |
246 |
Section 79:
Determining Yield Volatilities and the Basics of Constructing Binomial
Trees in the Black-Derman-Toy (BDT) Interest-Rate Model |
250 |
Section 80:
Equity-Linked Insurance Contracts |
254 |
Section 81:
Historical Volatility |
258 |
Section 82:
Applications of Derivatives, the Garman-Kohlhagen Formula, and Brownian
Motion to International Business Contracts |
262 |
Section 83:
Valuing Claims on Derivatives Whose Price is the Underlying Asset Price
Taken to Some Power |
267 |
Section 84:
Assorted Exam-Style Questions and Solutions for Exam 3F / Exam MFE |
271 |
Section 85:
Yield to Maturity of an Infinitely Lived Bond in the Vasicek Model |
277 |
About Mr.
Stolyarov |
279 |
Gennady Stolyarov II (G. Stolyarov II) is an actuary, science-fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress.
In December 2013, Mr. Stolyarov published Death is Wrong, an ambitious children’s book on life extension illustrated by his wife Wendy. Death is Wrong can be found on Amazon in paperback and Kindle formats.
Mr. Stolyarov has contributed articles to the Institute for Ethics and Emerging Technologies (IEET), The Wave Chronicle, Le Quebecois Libre, Brighter Brains Institute, Immortal Life, Enter Stage Right, Rebirth of Reason, The Liberal Institute, and the Ludwig von Mises Institute. Mr. Stolyarov also published his articles on Associated Content (subsequently the Yahoo! Contributor Network) from 2007 until its closure in 2014, in an effort to assist the spread of rational ideas. He held the highest Clout Level (10) possible on the Yahoo! Contributor Network and was one of its Page View Millionaires, with over 3.1 million views.
Mr. Stolyarov holds the professional insurance designations of Associate of the Society of Actuaries (ASA), Associate of the Casualty Actuarial Society (ACAS), Member of the American Academy of Actuaries (MAAA), Chartered Property Casualty Underwriter (CPCU), Associate in Reinsurance (ARe), Associate in Regulation and Compliance (ARC), Associate in Personal Insurance (API), Associate in Insurance Services (AIS), Accredited Insurance Examiner (AIE), and Associate in Insurance Accounting and Finance (AIAF).
Mr. Stolyarov has written a science fiction novel, Eden against the Colossus, a philosophical treatise, A Rational Cosmology, a play, Implied Consent, and a free self-help treatise, The Best Self-Help is Free. You can watch his YouTube Videos. Mr. Stolyarov can be contacted at gennadystolyarovii@gmail.com.
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Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.Read Mr. Stolyarov's new comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.