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Section 84 of The Actuary's Free Study Guide for Exam 3F / Exam MFE reviews concepts covered throughout the study guide by offering actuarial students five particularly challenging exam-style questions. Solutions are provided.

Mr. Stolyarov presents both general and exam-specific studying approaches that can help actuarial students put in the effort and learn the materials necessary for doing well on Exam 3F/MFE. This article accompanies Mr. Stolyarov's extensive free study guide.

Mr. Stolyarov renders available information on all freely available review notes and practice problems and solutions for Exam 3F / Exam MFE. Links to a total of 574 questions and solutions by various authors are provided.

Mr. Stolyarov discusses the failure of the Spring 2008 Actuarial Exam 3F / Exam MFE to follow essential principles conducive to the uplifting of the actuarial profession. He offers these remarks in the hope of influencing a change in future exams.

Mr. Stolyarov provides information regarding still other freely available practice problems and solutions for the financial economics segment of the third actuarial exam.

Mr. Stolyarov corrects a formula that was inaccurately presented in Section 19 of The Actuary's Free Study Guide for Exam 3F / Exam MFE. He also gives revised versions of the solutions affected by the correction.

This is a correction issued for a mistake in the solution for Problem ESQBSF5 in The Actuary's Free Study Guide for Exam 3F / Exam MFE.

Section 64 of The Actuary's Free Study Guide for Exam 3F / Exam MFE introduces a formula for performing probability calculations with geometric Brownian motion. Five practice problems and solutions are provided.

Section 65 of The Actuary's Free Study Guide for Exam 3F / Exam MFE to explores the connection between the Sharpe ratios of two different perfectly correlated assets following geometric Brownian motions. 5 practice problems and solutions are given.

Section 63 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems and solutions involving probability calculations using arithmetic Brownian motion.

Section 62 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the statement of Ito's Lemma as applicable to arithmetic, mean-reversion, and geometric Brownian motion. 5 practice problems and solutions are available.

Section 66 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents a form of Ito's Lemma for geometric Brownian motion -- expressing dC(S, t) in terms of dS, dt, and partial derivatives of C. 5 problems and solutions are available.

Section 69 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents 5 additional exam-style questions on Ito's Lemma and Brownian motion, as well as several shortcuts and techniques for solving specific problem types.

Section 70 of The Actuary's Free Study Guide for Exam 3F / Exam MFE introduces the Vasicek interest rate model and gives 5 practice problems and solutions to acquaint actuarial students with it.

Section 61 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives an introduction to mean reversion processes in Brownian motion -- including the Ornstein-Uhlenbeck process. 5 practice problems and solutions are provided.

Section 68 of The Actuary's Free Study Guide for Exam 3F / Exam MFE offers a set of tools for solving conceptual questions regarding Brownian motion that might appear on the exam. 5 practice problems and solutions are provided.

Section 67 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives some multiplication rules applicable to Brownian motion problems, as well as exam-style questions involving Brownian Motion and Ito's Lemma. Solutions are provided.

Section 58 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five exam-style questions on exotic options. These questions are similar to what is likely to appear on the actuarial exam. Solutions are available.

Section 54 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems regarding compound options -- options on options -- and the parity relationship that holds for them.

Section 53 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explains the various kinds of barrier options available and gives five practice problems and solutions regarding them.

Section 52 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the eight different types of Asian options, formulas for calculating arithmetic and geometric averages, and 5 practice problems and solutions.

Section 51 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems on market-making and delta-hedging similar to those that are likely to appear on the actuarial exam. Solutions are provided.

Section 55 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents formulas which can be useful in pricing options on stocks that pay one-time discrete dividends. The connection between these formulas and compound options is also presented.

Section 56 of The Actuary's Free Study Guide for Exam 3F / Exam MFE addresses gap options -- options for which the trigger price and strike price are different. 5 practice problems and solutions about pricing these options are available.

Section 59 of The Actuary's Free Study Guide for Exam 3F / MFE gives a gentle introduction to the definition of Brownian motion and the expression for arithmetic Brownian motion. If you want to gradually build up your knowledge of this subject, this is the section for you.

Mr. Stolyarov presents a revised version of Section 49 of The Actuary's Free Study Guide for Exam 3F / Exam MFE. The correct formula is now given, with proper adjustments made to the five practice problems and solutions.

This is the most recently updated and corrected version of Section 49 of The Actuary's Free Study Guide for Exam 3F / Exam MFE, concerning the Black-Scholes partial differential equation . All further adjustments to this section will be made on this page.

Section 57 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents exchange options or outperformance options and the generalized Black-Scholes formula for calculating their prices.

Section 60 of The Actuary's Free Study Guide for Exam 3F / Exam MFE continues to introduce students to Brownian motion, this time focusing on geometric Brownian motion and basic applications. 5 problems and solutions are available.

The revised Section 13 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains 5 exam-style problems and solutions on put-call parity and arbitrage. Solution ESQPCP4 has now been corrected.

Section 80 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses equity-linked insurance contracts whose payoff is contingent on the price of a stock or some derivative based on the stock. 5 practice problems and solutions are given.

Section 79 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems and solutions regarding the determination of yield volatilities and the construction of one-period binomial trees in the Black-Derman-Toy (BDT) interest rate model.

Section 78 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems and solutions on pricing caplet options using the Black-Derman-Toy (BDT) interest rate model.

The revised Section 60 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five introductory practice problems and solutions regarding geometric Brownian motion. A previous error in Solution BGBM5 has now been corrected.

Section 81 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents a step-by-step procedure for calculating the historical volatility of returns on a stock over a given time period. 5 practice problems and solutions are given, including one exam-style question.

Section 82 of The Actuary's Free Study Guide for Exam 3F / Exam MFE walks students through an exam-style question involving a conceptual understanding of Brownian motion as well as an application of the Garman-Kohlhagen formula to an international business contract.

The revised Section 46 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains five exam-style questions on option elasticity and option volatility, with a correction made in Solution ESQOEOVBSF3.

An important formula to memorize for the Vasicek model is the formula for r-bar, the yield to maturity of an infinitely-lived bond. Section 85 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 problems and solutions that aid in learning this formula.

Section 83 of The Actuary's Free Study Guide for Exam 3F / Exam MFE deals with applications of Ito's Lemma to valuing derivatives whose price (S^a) is the price of the underlying asset (S) taken to some power (a). 5 practice problems and solutions are given.

Section 77 of The Actuary's Free Study Guide for Exam 3F / Exam MFE introduces the Black-Derman-Toy (BDT) interest rate model and gives five practice problems and solutions to introduce actuarial students to its basic elements.

The revised Section 56 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains five practice problems and solutions on gap options. An error affecting solutions GO3, GO4, and GO5 has now been fixed.

Section 73 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the Black formula for pricing European options on bonds. 5 practice problems and solutions are available.

Section 72 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses the the Cox-Ingersoll-Ross (CIR) interest rate model and compares it to the Vasicek model. 5 practice problems and solutions, as well as conceptual discussions relevant to the exam, are provided.

Section 71 of The Actuary's Free Study Guide for Exam 3F / Exam MFE offers five exam-style questions on the Vasicek interest rate model as well as a convenient formula for solving this type of problem.

The revised Section 53 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems and solutions regarding barrier options. Solution BO3 has been corrected from the previous version of this section.

The revised Section 5 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains five practice problems and solutions regarding parity of options on bonds. A prior error in solution POB3 has been corrected.

Section 74 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses forward rate agreements and caplets and gives 5 practice problems and solutions regarding them.

The revised Section 54 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains five practice problems and solutions on compound options. An error in Solution CO4 has been fixed.

Section 76 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses binomial interest rate models and offers a procedure for working with them to find prices of interest rate caps. Five practice problems and solutions are available.

Section 75 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains 5 practice problems and solutions regarding interest rate caps and pricing caplets using the Black formula.

The revised Section 50 of The Actuary's Free Study Guide for Exam 3F / Exam MFE contains 5 practice problems and solutions regarding the return and variance of the return to a delta-hedged market-maker. Previous errors in Solution RVRDHMM5 have been corrected.

Section 50 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents formulas for the return and the variance of the return to a delta-hedged market-maker. 5 practice problems and solutions are available.

Section 19 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses an approach toward binomial option pricing of put options and presents 5 original practice problems and solutions. As a special bonus, an extremely useful time-saving formula is introduced.

Section 18 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explores approaches to the binomial option pricing model involving multiple periods. Five practice problems and solutions are included.

Section 17 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explores a method of constructing binomial trees in the one-period binomial option pricing model. It includes 5 practice problems and solutions

Section 16 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas and practice problems for the risk-neutral probability of an increase in the stock price within the one-period binomial option pricing model.

Section 20 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses how to use the binomial option pricing model to determine the prices of American call and put options. 5 sample problems and solutions are provided.

Section 21 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions for how to apply the binomial option pricing model to options on currencies.

Section 25 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses the conditions under which early exercise for American call and put options is or is not optimal - depending on stock price, strike price, interest rate, dividends, and volatility.

Section 24 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents four additional practice problems on binomial option pricing of the kind and difficulty that are likely to appear on the actuarial exam.

Section 49 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the Black-Scholes partial differential equation relation option price to the values of the option Greeks. 5 practice problems and solutions are given.

Section 22 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas and practice problems and solutions for finding the prices of options on futures contracts using the binomial model.

Mr. Stolyarov presents five more original problems on put-call parity which are designed to be similar to the questions likely to be asked on actuarial exam 3F / MFE.

Mr. Stolyarov presents five original problems on put-call parity and arbitrage opportunities in derivatives markets. These problems were designed to be similar to those offered by the Society of Actuaries and the Casualty Actuarial Society in Exam 3F / Exam MFE.

Mr. Stolyarov discusses the formula for parity of options on bonds and presents five original practice problems and solutions in this 5th section of The Actuary's Free Study Guide for Exam 3F / Exam MFE.

Mr. Stolyarov presents the formula for put-call parity on currency options and offers five practice problems and solutions for actuaries preparing for Exam 3F / Exam MFE.

Mr. Stolyarov continues his free study guide for actuaries preparing for Exam 3F / MFE with this series of original practice problems on put-call parity for European stock options.

Mr. Stolyarov presents the equations for put-call parity and gives five original sample problems and solutions using which actuaries can internalize the concepts involved. This section is particularly suited to studying for Exam 2 / Exam FM and Exam 3F / Exam MFE.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses the boundaries and constraints on prices of American and European call options and presents five original problems and solutions on this topic.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses when it is never optimal to exercise American put and call options early and when such exercise might be optimal. Practice problems and solutions are provided.

In Section 12 of The Actuary's Free Study Guide for Exam 3F / Exam MFE, the concept of strike price convexity is discussed and sample problems and solutions are presented.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE describes the various relationships among prices of options with different strike prices. 5 practice problems and solutions are included.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses how time to expiration affects the prices of European and American call and put options. Five practice problems and solutions are provided.

Section 26 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explores how treatment of the risk-neutral probability of an upward movement in stock prices compares with treatment of the true probability of such a movement.

Section 23 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents five practice questions similar to the ones likely to appear on the actuarial exam. Solutions are provided as well.

Section 42 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the concepts of option elasticity and option price volatility and 5 practice problems and solutions regarding them.

Section 27 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explains how to use the binomial model to price European call options using true probabilities of changes in the underlying stock price.

Section 40 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the option Greeks gamma and vega and 5 practice problems and solutions to help actuarial students and other interested individuals learn these measures.

Section 39 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems and solutions regarding the option Greek delta, which measures the option price change when the stock price increases by $1.

Section 43 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas for the risk premium and Sharpe ratio of an option, along with 5 practice problems and solutions to help actuarial students.

Section 44 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas for the elasticity and risk premiums of call option portfolios consisting of options on the same underlying asset. 5 practice problems and solutions are provided.

Section 48 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions on the delta-gamma-theta approximation for changes in option prices and market-maker profits.

The delta-gamma approximation is used to estimate option price movements if the underlying stock price changes. Section 47 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions regarding this approximation.

Section 46 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents some of the most difficult problems on option elasticity, option volatility, and the Black-Scholes formula that are likely to appear on the actuarial exam.

Section 45 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the concepts of calendar spreads and implied volatility and 5 practice problems and solutions regarding them.

Section 38 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents five problems and solutions regarding the Black-Scholes option pricing model that are likely to appear on the actuarial exam.

Section 41 of The Actuary's Free Study Guide for Exam 3F / Exam MFE introduces the option Greeks theta, rho, and psi, as well as a formula for obtaining the Greek measures for entire portfolios consisting of various options. 5 practice problems and solutions are given.

Section 31 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions regarding Schroder's method for constructing binomial stock price trees when the stock pays discrete dividends.

Section 30 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses alternative approaches to constructing binomial trees - including the Cox-Rubinstein binomial tree and the lognormal tree. 5 practice problems and solutions are given.

Section 37 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the Black formula for pricing European options on a futures contract and 5 practice problems and solutions regarding it.

Section 28 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explains the random walk model for coin flips and how the random walk model can be applied to stock prices by adding assumptions about continuously compounded returns.

Section 32 of The Actuary's Free Study Guide for Exam 3F / Exam MFE provides a comprehensive review of binomial option pricing and put-call parity by offering five exam-style questions and solutions that apply the concepts.

Section 29 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses the relationships among standard deviations of returns on an asset for various periods of time, as well as a formula for obtaining probabilities at any node of a multi-period binomial tree.