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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 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 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 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 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.

The binomial option pricing model makes the simplified assumption that within any given time period, a stock price can only move up by a discrete amount or down by a discrete amount. Mr. Stolyarov explores this model for one time period.

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 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.

This paper aims to compare the difference between the Real Option Valuation and the Discounted Cash Flow method. I show that there is only one conceptual difference between the 2 valuation tools.

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.

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.

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 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.

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 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 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 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 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.

Mr. Stolyarov presents 5 practice problems pertaining to Robert Deacon's model of forest economics and the benefits and costs of harvesting a forest. Solutions are provided. This section is recommended for students of mathematical economics.

Mr. Stolyarov presents mathematical problems and solutions regarding the economics of fisheries -- including problems pertaining to the logistic population growth model, the Schaefer model, and the Gordon model.

Mr. Stolyarov presents 8 additional practice problems involving the Schaefer and Gordon models of fisheries. Solutions are provided. This section is highly recommended for students of mathematical economics.

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.

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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.

Section 12 of Mr. Stolyarov's Mathematical Economics Problems and Solutions explores contracts that can be designed under conditions of asymmetric information to give managers incentives to work hard. This section concerns ways to get around the principal-agent problem.

In Section 11 of his Mathematical Economics Problems and Solutions, Mr. Stolyarov presents detailed answers to four problems regarding expected utility and its relationship to concepts such as insurance and indifference curves.

Mr. Stolyarov presents four practice problems and solutions involving constrained optimization using the Lagrangian method. This section is highly recommended for students of mathematical economics.

Mr. Stolyarov presents and solves several optimization problems in mathematical economics, where the objective function is subject to multiple inequality constraints. Graphical illustrations are provided.

Mr. Stolyarov offers two additional constrained optimization problems involving inequality constraints and the Kuhn-Tucker conditions. Solutions to both problems are provided. This section is highly recommended for students of mathematical economics.

Section 10 of Mr. Stolyarov's Mathematical Economics Problems and Solutions gives solutions to four problems involving the use of second order conditions in functions with two choice variables.

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 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.

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.

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 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 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 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 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 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.

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 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 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 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 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 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 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 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 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.

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.

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.

We all spend hours upon hours studying for all kind of different math's exams during high school. So it's natural for us to think, "What' is the point in this? What is the point in spending so many hours dedicated to studying mathematics?"

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 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.

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.

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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 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.

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.

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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 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 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 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.

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.

Hungarian scientists working at the Budapest University of Technology and Economics discovered a shape, which stirred up the scientific world: homogenous convex object with only one stable and one unstable point of equilibrium (balance point).

Step-by-step solutions to higher mathematics problems will always be in demand among hundreds of thousands of students taking higher math courses. Writing such problems and making their solutions available online will generate sustainable long-term interest.

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The colossal number of topics listed on the actuarial exam syllabus may seem intimidating to many, but you do not need to learn all of them to get high grades on the exam. Mr. Stolyarov recently passed Exam 1P and can offer some advice on what you need to know.

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What I'm referring to are called trading options. An option is a contract whereby one party has the right but not the obligation to exercise a feature of a contract on or before a future date.

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Will a proposed expansion of Interstate 95 solve congestion problems plaguing this shoreline highway? The article explores what rail options residents and visitors have and talks to a former DOT engineer from Old Saybrook

There are many possible ear problems that your dog may have. This article covers the most common treatment for dog ear problems.

With the growing popularity of violent video games comes other sorts of problems including mental issues in younger people. Certain things such as copying the stunts that are being performed in video games are an ongoing problem in our world today.

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Allentown, Pennsylvania isn't a HUGE city but big enough to make walking a hassle. If you don't have a car, it's important to know the public transpiration options that are available to you in Allentown, Pennsylvania.

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Affecting less than 200,000 Americans each year, achalasia is often misdiagnosed and is left untreated. Understanding the diagnostic and treatment options, at any age, can relieve the painful symptoms.

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