SOA - Examination and Other Requirement Details(4)
Spring 2007 Basic Education
Catalog
Examination and Other Requirement
Details
Exam M Actuarial Models
The examination for this material consists of
five hours of multiple-choice questions offered in two independent
segments: a 3-hour life contingencies segment (Exam MLC) and a
2-hour financial economics segment (Exam MFE). Each segment will be
graded separately. In addition, a candidate will not be required to
take both segments during the same exam administration period.
This material develops the candidate's
knowledge of the theoretical basis of certain actuarial models and
the application of those models to insurance and other financial
risks. A thorough knowledge of calculus, probability and interest
theory is assumed. Knowledge of risk management at the level of
Exam P is also assumed.
A variety of tables will be provided to the
candidate in the study note package and at the examination. These
include values for the standard normal distribution and
illustrative life tables. These tables are also available on the
SOA Web site. Since they will be included with the examination,
candidates will not be allowed to bring copies of the tables into
the examination room.
Learning Objectives-Life Contingencies
Segment
Survival models
Define survival-time random variables
for one life, both in the single-and multiple-decrement
models;
for two lives, where the lives are independent or dependent
(including the common shock model).
Calculate the expected values, variances, probabilities, and
percentiles for survival-time random variables.
Define the continuous survival-time random variable that arises
from the discrete survival-time random variable using a:
uniform distribution;
constant force of mortality; or
hyperbolic assumption
Markov Chain Models
Define non-homogeneous and homogeneous discrete-time Markov
Chain models and calculate the probabilities of
being in a particular state;
transitioning between particular states
Life insurances and annuities
Define present-value-of-benefit random variables defined on
survival-time random variables:
for one life, both in the single-and multiple-decrement
models;
for two lives, where the lives are independent or dependent
(including the common shock model)
.
Define and calculate the expected values, variances and
probabilities for:
present-value-of-benefit random variables;
present-value-of-loss-at-issue random variables, as a function
of the considerations (premiums);and
present-value-of-loss random variables, as a function of the
considerations (premiums).
Calculate considerations (premiums) for life insurances and
annuities,
using the Equivalence Principle; and
using percentiles.
Calculate liabilities, analyzing the
present-value-of-future-loss random variables:
using the prospective method;
using the retrospective method;
using special formulas.
Calculate
gross considerations (expense-loaded premiums);
expense-loaded liabilities (reserves);
asset shares.
Using recursion, calculate expected values (reserves) and
variances of present-value-of-future -loss random variables for
general fully-discrete life insurances written on a single
life.
Extend the present-value-of-benefit, present-value-of-loss-at-
issue, present-value-of-future-loss random variables and
liabilities to discrete-time Markov Chain models, to calculate
actuarial present values of cash flows at transitions between
states;
actuarial present values of cash flows while in a state;
considerations (premiums) using the Equivalence Principle;
liabilities (reserves) using the prospective method.
Poisson processes
Define Poisson process and compound Poisson process.
Define and calculate expected values, variances, and
probabilities for Poisson processes,
using increments in the homogeneous case;
using interevent times in the homogeneous case;
using increments in the non-homogeneous case.
Note: Concepts, principles and techniques
needed for Exam M are covered in the references listed below.
Candidates and professional educators may use other references, but
candidates should be very familiar with the notation and
terminology used in the listed references.
Texts-Life Contingencies Segment
Introduction to Probability Models (Eighth Edition), 2003, by
Ross, S.M., Chapter 5, Sections 5.3.1, 5.3.2 (through Definition
5.1), 5.3.3, 5.3.4 (through Example 5.14 but excluding Example
5.13), Proposition 5.3 and the preceding paragraph, Example 5.18,
5.4.1(up to example 5.23), 5.4.2 (excluding Example 5.25), 5.4.3,
and Exercise 40. (available as study note MLC-27-07 below)
# Models for Quantifying Risk, Second Edition 2006, by
Cunningham, R., Herzog, T. and London, R.L., Chapters 3- 10,
excluding section 10.7. [Candidates may also use the First Edition,
2005, Chapters 5-6, 9-13,15, Sections 15.1-15.4, 15.6-15.7.
Candidates using the First Edition will need to supplement the text
with the Errata Package available on the Actex web
site.]
Note: It is anticipated that candidates will
have done the relevant exercises in the texts.
Study Notes-Life Contingencies Segment
Candidates should be sure to check this Study Note
Information page site periodically for additional corrections
or notices.
Evaluate features of the Vasicek and
Cox-Ingersoll-Ross bond price models.
Explain why the time-zero yield curve in the Vasicek
and Cox-Ingersoll-Ross bond price models cannot be exogenously
prescribed.
Construct a Black-Derman-Toy binomial model matching a
given time-zero yield curve and a set of volatilities
Use put-call parity to determine the relationship
between prices of European put and call options and to identify
arbitrage opportunities.
Calculate the value of European and American options
using the binomial model.
Calculate the value of European and American options
using the Black-Scholes option-pricing model.
Interpret the option Greeks.
Explain the cash flow characteristics of the following
exotic options: Asian, barrier, compound, gap, and exchange.
Explain what it means to say that stock prices follow
a diffusion process.
Apply Ito's lemma in the one-dimensional case.
Apply option pricing concepts to actuarial problems
such as equity-linked insurance.
Explain and demonstrate how to control risk using the
method of delta-hedging.
Note: Concepts, principles and techniques
needed for Exam M are covered in the reference listed below.
Candidates and professional educators may use other references, but
candidates should be very familiar with the notation and
terminology used in the listed references.
Texts-Financial Economics Segment
# Derivatives Markets (Second Edition), 2006, by McDonald,
R.L., Chapter 9-14 (excluding appendices), Chapter 20 through
"Functions of an Ito Process", Chapter 24.
Study Notes-Financial Economics Segment
Candidates should be sure to check this Study Note
Information page site periodically for additional corrections
or notices.
