CM2 – Financial

Engineering and Loss

Reserving

Syllabus

for the 2021 exams

June 2020

© Institute and Faculty of Actuaries 1

CM2 – Financial Engineering

and Loss Reserving

Aim

The aim of the Financial Engineering and Loss Reserving subject is to provide a grounding in the principles of modelling as applied

to actuarial work – focusing particularly on stochastic asset-liability models and the valuation of fnancial derivatives. These skills

are also required to communicate with other fnancial professionals and to critically evaluate modern fnancial theories.

Competences

On successful completion of this subject, a student will be able to:

1 describe, interpret and discuss the theories on the behaviour of fnancial markets.

2 discuss the advantages and disadvantages of diﬀerent measures of investment risk.

3 describe, construct, interpret and discuss the models underlying asset valuations.

4 describe, construct, interpret and discuss the models underlying liability valuations.

5 describe, construct, interpret and discuss the models underlying option pricing.

Links to other subjects

Concepts are introduced in:

CS1 – Actuarial Statistics

CS2 – Risk Modelling and Survival Analysis

CM1 – Actuarial Mathematics

CB2 – Business Economics

Topics in this subject are further built upon in:

CP1 – Actuarial Practice

CP2 – Modelling Practice

SP5 – Investment and Finance Principles

SP6 – Financial Derivatives Principles

SP9 – Enterprise Risk Management Principles

Syllabus topics

1 Theories of fnancial market behaviour (15%)

2 Measures of investment risk (15%)

3 Stochastic investment return models (10%)

4 Asset valuations (20%)

5 Liability valuations (20%)

6 Option theory (20%)

These weightings are indicative of the approximate balance of the assessment of this subject between the main syllabus topics,

averaged over a number of examination sessions.

The weightings also have a correspondence with the amount of learning material underlying each syllabus topic. However, this

will also reﬂect aspects such as:

• the relative complexity of each topic and hence the amount of explanation and support required for it.

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CM2

• the need to provide thorough foundation understanding on which to build the other objectives.

• the extent of prior knowledge that is expected.

• the degree to which each topic area is more knowledge- or application-based.

Skill levels

The use of a specifc command verb within a syllabus objective does not indicate that this is the only form of question that can

be asked on the topic covered by that objective. The Examiners may ask a question on any syllabus topic using any of the agreed

command verbs, as are defned in the document ‘Command verbs used in the Associate and Fellowship written examinations’.

Questions may be set at any skill level: Knowledge (demonstration of a detailed knowledge and understanding of the topic), Application

(demonstration of an ability to apply the principles underlying the topic within a given context) and Higher Order (demonstration of an

ability to perform deeper analysis and assessment of situations, including forming judgements, taking into account diﬀerent points of

view, comparing and contrasting situations, suggesting possible solutions and actions and making recommendations).

In the CM subjects, the approximate split of assessment across the three skill types is 20% Knowledge, 65% Application and 15%

Higher Order skills.

Detailed syllabus objectives

1 Theories of fnancial market behaviour (15%)

1.1 Rational expectations theory.

1.1.1 Discuss the three forms of the Efcient Markets Hypothesis and their consequences for investment management.

1.1.2 Describe brieﬂy the evidence for or against each form of the Efcient Markets Hypothesis.

1.2 Rational choice theory.

1.2.1 Explain the meaning of the term ‘utility function’.

1.2.2 Explain the axioms underlying utility theory and the expected utility theorem.

1.2.3 Explain how the following economic characteristics of investors can be expressed mathematically in a utility function:

• Non-satiation

• Risk aversion, risk neutrality and risk seeking

• Declining or increasing absolute and relative risk aversion.

1.2.4 Discuss the economic properties of commonly used utility functions.

1.2.5 Discuss how a utility function may depend on current wealth and discuss state-dependent utility functions.

1.2.6 Perform calculations using commonly used utility functions to compare investment opportunities.

1.2.7 State conditions for absolute dominance and for frst- and second-order dominance.

1.2.8 Analyse simple insurance problems in terms of utility theory.

1.3 Behavioural economics.

1.3.1 Describe the main features of Kahneman and Tversky’s prospect theory critique of expected utility theory.

1.3.2 Explain what is meant by ‘framing’, ‘heuristics’ and ‘bias’ in the context of fnancial markets and describe the following

features of behaviour in such markets:

• The herd instinct

• Anchoring and adjustment

• Self-serving bias

• Loss aversion

• Confrmation bias

• Availability bias

• Familiarity bias.

1.3.3 Describe the Bernartzi and Thaler solution to the equity premium puzzle.

2 Measures of investment risk (15%)

2.1 Properties of risk measures.

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CM2

2.1.1 Defne the following measures of investment risk:

• Variance of return

• Downside semi-variance of return

• Shortfall probabilities

• Value at Risk (VaR)

• Tail VaR (also referred to as Expected Shortfall).

2.1.2 Describe how the risk measures listed in 2.1.1 are related to the form of an investor’s utility function.

2.1.3 Perform calculations using the risk measures listed in 2.1.1 to compare investment opportunities.

2.1.4 Explain how the distribution of returns and the thickness of tails will inﬂuence the assessment of risk.

2.2 Risk and insurance companies.

2.2.1 Describe how insurance companies help to reduce or remove risk.

2.2.2 Explain what is meant by the terms ‘moral hazard’ and ‘adverse selection’.

3 Stochastic interest rate of return models (10%)

3.1 Show an understanding of simple stochastic models for investment returns.

3.1.1 Describe the concept of a stochastic investment return model and the fundamental distinction between this and a

deterministic model.

3.1.2 Derive algebraically, for the model in which the annual rates of return are independently and identically distributed

and for other simple models, expressions for the mean value and the variance of the accumulated amount of a

single premium.

3.1.3 Derive algebraically, for the model in which the annual rates of return are independently and identically distributed,

recursive relationships that permit the evaluation of the mean value and the variance of the accumulated amount of

an annual premium.

3.1.4 Derive analytically, for the model in which each year the random variable (1 + r ) has an independent log-normal

distribution, the distribution functions for the accumulated amount of a single premium and for the present value of a

sum due at a given specifed future time.

3.1.5 Apply the above results to the calculation of the probability that a simple sequence of payments will accumulate to a

given amount at a specifc future time.

4 Asset valuations (20%)

4.1 Mean-variance portfolio theory.

4.1.1 Describe and discuss the assumptions of mean-variance portfolio theory.

4.1.2 Discuss the conditions under which application of mean-variance portfolio theory leads to the selection of an

optimum portfolio.

4.1.3 Calculate the expected return and risk of a portfolio of many risky assets, given the expected return, variance and

covariance of returns of the individual assets, using mean-variance portfolio theory.

4.1.4 Explain the benefts of diversifcation using mean-variance portfolio theory.

4.2 Asset pricing models.

4.2.1 Describe the assumptions, principal results and uses of the Sharpe–Lintner–Mossin Capital Asset Pricing Model (CAPM).

4.2.2 Discuss the limitations of the basic CAPM and some of the attempts that have been made to develop the theory to

overcome these limitations.

4.2.3 Perform calculations using the CAPM.

4.2.4 Discuss the main issues involved in estimating parameters for asset pricing models.

4.3 Single and multifactor models for investment returns.

4.3.1 Describe the three types of multifactor models of asset returns:

• Macroeconomic models

• Fundamental factor models

• Statistical factor models.

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4.3.2 Discuss the single-index model of asset returns.

4.3.3 Discuss the concepts of diversifable and non-diversifable risk.

4.3.4 Discuss the construction of the diﬀerent types of multifactor models.

4.3.5 Perform calculations using both single and multifactor models.

4.4 Stochastic models for security prices.

4.4.1 Discuss the continuous time log-normal model of security prices and the empirical evidence for or against the model.

4.4.2 Explain the defnition and basic properties of standard Brownian motion or Wiener process.

4.4.3 Demonstrate a basic understanding of stochastic diﬀerential equations, the Ito integral, diﬀusion and mean-reverting

processes.

4.4.4 State Ito’s Lemma and be able to apply it to simple problems.

4.4.5 Write down the stochastic diﬀerential equation for geometric Brownian motion and show how to fnd its solution.

4.4.6 Write down the stochastic diﬀerential equation for the Ornstein–Uhlenbeck process and show how to fnd its solution.

4.5 Models of the term structures of interest rates.

4.5.1 Explain the principal concepts and terms underlying the theory of a term structure of interest rates.

4.5.2 Describe the desirable characteristics of models for the term structure of interest rates.

4.5.3 Apply the term structure of interest rates to modelling various cashﬂows, including calculating the sensitivity of the

value to changes in the term structure.

4.5.4 Describe, as a computational tool, the risk-neutral approach to the pricing of zero-coupon bonds and interest-rate

derivatives for a general one-factor diﬀusion model for the risk-free rate of interest.

4.5.5 Describe, as a computational tool, the approach using state-price deﬂators to the pricing of zero-coupon bonds and

interest-rate derivatives for a general one-factor diﬀusion model for the risk-free rate of interest.

4.5.6 Demonstrate an awareness of the Vasicek, Cox–Ingersoll–Ross and Hull–White models for the term structure of

interest rates.

4.5.7 Discuss the limitations of these one-factor models and show an awareness of how these issues can be addressed.

4.6 Simple models for credit risk.

4.6.1 Defne the terms ‘credit event’ and ‘recovery rate’.

4.6.2 Describe the diﬀerent approaches to modelling credit risk: structural models, reduced form models, intensity-based

models.

4.6.3 Demonstrate a knowledge and understanding of the Merton model.

4.6.4 Demonstrate a knowledge and understanding of a two-state model for credit ratings with a constant transition intensity.

4.6.5 Describe how the two-state model can be generalised to the Jarrow–Lando–Turnbull model for credit ratings.

4.6.6 Describe how the two-state model can be generalised to incorporate a stochastic transition intensity.

5 Liability valuations (20%)

5.1 Ruin theory.

5.1.1 Explain what is meant by the aggregate claim process and the cashﬂow process for a risk.

5.1.2 Use the Poisson process and the distribution of inter-event times to calculate probabilities of the number of events in

a given time interval and waiting times.

5.1.3 Defne a compound Poisson process and calculate probabilities using simulation.

5.1.4 Defne the probability of ruin in infnite/fnite and continuous/discrete time and state, and explain relationships

between the diﬀerent probabilities of ruin.

5.1.5 Describe the eﬀect on the probability of ruin, in both fnite and infnite time, of changing parameter values by

reasoning or simulation.

5.1.6 Calculate probabilities of ruin by simulation.

5.2 Run-oﬀ triangles.

5.2.1 Defne a development factor and show how a set of assumed development factors can be used to project the future

development of a delay triangle.

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5.2.2 Describe and apply a basic chain ladder method for completing the delay triangle using development factors.

5.2.3 Show how the basic chain ladder method can be adjusted to make explicit allowance for inﬂation.

5.2.4 Describe and apply the average cost per claim method for estimating outstanding claim amounts.

5.2.5 Describe and apply the Bornhuetter–Ferguson method for estimating outstanding claim amounts.

5.2.6 Describe how a statistical model can be used to underpin a run-oﬀ triangles approach.

5.2.7 Discuss the assumptions underlying the application of the methods in 5.2.1 to 5.2.6 above.

5.3 Value basic beneft guarantees using simulation techniques.

6 Option theory (20%)

6.1 Option pricing and valuations.

6.1.1 State what is meant by arbitrage and a complete market.

6.1.2 Outline the factors that aﬀect option prices.

6.1.3 Derive specifc results for options that are not model dependent:

• Show how to value a forward contract.

• Develop upper and lower bounds for European and American call and put options.

• Explain what is meant by put-call parity.

6.1.4 Show how to use binomial trees and lattices in valuing options and solve simple examples.

6.1.5 Derive the risk-neutral pricing measure for a binomial lattice and describe the risk-neutral pricing approach to the

pricing of equity options.

6.1.6 Explain the diﬀerence between the real-world measure and the risk-neutral measure. Explain why the risk-neutral pricing

approach is seen as a computational tool (rather than a realistic representation of price dynamics in the real world).

6.1.7 State the alternative names for the risk-neutral and state-price deﬂator approaches to pricing.

6.1.8 Demonstrate an understanding of the Black–Scholes derivative-pricing model:

• Explain what is meant by a complete market.

• Explain what is meant by risk-neutral pricing and the equivalent martingale measure.

• Derive the Black–Scholes partial diﬀerential equation both in its basic and Garman–Kohlhagen forms.

• Demonstrate how to price and hedge a simple derivative contract using the martingale approach.

6.1.9 Show how to use the Black–Scholes model in valuing options and solve simple examples.

6.1.10 Discuss the validity of the assumptions underlying the Black–Scholes model.

6.1.11 Describe and apply in simple models, including the binomial model and the Black–Scholes model, the approach to

pricing using deﬂators and demonstrate its equivalence to the risk-neutral pricing approach.

6.1.12 Demonstrate an awareness of the commonly used terminology for the frst and, where appropriate, second partial

derivatives (the Greeks) of an option price.

Assessment

Combination of a one-hour and forty-fve-minute computer-based modelling assignment and a three-hour and ffteen-minute

written examination.

END