Dear potential participant
The TACIS Project – Support to Ukrainian Insurance Sector – will be organising over the next one and a half years a series of six one-week seminars on actuarial subjects.
The content of the first Seminar – Financial Economics – to be held on March 13-17, 2007 in Kyiv, is as follows
• The advantages and disadvantages of different measures of investment risk.
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The assumptions of mean-variance portfolio theory and its principal results.
The properties of single and multifactor models of asset returns.
Asset pricing models, including the principal results and assumptions and the limitations of such models.
• The various forms of the Efficient Markets Hypothesis and the evidence for and against the hypothesis.
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Stochastic models of the behaviour of security prices.
The main concepts of Brownian motion (or Wiener Processes).
• The properties of option prices, valuation methods and hedging techniques.
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Models of the term structure of interest rates.
A more detailed content can be provided on request.
The aim of the seminar is to help bring the knowledge of the existing actuaries in Ukraine up to an acceptable international level.
The Lecturer will be Mr Matt Wood, who is a Mathematics graduate of Cambridge University and also has a Certificate of Advanced Studies in Mathematics from the same University. He is a Fellow
(Full Member) of the British Institute of Actuaries and works as an actuary within the Government
Actuary’s Department in London, Great Britain.
Learning material will be made available in both Ukrainian and English languages. The Seminar will be given in English with consecutive translation into Ukrainian.
The intended audience for this seminar is all those working as actuaries within the insurance sector in
Ukraine, for example within insurance companies or within the NBFIR, and those teaching actuarial subjects within universities.
It will be assumed that participants have a university degree in mathematics, statistics or something similar and are familiar with basic actuarial mathematics.
Following the seminar there will be an examination. It is the intention, subject to final formal approval from the NBFIR, that successful completion of each examination will be recognised as helping to meet the education requirement for licensing actuaries. In particular, those actuaries licensed in 1999 will be expected to attend these seminars and successfully complete the examinations, if they wish to have their license renewed.

Seminar 1 – Financial Economics
(i) The advantages and disadvantages of different measures of investment risk.
1. Definition of the following measures of investment risk: variance of return downside semi-variance of return shortfall probabilities
Value at Risk (VaR) / Tail VaR
2. Description of how the risk measures listed in (i) 1. are related to the form of an investor’s utility function.
3. Performance of calculations using the risk measures listed above to compare investment opportunities.
4. Explanation of how the distribution of returns and the thickness of tails will influence the assessment of risk.
(ii) The assumptions of mean-variance portfolio theory and its principal results.
1. Description and discussion of the assumptions of mean-variance portfolio theory.
2. Discussion of the conditions under which the application of mean-variance portfolio theory leads to the selection of an optimum portfolio.
3. Calculation of 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 meanvariance portfolio theory.
4. Explanation of the benefits of diversification using mean-variance portfolio theory.
5. Explanation of what is meant by: opportunity set, efficient frontier, indifference curves and the optimum portfolio, in the context of mean-variance portfolio theory.
(iii) The properties of single and multifactor models of asset returns.
1. Description of the three types of multifactor models of asset returns: macroeconomic models fundamental factor models statistical factor models
2. Discussion of the single index model of asset returns.
3. Discussion of the concepts of diversifiable and non-diversifiable risk.
4. Discussion of the construction of the different types of multifactor models.
5. Performance of calculations using both single and multi-factor models.

(iv) Asset pricing models, including the principal results and assumptions and the limitations of such models.
1. Description of the assumptions and the principal results of the Sharpe-Lintner-Mossin
Capital Asset Pricing Model (CAPM).
2. Discussion of the limitations of the basic CAPM and some of the attempts that have been made to develop the theory to overcome these limitations.
3. Discussion of the assumptions, principal results and limitations of the Ross Arbitrage
Pricing Theory model (APT).
4. Performance of calculations using the CAPM.
(v) The various forms of the Efficient Markets Hypothesis and the evidence for and against the hypothesis.
1. Discussion of the three forms of the Efficient Markets Hypothesis and their consequences for investment management.
2. Brief description of the evidence for or against each form of the Efficient Markets
Hypothesis.
(vi) Stochastic models of the behaviour of security prices.
1. Discussion of the continuous time log-normal model of security prices and the empirical evidence for and against the model.
2. Discussion of the structure of auto-regressive models of security prices and other economic variables, such as the Wilkie model, and description of the economic justification for such models.
3. Discussion of the main alternatives to the models covered in (vi) 1. and (vi) 2. and description of their strengths and weaknesses.
4. Performance of simple calculations involving the models described above.
5. Discussion of the main issues involved in estimating parameters for asset pricing models: data availability data errors outliers stationarity of underlying time series the role of economic judgement
(vii) The main concepts of Brownian motion (or Wiener Processes).
1. Explanation of the definition and basic properties of standard Brownian motion or Wiener process.
2. Explanation of the definition and basic properties of martingales.

3. Demonstration that the discrete sampling of a Wiener process gives a normally distributed random walk, and that it can also be seen as the limit of such a random walk.
4. Demonstration of a basic understanding of stochastic differential equations, the Ito integral, diffusion and nean-reverting processes.
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Statement of Ito’s formula and its application to simple problems.
6. Statement of the stochastic differential equation for geometric Brownian motion and demonstration of how to find its solution.
7. Statement of the stochastic differential equation for the Ornstein-Uhlenbeck process and demonstration of how to find its solution.
8. Explanation of the concept of multivariate Brownian motion , possibly with correlation.
(viii) The properties of option prices, valuation methods and hedging techniques.
1. Statement of what is meant by arbitrage and a complete market, and explanation of why arbitrage may be considered impossible in many markets.
2. Calculation of the price of a forward contract in the absence of arbitrage assuming: no income or expenditure associated with the underlying asset during the term of the contract a fixed income from the asset during the term a fixed dividend yield from the asset during the term.
3. Explanation of what is meant by hedging in the case of a forward contract.
4. Calculation of the value of a forward contract at any time during the term of the contract in the absence of arbitrage, in the situations listed in 2. above.
5. Outlining of the factors that affect option prices.
6. Derivation of specific results for options which are not model dependent:
Derivation of how to value a forward contract.
Development of upper and lower bounds for European and American call and put options.
Explanation of what is meant by put-call parity.
7. Demonstration of how to use binomial trees and lattices in valuing options and solution of simple examples.
8. Derivation of the risk-neutral pricing measure for a binomial lattice and description of the risk-neutral pricing approach to the pricing of equity options.
9. Explanation of the difference between the real-world measure and the risk-neutral measure. Explanation of why the risk-neutral pricing approach is seen as a computational tool (rather than a realistic representation of price dynamics in the real world).
10. Statement of the alternative names for the risk-neutral and state-price deflator approaches to pricing.

11. The Black-Scholes derivative-pricing model:
Explanation of what is meant by a complete market.
Explanation of what is meant by risk-neutral pricing and the equivalent martingale measure.
Derivation of the Black-Scholes partial differential equation both in its basic and
Garman- Kohlhagen forms.
Demonstration of how to price and hedge a simple derivative contract using the martingale approach.
12. Demonstration of how to use the Black-Scholes model in valuing options and solution of simple examples.
13. Discussion of the validity of the assumptions underlying the Black-Scholes model.
14. Description, and its application in simple models including the binomial model and the
Black- Scholes model, of the approach to pricing using deflators and demonstration of its equivalence to the risk-neutral pricing approach.
15. Awareness of the commonly used terminology for the first, and where appropriate second, partial derivatives (the Greeks) of an option price.
16. Description of how the Greeks are used in the risk management of a portfolio of derivatives.
17. Derivation of the partial derivatives described above for Black-Scholes European option prices and description of their general characteristics.
18. The concept of delta-hedging and demonstration of how to apply it.
(ix) Models of the term structure of interest rates.
1. Description of the desirable characteristics of a model for the term-structure of interest rates.
2. Description, as a computational tool, of the risk-neutral approach to the pricing of zerocoupon bonds and interest-rate derivatives for a general one-factor diffusion model for the risk-free rate of interest.
3. Description, as a computational tool, of 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. Statement of the Vasicek, Cox-Ingersoll-Ross and Hull-White models for the termstructure of interest rates.
5. Discussion of the limitations of these one-factor models and statement of how these issues can be addressed.