Financial Mathematics

Admission requirements are available here. 

FINANCIAL MATHEMATICS, RISK MANAGEMENT

1. Amount function, percentage, and accumulation function. Effective rate of interest and rate of discount. Accumulation with simple and compound interest.
2. Nominal rate of interest. Continuous compounding.
3. Discounting. Present value. Discount function and discount factor.
4. Present and future values of cash flow. Annuities calculated at the beginning and end of the period (postnumerando, prenumerando). Calculation of their present and accumulated values.
5. General loan repayment scheme. Calculation of loan balance by prospective and retrospective methods.
6. Loan repayment amortization scheme, option with equal payments (annuity).
7. Net Present Value (NPV). Internal rate of return (IRR). The existence and uniqueness of the internal rate of return.
8. Bonds, their classification. Characteristics of bonds.
9. Bond price dependence on calculation parameters. from coupon, yield to maturity and maturity.
10. Duration of cash flow. Bond (Macaulay) Duration. Change in bond price due to change in yield to maturity. Modified Bond Duration. Bond convexity.
11. Dependence of bond Duration on parameters. from the coupon rate, from the yield to maturity, from the number of coupons.
12. Duration of the bond portfolio.
13. Shares, types of shares: common, preferred. The discounted dividend method of calculating the share price. Stock returns.
14. Forward and futures contracts, differences. Calculating the forward price in arbitrage-free markets (one-step binomial model).
15. Option contracts, types. Valuation of options in arbitrage-free markets (one-step binomial model).

MAIN LITERATURE

• S. Garrett. An Introduction to the Mathematics of Finance: A Deterministic Approach. Elsevier Science, 2013.
• D.G. Luenberger. Investment Science. Oxford University Press, 2009.
• S. Kellison, The Theory of Interest, 3rd Edition, 2009 
• J.C. Hull. Options, Futures, and Other Derivatives. Pearson Education, 2014.
• D. Lovelock, M. Mendel, and A.L. Wright. An Introduction to the Mathematics of Money: Saving and Investing. Texts in applied mathematics. Springer, 2007.
• D.J. Smith. Bond Math: The Theory Behind the Formulas, + Website. Wiley Finance. Wiley, 2014.

ACTUARIAL MATHEMATICS

1. The main probabilistic characteristics of random variable of time to death (Survival function, mortality rate).
2. Distribution of residual time of life and related basic formulas.
3. Approximations for fractional ages (linear, exponential and hyperbolic). Integral characteristics of residual life expectancy for fractional ages.
4. Analysis of short-term life insurance models (estimation of ruin probability, assessment of individual risks).
5. Total risk premium in case of short-term life insurance.
6. Models of short-term life insurance. Principles of determining the insurance premium. Methods for risk loading to the k-th contract (3 main models).
7. Calculation of the net insurance premium for n-year endowment insurance model (discrete and continuous cases).
8. Calculation of the net insurance premium for m-years deferred life insurance (discrete and continuous cases).
9. Calculation of the net insurance premium for the life insurance model with annual increasing benefits (discrete and continuous cases).
10. Connections between discrete and continuous insurance models.
11. Derivation of the actuarial present value of a term annuity using the aggregate payment and current payment methods.
12. Annuities payable m-thly. Approximation of annuities payable m-thly in terms of annual annuities in case of uniform distribution of deaths during the year.
13. Franchise and liability limits.
14. Reinsurance and its types. Average compensation for excess of loss reinsurance from the insurer's perspective.
15. Reinsurance and its types. Average compensation for excess of loss reinsurance from the reinsurer's perspective.

MAIN LITERATURE

• Фалин Г.И. “Математические основы теории страхования жизни и пенсионных схем”, Москва, 2007
• Dickson David C.M. “Actuarial Mathematics of life contingent risks”, Cambrige University Press, 2009
• Бауэрс, Н. и др. ”Актуарная Математика”, Москва, 2001
• Bowers at. all, “Actuarial Mathematics”, SOA

ECONOMETRICS

1. Ordinary least squares estimates for simple regression model.
2. Deriving and interpretation of coefficient of determination.
3. The Gauss-Markov theorem for multiple regression models.
4. Testing hypotheses about linear regression population parameters. The t and F tests.
5. Consistency and asymptotic normality theorems of ordinary least squares estimators.
6. Multilpe regression analysis with qualitative information: Dummy Variables.
7. Sources, consequences and testing of heteroskedasticity.
8. Weighted least squares estimation and feasible GLS estimation.
9. Sources and consequences of endogeneity, instrumental variables.

MAIN LITERATURE

• Jeffrey M. Wooldridge, Introductory Econometrics, South-Western Cengage Learning, 2013․

FINANCIAL RISK MANAGEMENT 

1. The role and importance of risk management in financial and non-financial institutions.
2. Market risk. Methods of market risk management in banks.
3. Credit risk. Assessment of expected and unexpected credit losses. Probability of default estimation methods. 
4. Definition of VaR. Parametric and non-parametric methods of VaR estimation.
5. Liquidity risk and its assessment methods in financial institutions.
6. Fund transfer pricing and its assessment methods.
7. Stress testing: historic, hypothetic and algorithmic approaches to stress testing. 

BASIC LITERATURE

• Crouhy, M., et al. 2013, The Essentials of Risk Management, Second Edition, McGraw-Hill.
• Մելիք-Փարսադանյան, Վ․ և Վարդումյան, Է․, Քանակական մեթոդները ֆինանսաներում, ԵՊՀ, 2017:
• Fiedler, R., 2011, Liquidity Modelling, Risk books.

MICROECONOMICS, MACROECONOMICS

1. Utility function, utility maximization, and consumer cost minimization problems.
2. Substitution and income effects, Slutsky equation.
3. The problem of minimization of production costs, the demand for resources of firms and the supply of products.
4. Equilibrium in the short run, equilibrium in the long run in cases of constant, increasing, decreasing curves of scale and U-shaped LRAC.
5. Profit maximization under monopoly conditions, price discrimination, natural monopolies and their regulation.
6. Oligopoly, quantity and price leadership. Cournot and Steckelberg equilibria.
7. Production efficiency, Pareto-best, general equilibrium, welfare theorems.
8. Labor demand and supply in neo-classical and Keynesian concepts. Equilibrium in a competitive labor market.
9. Consumption. Keynesian consumption function, intertemporal budget constraint, life cycle and permanent income theories.
10. Investments. Basic investment theory, the investment accelerator model, and settlement costs.
11. State sector. Ricardian equivalence, temporary and permanent increases in government spending.
12. Demand for money. Baumol-Tobin model, speculative demand for money, precautionary demand for money.
13. Money supply, money multipliers, fundamental equation of money base change, equilibrium in the money market.
14. IS-LM model in closed and open economies, Keynes multiplier, aggregate demand.

BASIC LITERATURE

• Hal R. Varian, Intermediate Microeconomics, W.W. Norton & Company, 2001․
• B. Binger, E. Hoffmann, Microeconomics with Calculus, Pearson, 1998․
• N. Gregory Mankiw, Macroeconomics, Worth Publishers, 2016․
• Սաքս Ջ., Լարրեյն Բ. Մակրոտնտեսագիտությունը գլոբալ տնտեսությունում, Երևան, Տնտեսագետ, 2002։

BIBLIOGRAPHY

1. S. Garrett. An Introduction to the Mathematics of Finance: A Deterministic Approach. Elsevier Science, 2013.
2. D.G. Luenberger. Investment Science. Oxford University Press, 2009.
3. S. Kellison, The Theory of Interest, 3rd Edition, 2009․
4. J.C. Hull. Options, Futures, and Other Derivatives. Pearson Education, 2014.
5. D. Lovelock, M. Mendel, and A.L. Wright. An Introduction to the Mathematics of Money: Savin Gand Investing. Texts in applied mathematics. Springer, 2007.
6. D.J. Smith. Bond Math: The Theory Behind the Formulas, + Website. Wiley Finance. Wiley, 2014.
7. Фалин Г.И. “Математические основы теории страхования жизни и пенсионных схем”, Москва, 2007․
8. Dickson David C.M. “Actuarial Mathematics of life contingent risks”, Cambrige University Press, 2009․
9. Бауэрс, Н. и др. ”Актуарная Математика”, Москва, 2001․
10. Bowers at. all, “Actuarial Mathematics”, SOA․
11. Crouhy, M., et al. 2013, The Essentials of Risk Management, Second Edition, McGraw-Hill․
12. Fiedler, R., 2011, Liquidity Modelling, Risk books.
13. Jeffrey M. Wooldridge, Introductory Econometrics, South-Western Cengage Learning, 2013․
14. Hal R. Varian, Intermediate Microeconomics, W.W. Norton & Company, 2001․
15. B. Binger, E. Hoffmann, Microeconomics with Calculus, Pearson, 1998․
16. N. Gregory Mankiw, Macroeconomics, Worth Publishers, 2016․
17. Մելիք-Փարսադանյան, Վ․ և Վարդումյան, Է․, Քանակական մեթոդները ֆինանսաներում, ԵՊՀ, 2017:
18. Սաքս Ջ., Լարրեյն Բ. Մակրոտնտեսագիտությունը գլոբալ տնտեսությունում, Երևան, Տնտեսագետ, 2002։