Stochastic Modeling in Economics and Finance (Applied Optimization)
Language: English
Pages: 386
ISBN: 1441952314
Format: PDF / Kindle (mobi) / ePub
In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities.
Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects.
Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study.
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Thus the taxation reduces the returns. Moreover, the taxes are often different for various types of investment and sometimes are progressive, i.e., the higher the return, the higher the taxes. Thus any investment should be carefully valued with respect to tax consideration. 2.4 Decomposition of the Interest Rate Taking into account all the factors which affect the so called quoted or nominal interest rate we can write where denotes the risk free interest rate if we do not consider inflation,
the difference is negligible. We also have and Since the convexities fulfil the inequality we can decide in favor of project C against A. Further, the crossover rate for projects C and E is Thus to summarize, for we accept C and for we accept E, among the candidates A, C, E. If we consider all the five projects, then we obviously select B for and E for greater values of 3.7.4 Internal Value Suppose that the cash flow in question depends also on another variable or parameter say, For decision
has an obvious disadvantage for the issuer; if the interest rates fall during the bond life, it is often possible for the issuer to get cheaper funds, for instance by issuing bonds with lower coupon. The security which partly gets rid of this feature is callable bond. The situation is the same as with the usual coupon bonds but in this case, the issuer has the right to buy some or all issued bonds prior to the original maturity date or to call them, in other words. Since the earlier repayment of
of the type (11) – (12) from Section II.2.2. Comparing this procedure with the general hints, the three stages correspond to the planning horizon of three years, the chosen structure of the scenario tree, was partly given by the limitations of the computational technology twenty years ago. Another reported structure used four stages covering two years by periods of 174 STOCHASTIC MODELING IN ECONOMICS AND FINANCE 3 months, 3 months, 6 months and one year which reflects the increasing
of the same entity. There is a numerical evidence in favor of performance of stochastic programs based on scenario trees with moment values fitted at each node over those based only on a few randomly sampled realizations. Moreover, taking into account the wish to approximate well the expectation offunction which appears in the objective function of the stochastic program (4), it is possible to search for extremal scenarios, the atoms of the worst or best discrete probability distributions which
