[...]... 0, , 6 is (-9 0000, -1 5200, 45000, 60000, 25000, 22000, 27000=12000+15000) Graphical illustration is given in Figure 1 1.5 Financial and Real Estate Investment Since handling money and capital itself is a rather complicated task, there are financial intermediaries and other financial institutions which should, in principle, handle money and capital efficiently Financial institutions are business firms... R Martindale for publishing the book J Hurt, and 1 2 3 MSM 1132000008 Mathematical Methods in Stochastics 402/99/1136, 201/99/0264, 201/00/0770 INCO’95, HPC /Finance Project, no 951139 xiii 1 Part I FUNDAMENTALS I.1 MONEY, CAPITAL, AND SECURITIES money, capital, investment, interest, cash flows, financing business, securities, financial market, financial institutions, financial system 1.1 Money and Capital... The present value is a linear function on in the following sense: if then Let us consider the payments at equally spaced time instants 0, , T, again, but with different interest rates in the compounding periods 22 STOCHASTIC MODELING IN ECONOMICS AND FINANCE where is the interest rate applied in the period Then the present value of the given cash flow is where by definition Finally, let us assume that... corresponding expected inflation is a one-year inflation, and the risk free-rate is derived from one-year T-bills rates and the maturity risk premium has a negligible influence on the nominal rate in a stable economy For a ten-years’ quoted interest rate we should take ten-years yields of the government bonds for the riskless rate and carefully consider the other factors affecting the nominal interest... – an out-barrier , or if the asset price crosses a certain value – an in- barrier during the life of the option contract There are four possible cases: (1) up -and -in; the option pays only if the barrier is reached from below, (2) down -and -in; the option pays only if the barrier is reached from above, (3) up -and- out; the option pays only if the barrier is not reached from below, (4) down -and- out; the... assets in the form of either financial assets or claims like stocks, bonds, and loans Financial institutions make loans and offer a variety of financial services (investment, life and general insurance, savings, pensions, credits, mortgages, leasing, real estates, etc.) 1.5.1 Financing the Business – Description Almost every economic activity (of an individual, firm, bank, city, government) must be financed... The idea of continuous compounding comes from the usual concept of compounding for the number of compounding periods approaching to infinity In this case, we consider the nominal interest rate called the force of interest or often interest rate in the continuous financial mathematics) per unit time so that the future value FV of the initial investment PV (at time after time T becomes In other words,... its investment Simply, interest is Typeset by 2 STOCHASTIC MODELING IN ECONOMICS AND FINANCE the price of deferred consumption paid to ultimate savers Note that the actual allocation of savings in a reasonably functioning economy is accomplished through interest rates, see next Section In other words, capital in a free economy is allocated through a certain price system and the interest rate expresses... Fixed-income securities are debt instruments characterized by a specified maturity date (the date of payoff the debt) and a known schedule of repaying the principal and interest 1.6.1.2 Demand Deposits Commercial banks and saving societies offer to their clients checking accounts or demand deposits which are interest bearing but the interest is usually very small A better situation is with savings... or contingent claims are the instruments where the payment of either party depends on the value of an underlying asset or assets The underlying assets in question may be of a rather general form, e.g stocks, bonds, commodities, currencies, stock exchange indexes, interbank offer rates, and even derivatives themselves The underlying assets thus fall into two main groups; 8 STOCHASTIC MODELING IN ECONOMICS . exchange indexes, interbank offer rates, and even derivatives themselves. The underlying assets thus fall into two main groups; 8 STOCHASTIC MODELING IN ECONOMICS AND FINANCE commodity assets and financial. speaking, the callable bond is not a fixed-income security since the payments coming from it are uncertain and depend both on the issuer policy and market interest rates. 6 STOCHASTIC MODELING IN. given in Figure 1. 1.5 Financial and Real Estate Investment Since handling money and capital itself is a rather complicated task, there are financial intermediaries and other financial institutions