reverses – compare addition and subtraction‚ multiplication and division‚ and powers and roots. The reverse of differentiation is antidifferentiation. A function F is an antiderivative of a function f if . ‚ ‚ then the functions differ ‚ If the derivatives of two functions are equal on an open interval by at most a constant. Symbolically: If F and G are differentiable functions on the interval for all x in ‚ ‚ then ‚ for some constant k. We use the symbol and called the indefinite integral‚ to
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Structure Lattice Models 1 Binomial-Lattice Models In these lecture notes1 we introduce binomial-lattice models for modeling the “short-rate”‚ i.e. the one-period spot interest rate. We will also use these models to introduce various interest rate derivatives that are commonly traded in the financial markets. First we define what an arbitrage means. Arbitrage A type A arbitrage is an investment that produces immediate positive reward at t = 0 and has no future cost at t = 1. An example of a type A
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Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations 1.0 Introduction In mathematics‚ if y is a function of x‚ then an equation that involves x‚ y and one or more derivatives of y with respect to x is called an ordinary differential equation (ODE). The ODEs which do not have additive solutions are non-linear‚ and finding the solutions is much more sophisticated because it is rarely possible to represent them by elementary function in close
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[pic] Fourier Series: Basic Results [pic] Recall that the mathematical expression [pic] is called a Fourier series. Since this expression deals with convergence‚ we start by defining a similar expression when the sum is finite. Definition. A Fourier polynomial is an expression of the form [pic] which may rewritten as [pic] The constants a0‚ ai and bi‚ [pic]‚ are called the coefficients of Fn(x). The Fourier polynomials are [pic]-periodic functions. Using the trigonometric
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Credit default swap: is a financial swap agreement that the seller of the CDS will compensate the buyer in the event of a loan default or other credit event. The buyer of the CDS makes a series of payments (the CDS "fee" or "spread") to the seller and‚ in exchange‚ receives a payoff if the loan defaults. In the event of default the buyer of the CDS receives compensation (usually the face value of the loan)‚ and the seller of the CDS takes possession of the defaulted loan.[1] However‚ anyone can purchase
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asset. Where the transaction is secured by eligible collateral‚ guarantee or credit derivative‚ the credit risk mitigation techniques detailed in AGN 112.3 Standardised Approach to Credit Risk: Simple Approach to Credit Risk Mitigation‚ AGN 112.4 Standardised Approach to Credit Risk: Comprehensive Approach to Credit Risk Mitigation and AGN 112.6 Standardised Approach to Credit Risk: Treatment of Credit Derivatives in the Banking Book may be used to reduce the regulatory capital charge of the exposure
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Brandon Deonath Add maths SBA Mrs. Ramnarine 5s Title: To find the maximum volume of a box using the method of differentiation. Problem statement: Mr. Lee‚ owner of a private cake company‚ sells a square 5 inch cake in a box made from 50 x 50 cm sheets of material. He would like to put a bigger square 8 inch cake in a box made from the same 50 x 50 com sheets of material. He decided to use the method of differentiation to help him with his task. Method: 1. Three squares measuring
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DERIVATIVES IN ISLAMIC FINANCE ANDREAS A. JOBST (forthcoming in Islamic Economic Studies‚ Vol. 15‚ No. 1) Paper presented at the International Conference on Islamic Capital Markets held in Jakarta‚ Indonesia during August 27-29‚ 2007 jointly organized by Islamic Research and Training Institute (IRTI) of the Islamic Development Bank (IDB)‚ Jeddah‚ Saudi Arabia‚ and Muamalat Institute‚ Jakarta‚ Indonesia. DERIVATIVES IN ISLAMIC FINANCE ANDREAS A. JOBST# ABSTRACT Despite their importance for
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EMG 211: ENGINEERING MATHEMATICS I COURSE OUTLINES PART ONE • • • • Maxima and Minima of Functions of a Single Independent Variable Tangents and Normals Differentiation Techniques of Differentiation PART TWO • Techniques of Integration: Indefinite Integrals‚ Integration by Parts‚ Definite Integrals‚ Improper Integrals • • Applications to Engineering Systems Introduction to Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) PART THREE • • • Properties and Evaluation
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MODERN FINANCIAL SYSTEM Lecture objectives * Understand the functions of a modern financial system ‘ * Comprises the interplay between interconnected financial institutions‚ markets and instruments. * Adjustment of current and future time periods Effective flow of funds through enabling modification of consumption between time periods “transfer today’s income for future consumption.” * Provides financial/economic information to participants generally reflects the state of the
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