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Bond Convexity
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates ( duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller. Calculation of convexity Duration is a linear measure or 1st derivative of how the price of a bond changes in response to interest rate changes. As interest rates change, the price is not likely to change linearly, but instead it would change over some curved function of interest rates. The more curved the price function of the bond is, the more inaccurate duration is as a measure of the interest rate sensitivity. Convexity is a measure of the curvature or 2n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Embedded Option
An embedded option is a component of a financial bond or other security, which provides the bondholder or the issuer the right to take some action against the other party. There are several types of options that can be embedded into a bond; common types of bonds with embedded options include callable bond, puttable bond, convertible bond, extendible bond, exchangeable bond, and capped floating rate note. A bond may have several options embedded if they are not mutually exclusive. Securities other than bonds that may have embedded options include senior equity, convertible preferred stock and exchangeable preferred stock. See Convertible security. The valuation of these securities couples bond- or equity-valuation, as appropriate, with option pricing. For bonds here, there are two main approaches, as follows. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finance
Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Administration wich study the planning, organizing, leading, and controlling of an organization's resources to achieve its goals. Based on the scope of financial activities in financial systems, the discipline can be divided into Personal finance, personal, Corporate finance, corporate, and public finance. In these financial systems, assets are bought, sold, or traded as financial instruments, such as Currency, currencies, loans, Bond (finance), bonds, Share (finance), shares, stocks, Option (finance), options, Futures contract, futures, etc. Assets can also be banked, Investment, invested, and Insurance, insured to maximize value and minimize loss. In practice, Financial risk, risks are always present in any financial action and entities. Due ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Securities Industry And Financial Markets Association
A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any form of financial instrument, even though the underlying legal and regulatory regime may not have such a broad definition. In some jurisdictions the term specifically excludes financial instruments other than equity and fixed income instruments. In some jurisdictions it includes some instruments that are close to equities and fixed income, e.g., equity warrants. Securities may be represented by a certificate or, more typically, they may be "non-certificated", that is in electronic ( dematerialized) or " book entry only" form. Certificates may be ''bearer'', meaning they entitle the holder to rights under the security merely by holding the security, or ''registered'', meaning they entitle the holder to rights only if they appear on a securit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Fabozzi
Frank J. Fabozzi is an American economist, educator, writer, and investor, currently Professor of Practice at The Johns Hopkins University Carey Business School and a Member of Edhec Risk Institute. He was previously a professor of finance at EDHEC Business School, Professor in the Practice of Finance and Becton Fellow in the Yale School of Management, and a visiting professor of finance at the Sloan School of Management at the Massachusetts Institute of Technology. He has authored and edited many books, three of which were coauthored with Nobel laureates, Franco Modigliani and Harry Markowitz. He has been the editor of the '' Journal of Portfolio Management'' since 1986 and is on the board of directors of the BlackRock complex of closed-end funds. Early life and education He earned a BA (magna cum laude) and a Master of Economics from the City College of New York, both in 1970. He also earned a doctorate in economics from the Graduate Center of the City University of New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Finance Topics
A list is a set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of the list-maker, but lists are frequently written down on paper, or maintained electronically. Lists are "most frequently a tool", and "one does not ''read'' but only ''uses'' a list: one looks up the relevant information in it, but usually does not need to deal with it as a whole". Lucie Doležalová,The Potential and Limitations of Studying Lists, in Lucie Doležalová, ed., ''The Charm of a List: From the Sumerians to Computerised Data Processing'' (2009). Purpose It has been observed that, with a few exceptions, "the scholarship on lists remains fragmented". David Wallechinsky, a co-author of '' The Book of Lists'', described the attraction of lists as being "because we live in an era of overstimulation, especially in terms of information, and lists help ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Immunization (finance)
In finance, interest rate immunization is a portfolio management strategy designed to take advantage of the offsetting effects of interest rate risk and reinvestment risk. In theory, immunization can be used to ensure that the value of a portfolio of assets (typically bonds or other fixed income securities) will increase or decrease by the same amount as a designated set of liabilities, thus leaving the equity component of capital unchanged, regardless of changes in the interest rate. It has found applications in financial management of pension funds, insurance companies, banks and savings and loan associations. Immunization can be accomplished by several methods, including cash flow matching, duration matching, and volatility and convexity matching. It can also be accomplished by trading in bond forwards, futures, or options. Other types of financial risks, such as foreign exchange risk or stock market risk, can be immunised using similar strategies. If the immunizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bond Valuation
Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. Various related yield-measures are then calculated for the given price. Where the market price of bond is less than its par value, the bond is selling at a discount. Conversely, if the market price of bond is greater than its par value, the bond is selling at a premium. For this and other relationships between price and yield, see below. If the bond includes embedded options, the valuation is more difficult and combines option pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black–Scholes Equation
In mathematical finance, the Black–Scholes equation, also called the Black–Scholes–Merton equation, is a partial differential equation (PDE) governing the price evolution of derivatives under the Black–Scholes model. Broadly speaking, the term may refer to a similar PDE that can be derived for a variety of options, or more generally, derivatives. Consider a stock paying no dividends. Now construct any derivative that has a fixed maturation time T in the future, and at maturation, it has payoff K(S_T) that depends on the values taken by the stock at that moment (such as European call or put options). Then the price of the derivative satisfies :\begin \frac + \frac\sigma^2 S^2 \frac + rS\frac - rV = 0 \\ V(T, s) = K(s) \quad \forall s \end where V(t, S) is the price of the option as a function of stock price ''S'' and time ''t'', ''r'' is the risk-free interest rate, and \sigma is the volatility of the stock. The key financial insight behind the equation is that, under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield Curve
In finance, the yield curve is a graph which depicts how the Yield to maturity, yields on debt instruments – such as bonds – vary as a function of their years remaining to Maturity (finance), maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity. Those who issue and trade in forms of debt, such as loans and bonds, use yield curves to determine their value. Shifts in the shape and slope of the yield curve are thought to be related to investor expectations for the economy and interest rates. Ronald Melicher and Merle Welshans have identified several characteristics of a properly constructed yield curve. It should be based on a set of securities which have differing lengths of time to maturity, and all yields should be calculated as of the same point in time. Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valuation Of Options
In finance, a price (premium) is paid or received for purchasing or selling options. The calculation of this premium will require sophisticated mathematics. Premium components This price can be split into two components: intrinsic value, and time value (also called "extrinsic value"). Intrinsic value The ''intrinsic value'' is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call option, the option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price. For a put option, the option is in-the-money if the ''strike'' price is higher than the underlying spot price; then the intrinsic value is the strike price minus the underlying spot price. Otherwise the intrinsic value is zero. For example, when a DJI call (bullish/long) option is 18,000 and the underlying DJI Index is priced at $18,050 then the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference
A finite difference is a mathematical expression of the form . Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly denoted \Delta, is the operator (mathematics), operator that maps a function to the function \Delta[f] defined by \Delta[f](x) = f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations. Certain Recurrence relation#Relationship to difference equations narrowly defined, recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for #Relation with derivatives, approximating derivatives, and the term "finite difference" is often used a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
