|
Bond Option
In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC. *A European bond option is an option to buy or sell a bond at a certain date in future for a predetermined price. *An American bond option is an option to buy or sell a bond ''on or before'' a certain date in future for a predetermined price. Generally, one buys a call option on the bond if one believes that interest rates will fall, causing an increase in bond prices. Likewise, one buys the put option if one believes that interest rates will rise. One result of trading in a bond option, is that the price of the underlying bond is "locked in" for the term of the contract, thereby reducing the credit risk associated with fluctuations in the bond price. Valuation Bonds, the underlyers in this case, exhibit what is known as pull-to-par: as the bond reaches its maturity date, all of the prices involved with the bond be ... [...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] |
Black–Derman–Toy Model
In mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ..., the Black–Derman–Toy model (BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see . It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean reversion (finance), mean-reverting behaviour of the short rate with the log-normal distribution, and is still widely used. History The model was introduced by Fischer Black, Emanuel Derman, and Bill Toy. It was first developed for in-house use by Goldman Sachs in the 1980s and was published in the ''Financial Analysts Journal'' in 1990. A personal account of the development o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk Neutrality
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences. Many different definitions have been proposed. One international standard definition of risk is the "effect of uncertainty on objectives". The understanding of risk, the methods of assessment and management, the descriptions of risk and even the definitions of risk differ in different practice areas (business, economics, environment, finance, information technology, health, insurance, safety, security, privacy, etc). This article provides links to more detailed articles on these areas. The international standard for risk management, ISO 31000, provides principles and general guidelines on managing risks faced by organizations. Definitions of risk Oxford English Dictionary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Measure
In finance, a ''T''-forward measure is a pricing measure equivalent to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity ''T''. The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds. Mathematical definition Let : B(T) = \exp\left(\int_0^T r(u)\, du\right) be the bank account or money market account numeraire and : D(T) = 1/B(T) = \exp\left(-\int_0^T r(u)\, du\right) be the discount factor in the market at time 0 for maturity ''T''. If Q_* is the risk neutral measure, then the forward measure Q_T is defined via the Radon–Nikodym derivative given by :\frac = \frac = \frac. Note that this implies that the forward measure and the risk neutral measure coincide when interest rates are deterministic. Also, this is a particular form of the change of numeraire formula by changing the numeraire from the money market or bank accou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield To Maturity
The yield to maturity (YTM), book yield or redemption yield of a fixed-interest security is an estimate of the total rate of return anticipated to be earned by an investor who buys it at a given market price, holds it to maturity, and receives all interest payments and the capital redemption on schedule. It is the theoretical internal rate of return, or the overall interest rate, of a bond — the discount rate at which the present value of all future cash flows from the bond is equal to the current price of the bond. The YTM is often given in terms of annual percentage rate (APR), but more often market convention is followed. In a number of major markets, the convention is to quote annualized yields with semi-annual compounding. Main assumptions The YTM calculation formulates certain stability conditions of the security, its owner, and the market going forward: * The owner holds the security to maturity. * The issuer makes all interest and principal payments on time and in ... [...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] |
Compound Interest
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower. Compound interest is contrasted with Interest#Calculation, simple interest, where previously accumulated interest is not added to the principal amount of the current period. Compounded interest depends on the simple interest rate applied and the frequency at which the interest is compounded. Compounding frequency The ''compounding frequency'' is the number of times per given unit of time the accumulated interest is capitalized, on a regular basis. The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, continuous compounding, continuously, or not at all until maturity. For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirty Price
The price of a bond is the present value of its future cash-flows. To avoid the impact of the next coupon payment on the price of a bond, this cash flow is excluded from the price of the bond and is called the accrued interest. In finance, the dirty price is the price of a bond including any interest that has accrued since issue of the most recent coupon payment. This is to be compared with the clean price, which is the price of a bond excluding the accrued interest. : When bond prices are quoted on a Bloomberg Terminal, Reuters or FactSet they are quoted using the clean price. Bond pricing Bonds, as well as a variety of other fixed income securities, provide for coupon payments to be made to bond holders on a fixed schedule. The dirty price of a bond will decrease on the days coupons are paid, resulting in a saw-tooth pattern for the bond value. This is because there will be one fewer future cash flow (i.e., the coupon payment just received) at that point. To separate out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Price
The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the spot price and any dividends. For forwards on non-tradeables, pricing the forward may be a complex task. Forward price formula If the underlying asset is tradable and a dividend exists, the forward price is given by: : F = S_0 e^ - \sum_^N D_i e^ \, where :F is the forward price to be paid at time T :e^x is the exponential function (used for calculating continuous compounding interests) :r is the risk-free interest rate :q is the convenience yield :S_0 is the spot price of the asset (i.e. what it would sell for at time 0) :D_i is a dividend that is guaranteed to be paid at time t_i where 0< t_i < T. Proof of the forward price formula The two questions here are what price the short position ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spot Price
In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the trade date. The settlement price (or rate) is called spot price (or spot rate). A spot contract is in contrast with a forward contract or futures contract where contract terms are agreed now but delivery and payment will occur at a future date. Spot prices and future price expectations Depending on the item being traded, spot prices can indicate market expectations of future price movements in different ways. For a security or non-perishable commodity (e.g. silver), the spot price reflects market expectations of future price movements. In theory, the difference in spot and forward prices should be equal to the finance charges, plus any earnings due to the holder of the security, according to the cost of carry model. For example, on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bermudan Option
In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as " vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging. American and European options The key difference between American and European options relates to when the options can be exercised: * A European option may be exercised only at the expiration date of the option, i.e. at a single pre-defined point in time. * An American option on the other hand may be exercised at any time before the expiration date. For both, the payoff—when it occurs—is given by * \max\, for a call option * \max\, for a put option where K is the strike ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
