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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] |
Puttable Bond
Puttable bond (put bond, putable or retractable bond) is a bond with an embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal. The put option is exercisable on one or more specified dates. Overview This type of bond protects investors: if interest rates rise after bond purchase, the future value of coupon payments will become less valuable. Therefore, investors sell bonds back to the issuer and may lend proceeds elsewhere at a higher rate. Bondholders are ready to pay for such protection by accepting a lower yield relative to that of a straight bond. Of course, if an issuer has a severe liquidity crisis, it may be incapable of paying for the bonds when the investors wish. The investors also cannot sell back the bond at ''any'' time, but at specified dates. However, they would still be ahead of holders of non-puttable bonds, who may have no more right than 'timely payment of interest and principal' (wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bond (finance)
In finance, a bond is a type of security under which the issuer ( debtor) owes the holder ( creditor) a debt, and is obliged – depending on the terms – to repay the principal (i.e. amount borrowed) of the bond at the maturity date as well as interest (called the coupon) over a specified amount of time. The interest is usually payable at fixed intervals: semiannual, annual, and less often at other periods. Thus, a bond is a form of loan or IOU. Bonds provide the borrower with external funds to finance long-term investments or, in the case of government bonds, to finance current expenditure. Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in a company (i.e. they are owners), whereas bondholders have a creditor stake in a company (i.e. they are lenders). As creditors, bondholders have priority over stockholders. This means they will be repaid in advance of stockholders, but will rank b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option Premium
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the implementation; as well as generally. Premium components This price can be split into two components: intrinsic value, and time 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 (b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Convexity
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, 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 2nd derivative of h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Duration
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields. The dual use of the word "duration", as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. Both measures are termed "duration" and have the same (or close to the same) numerical value, but it is important to keep in mind the conceptual distinctions be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DV01
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields. The dual use of the word "duration", as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. Both measures are termed "duration" and have the same (or close to the same) numerical value, but it is important to keep in mind the conceptual distinctions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bond Convexity
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, 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 2nd derivative of h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bond Duration
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields. The dual use of the word "duration", as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. Both measures are termed "duration" and have the same (or close to the same) numerical value, but it is important to keep in mind the conceptual distinctions b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 bec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-rate Model
A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,. The short rate Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. The short rate, r_t \,, then, is the ( continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time t. Specifying the current short rate does not specify the entire yield curve. However, no-arbitrage arguments show that, under some fairly relaxed technical conditions, if we model the evolution of r_t \, as a stochastic process under a risk-neutral measure Q, then the price at time t of a zero-coupon bond maturing at time T with a payoff of 1 is given by : P(t,T) = \operatorname^Q\left \mathcal_t \right where \mathcal is the natural filtration for the process. The int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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