Bond Valuation
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Bond Valuation
Bond valuation is the determination of the fair price 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 face value (par value), the bond is selling at a discount. Conversely, if the market price of bond is greater than its face 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 pricing with discounting. Depending on the type of option, t ...
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Relative Valuation
Relative valuation also called valuation using multiples is the notion of comparing the price of an asset to the market value of similar assets. In the field of securities investment, the idea has led to important practical tools, which could presumably spot pricing anomalies. These tools have subsequently become instrumental in enabling analysts and investors to make vital decisions on asset allocation. Equities In equities, the concept separates into two areas—one pertaining to individual equities and the other to indices. Individual equities The most common method for individual equities is based on comparing certain financial ratios or multiples, such as the price to book value, price to earnings, EV/EBITDA, etc., of the equity in question to those of its peers. This type of approach, which is popular as a strategic tool in the financial industry, is mainly statistical and based on historical data. Equity indexes For an equity index the above fails mainly because ...
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Fair Price
In accounting and in most schools of economic thought, fair value is a rational and unbiased estimate of the potential market price of a good, service, or asset. The derivation takes into account such objective factors as the costs associated with production or replacement, market conditions and matters of supply and demand. Subjective factors may also be considered such as the risk characteristics, the cost of and return on capital, and individually perceived utility. Economic understanding Vs market price There are two schools of thought about the relation between the market price and fair value in any form of market, but especially with regard to tradable assets: * The efficient-market hypothesis asserts that, in a well organized, reasonably transparent market, the market price is generally equal to or close to the fair value, as investors react quickly to incorporate new information about relative scarcity, utility, or potential returns in their bids; see also Rational p ...
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Zero-coupon Bond
A zero coupon bond (also discount bond or deep discount bond) is a bond in which the face value is repaid at the time of maturity. Unlike regular bonds, it does not make periodic interest payments or have so-called coupons, hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par (or face) value. Examples of zero-coupon bonds include US Treasury bills, US savings bonds, long-term zero-coupon bonds, and any type of coupon bond that has been stripped of its coupons. Zero coupon and deep discount bonds are terms that are used interchangeably. In contrast, an investor who has a regular bond receives income from coupon payments, which are made semi-annually or annually. The investor also receives the principal or face value of the investment when the bond matures. Some zero coupon bonds are inflation indexed, and the amount of money that will be paid to the bond holder is calculated to have a set amount of purchasing power, rather than a se ...
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John C
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope ...
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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. Th ...
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Florida State University
Florida State University (FSU) is a public university, public research university in Tallahassee, Florida. It is a senior member of the State University System of Florida. Founded in 1851, it is located on the oldest continuous site of higher education in the state of Florida. Florida State University comprises 16 separate colleges and more than 110 centers, facilities, labs and institutes that offer more than 360 programs of study, including professional school programs. In 2021, the university enrolled 45,493 students from all 50 states and 130 countries. Florida State is home to Florida's only national laboratory, the National High Magnetic Field Laboratory, and is the birthplace of the commercially viable anti-cancer drug Taxol. Florida State University also operates the John & Mable Ringling Museum of Art, the State Art Museum of Florida and one of the largest museum/university complexes in the nation. The university is accredited by the Southern Association of Colleges and ...
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Black–Scholes Equation
In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put 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. For a European call or put on an underlying stock paying no dividends, the equation is: :\frac + \frac\sigma^2 S^2 \frac + rS\frac - rV = 0 where ''V'' 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 the model assumption of a frictionless market, one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently “eliminate risk". This hedge, in turn, implies that there is only one right price for the option, as returned by the Black–Sch ...
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Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the ex ...
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Stochastic Calculus
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created and started by the Japanese mathematician Kiyoshi Itô during World War II. The best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in honor of Norbert Wiener), which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the mos ...
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Deterministic
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. The opposite of determinism is some kind of indeterminism (otherwise called nondeterminism) or randomness. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible.For example, see Determinism is often used to mean ''causal determinism'', which in physics is known as cause-and-effect. This is the concept that events within a given paradigm are bound by causality in such a way that any state of an object or event is completely determined by its prior states. This meaning can be distinguished from other varieties of determinism mentioned below. Debates about determinism often concern the scope of determined systems; some maintain that the entire universe is a single determ ...
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Interest Rate Derivative
In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates. Modeling of interest rate derivatives is usually done on a time-dependent multi-dimensional Lattice ("tree") or using specialized simulation models. Both are calibrated to the underlying risk drivers, usually domestic or foreign short rates and foreign exchange market rates, and incorporate delivery- and day count conventions. The Heath–Jarrow–Morton framework is often used instead of short rates. Types The most basic subclassification of interest rate derivatives (IRDs) is to define linear and no ...
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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 becom ...
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