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Asset Pricing
In financial economics, asset pricing refers to a formal treatment and development of two interrelated Price, pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either General equilibrium theory, general equilibrium asset pricing or Rational pricing, rational asset pricing, the latter corresponding to risk neutral pricing. Investment theory, which is near synonymous, encompasses the body of knowledge used to support the decision-making process of choosing investments, and the asset pricing models are then applied in determining the Required rate of return, asset-specific required rate of return on the investment in question, and for hedging. General equilibrium asset pricing Under general equilibrium theory prices are determined through Market price, market pricing by supply and demand. See, e.g., Tim Bollerslev (2019)"Risk and Return in Equilibrium: The C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Corporate Finance
Corporate finance is an area of finance that deals with the sources of funding, and the capital structure of businesses, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to Shareholder value, maximize or increase valuation (finance), shareholder value.SeCorporate Finance: First Principles Aswath Damodaran, New York University's Stern School of Business Correspondingly, corporate finance comprises two main sub-disciplines. Capital budgeting is concerned with the setting of criteria about which value-adding Project#Corporate finance, projects should receive investment funding, and whether to finance that investment with ownership equity, equity or debt capital. Working capital management is the management of the company's monetary funds that deal with the short-term operating balance of current assets and Current liability, cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rendleman–Bartter Model
The Rendleman–Bartter model (Richard J. Rendleman, Jr. and Brit J. Bartter) in finance is a short-rate model describing the evolution of interest rates. It is a "one factor model" as it describes interest rate movements as driven by only one source of market risk. It can be used in the valuation of interest rate derivatives. It is a stochastic asset model. The model specifies that the instantaneous interest rate follows a geometric Brownian motion: :dr_t = \theta r_t\,dt + \sigma r_t\,dW_t where ''Wt'' is a Wiener process modelling the random market risk factor. The drift parameter, \theta, represents a constant expected instantaneous rate of change in the interest rate, while the standard deviation parameter, \sigma, determines the volatility of the interest rate. This is one of the early models of the short-term interest rates, using the same stochastic process as the one already used to describe the dynamics of the underlying price in stock options. Its main disadvantage i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Economics
Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on ''both sides'' of a trade".William F. Sharpe"Financial Economics", in Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy. It has two main areas of focus:Merton H. Miller, (1999). The History of Finance: An Eyewitness Account, ''Journal of Portfolio Management''. Summer 1999. asset pricing and corporate finance; the first being the perspective of providers of Financial capital, capital, i.e. investors, and the second of users of capital. It thus provides the theoretical underpinning for much of finance. The subject is concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment".See Fama and Miller (1972), ''The Theory of Finance'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LIBOR Market Model
The LIBOR market model, also known as the BGM Model (Brace Gatarek Musiela Model, in reference to the names of some of the inventors) is a financial model of interest rates. It is used for pricing interest rate derivatives, especially exotic derivatives like Bermudan swaptions, ratchet caps and floors, target redemption notes, autocaps, zero coupon swaptions, constant maturity swaps and spread options, among many others. The quantities that are modeled, rather than the short rate or instantaneous forward rates (like in the Heath–Jarrow–Morton framework) are a set of forward rates (also called forward LIBORs), which have the advantage of being directly observable in the market, and whose volatilities are naturally linked to traded contracts. Each forward rate is modeled by a lognormal In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normal distribution, normally distributed. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cheyette Model
In mathematical finance, the Cheyette Model is a quasi-Gaussian, quadratic volatility model of interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...s intended to overcome certain limitations of the Heath-Jarrow-Morton framework. By imposing a special time dependent structure on the forward rate volatility function, the Cheyette approach allows for dynamics which are Markovian, in contrast to the general HJM model. This in turn allows the application of standard econometric valuation concepts. External links and references * * Cheyette, O. (1994)''Markov representation of the Heath-Jarrow-Morton model''(working paper). Berkeley: BARRA Inc. * Chibane, M. and Law, D. (2013)''A quadratic volatility Cheyette model'' Risk.net Financial models Mathematical finance Fixe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heath–Jarrow–Morton Framework
The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curves – instantaneous forward rate curves in particular (as opposed to simple forward rates). When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. For direct modeling of simple forward rates the Brace–Gatarek–Musiela model represents an example. The HJM framework originates from the work of David Heath, Robert A. Jarrow, and Andrew Morton in the late 1980s, especially ''Bond pricing and the term structure of interest rates: a new methodology'' (1987) – working paper, Cornell University, and ''Bond pricing and the term structure of interest rates: a new methodology'' (1989) – working paper (revised ed.), Cornell University. It has its critics, however, with Paul Wilmott describing it as "...actually just a big rug for is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen Model
In finance, the Chen model is a mathematical model describing the evolution of interest rates. It is a type of "three-factor model" (short-rate model) as it describes interest rate movements as driven by three sources of market risk. It was the first stochastic mean and stochastic volatility model and it was published in 1994 by Lin Chen, economist, theoretical physicist and former lecturer/professor at Beijing Institute of Technology, American University of Beirut, Yonsei University of Korea, and SunYetSan University . The dynamics of the instantaneous interest rate are specified by the stochastic differential equations: : dr_t = \kappa(\theta_t-r_t)\,dt + \sqrt\,\sqrt\, dW_1, : d \theta_t = \nu(\zeta-\theta_t)\,dt + \alpha\,\sqrt\, dW_2, : d \sigma_t = \mu(\beta-\sigma_t)\,dt + \eta\,\sqrt\, dW_3. In an authoritative review of modern finance (''Continuous-Time Methods in Finance: A Review and an Assessment''), the Chen model is listed along with the models of Robert C. Merton ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longstaff–Schwartz 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 inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black–Karasinski Model
In financial mathematics, the Black–Karasinski model is a mathematical model of the term structure of interest rates; see short-rate model. It is a one-factor model as it describes interest rate movements as driven by a single source of randomness. It belongs to the class of no-arbitrage models, i.e. it can fit today's zero-coupon bond prices, and in its most general form, today's prices for a set of caps, floors or European swaptions. The model was introduced by Fischer Black and Piotr Karasinski in 1991. Model The main state variable of the model is the short rate, which is assumed to follow the stochastic differential equation (under the risk-neutral measure): : d\ln(r) = theta_t-\phi_t \ln(r)\, dt + \sigma_t\, dW_t where ''dW''''t'' is a standard Brownian motion. The model implies a log-normal distribution for the short rate and therefore the expected value of the money-market account is infinite for any maturity. In the original article by Fischer Black and Piotr Kara ... [...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] |
