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Monte Carlo Methods In Finance
Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions (sources of uncertainty) of the problem increase. Monte Carlo methods were first introduced to finance in 1964 by David B. Hertz through his ''Harvard Business Review'' article, discussing their application in Corporate Finance. In 1977, Phelim Boyle pioneered the use of simulation in derivative valuation in his seminal ''Journal of Financial Economics'' paper. This article discusses typical financial problems in which Monte Carlo methods are used. It also touches on the use of so-called "quasi-random" methods such as the use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during chemical reaction, reactions with other chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Net Present Value
The net present value (NPV) or net present worth (NPW) is a way of measuring the value of an asset that has cashflow by adding up the present value of all the future cash flows that asset will generate. The present value of a cash flow depends on the interval of time between now and the cash flow because of the Time value of money (which includes the annual effective discount rate). It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications. Time value of money dictates that time affects the value of cash flows. For example, a lender may offer 99 cents for the promise of receiving $1.00 a month from now, but the promise to receive that same dollar 20 years in the future would be worth much less today to that same person (lender), even if the payback in both cases was equally certain. This decrease in the current value of future c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic System (mathematics)
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state. In physics Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly. In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic. In mathematics The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic
Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday conversation, however, these terms are often used interchangeably. In probability theory, the formal concept of a '' stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including image processing, signal processing, computer science, information theory, telecommunications, chemistry, ecology, neuroscience, physics, and cryptography. It is also used in finance (e.g., stochastic oscillator), due to seemingly random changes in the different markets within the financial sector and in medicine, linguistics, music, media, colour theory, botany, manufacturing and geomorphology. Etymology The word ''stochastic'' in English was originally used as an adjective with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Analyst
A financial analyst is a professional undertaking financial analysis for external or internal clients as a core feature of the job. "Financial Analyst" '''' The role may specifically be titled securities analyst, research analyst, equity analyst, investment analyst, or ratings analyst. Financial Analysts |
Real Options Analysis
Real options valuation, also often termed real options analysis,Adam Borison (Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?'' (ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campbell, R. Harvey''Identifying real options'' Duke University, 2002. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, real options valuation could examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory.Nijssen, E. (2014)''Entrepreneurial Marketing; an effectual approach. Chapter 2'' Routelegde, 2014. Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction and is willing to exercise the options. Scope Real options are g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Project Finance
Project finance is the long-term financing of infrastructure and industrial projects based upon the projected cash flows of the project rather than the balance sheets of its sponsors. Usually, a project financing structure involves a number of equity investors, known as 'sponsors', and a 'syndicate' of banks or other lending institutions that provide loans to the operation. They are most commonly non-recourse loans, which are secured by the project assets and paid entirely from project cash flow, rather than from the general assets or creditworthiness of the project sponsors, a decision in part supported by financial modeling; see Project finance model. The financing is typically secured by all of the project assets, including the revenue-producing contracts. Project lenders are given a lien on all of these assets and are able to assume control of a project if the project company has difficulties complying with the loan terms. Generally, a special purpose entity is created for ... [...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] |
Rational Pricing
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Arbitrage mechanics Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.e. after transaction costs, storage costs, transport costs, dividends etc.) the arbitrageur can "lock in" a risk-free profit by purchasing and selling simultaneously in both markets. In general, arbitrage ensures that "the law of one price" will hold; arbitrage also equalises the prices of assets with identical cash flows, and sets the price of assets with known future cash flows. The law of one price The same asset must trade at the same ... [...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] |
