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Static Replication
In mathematical finance, a replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties (especially cash flows). This is meant in two distinct senses: static replication, where the portfolio has the same cash flows as the reference asset (and no changes need to be made to maintain this), and dynamic replication, where the portfolio does not have the same cash flows, but has the same "Greeks" as the reference asset, meaning that for small (properly, infinitesimal) changes to underlying market parameters, the price of the asset and the price of the portfolio change in the same way. Dynamic replication requires continual adjustment, as the asset and portfolio are only assumed to behave similarly at a single point (mathematically, their partial derivatives are equal at a single point). Given an asset or liability, an offsetting replicating portfolio (a "hedge") is called a static hedge or dynamic hedge, and constructing such a portfoli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios. French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical fina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Put–call Parity
In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract. The validity of this relationship requires that certain assumptions be satisfied; these are specified and the relationship is derived below. In practice transaction costs and financing costs (leverage) mean this relationship will not exactly hold, but in liquid markets the relationship is close to exact. Assumptions Put–call parity is a static replication, and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pricing
Pricing is the process whereby a business sets the price at which it will sell its products and services, and may be part of the business's marketing plan. In setting prices, the business will take into account the price at which it could acquire the goods, the manufacturing cost, the marketplace, competition, market condition, brand, and quality of product. Pricing is a fundamental aspect of product management and is one of the four Ps of the marketing mix, the other three aspects being product, promotion, and place. Price is the only revenue generating element amongst the four Ps, the rest being cost centers. However, the other Ps of marketing will contribute to decreasing price elasticity and so enable price increases to drive greater revenue and profits. Pricing can be a manual or automatic process of applying prices to purchase and sales orders, based on factors such as: a fixed amount, quantity break, promotion or sales campaign, specific vendor quote, price prevailing o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
With-profits Policy
A with-profits policy (Commonwealth) or participating policy (U.S.) is an insurance contract that participates in the profits of a life insurance company. The company is often a mutual life insurance company, or had been one when it began its with-profits product line. Similar arrangements are found in other countries such as those in continental Europe. With-profits policies evolved over many years. Originally they developed as a means of distributing unplanned surplus, arising e.g. from lower than anticipated death rates. More recently they have been used to provide flexibility to pursue a more adventurous investment policy to aim to achieve long-term capital growth. They have been accepted as a form of long-term collective investment whereby the investor chooses the insurance company based on factors such as financial strength, historic returns and the terms of the contracts offered. The premiums paid by with-profits and non-profit policyholders are pooled within the insura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discounting
Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee.See "Time Value", "Discount", "Discount Yield", "Compound Interest", "Efficient Market", "Market Value" and "Opportunity Cost" in Downes, J. and Goodman, J. E. ''Dictionary of Finance and Investment Terms'', Baron's Financial Guides, 2003. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date.See "Discount", "Compound Interest", "Efficient Markets Hypothesis", "Efficient Resource Allocation", "Pareto-Optimality", "Price", "Price Mechanism" and "Efficient Market" in Black, John, ''Oxford Dictionary of Economics'', Oxford University Press, 2002. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Net Premium Valuation
A net premium valuation is an actuarial calculation, used to place a value on the liabilities of a life insurer. Background It involves calculating a present value for the contractual liabilities of a contract, and deducting the value of future premiums. Both contractual liabilities, and future premiums in this calculation allow only for mortality and interest. The key with a net premium valuation is that the premiums being valued are theoretical measures - they make no reference to the actual premiums being charged by the insurer. This technique is a well-established actuarial valuation method, that became popular because of its simplicity, consistency, and ease of calculation. New methods With the advent of computers, the more complicated so-called gross premium valuation calculation (which is also more realistic than the net premium valuation) has become much more feasible, and is displacing the archaic net premium valuation further from its historical position of prominen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuary
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in the 17th century studies of probability and annuities. Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific; however, almost all processes share a rigorous schooling or examination structure and take many years ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Life Insurance
Life insurance (or life assurance, especially in the Commonwealth of Nations) is a contract between an insurance policy holder and an insurer or assurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death of an insured person (often the policyholder). Depending on the contract, other events such as terminal illness or critical illness can also trigger payment. The policyholder typically pays a premium, either regularly or as one lump sum. The benefits may include other expenses, such as funeral expenses. Life policies are legal contracts and the terms of each contract describe the limitations of the insured events. Often, specific exclusions written into the contract limit the liability of the insurer; common examples include claims relating to suicide, fraud, war, riot, and civil commotion. Difficulties may arise where an event is not clearly defined, for example, the insured knowingly incurred a risk by consenting to an experimental m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-financing Portfolio
In financial mathematics, a self-financing portfolio is a portfolio having the feature that, if there is no exogenous infusion or withdrawal of money, the purchase of a new asset must be financed by the sale of an old one. Mathematical definition Let h_i(t) denote the number of shares of stock number 'i' in the portfolio at time t , and S_i(t) the price of stock number 'i' in a frictionless market with trading in continuous time. Let : V(t) = \sum_^ h_i(t) S_i(t). Then the portfolio (h_1(t), \dots, h_n(t)) is self-financing if : dV(t) = \sum_^ h_i(t) dS_(t). Discrete time Assume we are given a discrete filtered probability space (\Omega,\mathcal,\_^T,P), and let K_t be the solvency cone (with or without transaction costs) at time ''t'' for the market. Denote by L_d^p(K_t) = \. Then a portfolio (H_t)_^T (in physical units, i.e. the number of each stock) is self-financing (with trading on a finite set of times only) if : for all t \in \ we have that H_t - H_ \in -K ... [...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 price on all m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Portfolio (finance)
In finance, a portfolio is a collection of investments. Definition The term “portfolio” refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial professionals, hedge funds, banks and other financial institutions. It is a generally accepted principle that a portfolio is designed according to the investor's risk tolerance, time frame and investment objectives. The monetary value of each asset may influence the risk/reward ratio of the portfolio. When determining asset allocation, the aim is to maximise the expected return and minimise the risk. This is an example of a multi-objective optimization problem: many efficient solutions are available and the preferred solution must be selected by considering a tradeoff between risk and return. In particular, a portfolio A is dominated by another portfolio A' if A' has a greater expected gain and a lesser risk than A. If no portfolio dominate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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