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Put–call Parity
In financial mathematics, the 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Mathematics
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the Finance#Quantitative_finance, financial field. In general, there exist two separate branches of finance that require advanced quantitative techniques: Derivative (finance), derivatives pricing on the one hand, and risk management, risk and Investment management#Investment managers and portfolio structures, 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 with the 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 investment ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covered Option
A covered option is a financial transaction in which the holder of securities sells (or "writes") a type of financial options contract known as a "call" or a " put" against stock that they own or are shorting. The seller of a covered option receives compensation, or "premium", for this transaction, which can limit losses; however, the act of selling a covered option also limits their profit potential to the upside. One covered option is sold for every hundred shares the seller wishes to cover. A covered option constructed with a call is called a "covered call", while one constructed with a put is a "covered put". This strategy is generally considered conservative because the seller of a covered option reduces both their risk and their return. Characteristics Covered calls are bullish by nature, while covered puts are bearish. The payoff from selling a covered call is identical to selling a short naked put. Both variants are a short implied volatility strategy. Covered cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vinzenz Bronzin
Vinzenz Bronzin (born 1872 in Rovigno – died 1970 in Trieste) was an Italian mathematics professor, known today for an early (rediscovered) option pricing formula, similar to, and predating, the Black–Scholes 1973 formula; he also provided a formulation of put–call parity, written up formally only in 1969 by Stoll. Bronzin was born in Rovigno (now Rovinj), Istria. He studied engineering at the Vienna Polytechnic Institute, and then mathematics and pedagogics at the University of Vienna. He was made a professor at the Accademia di Commercio e Nautica, Trieste, Italy, in 1900; his focus was "Political and Commercial Arithmetic", which included actuarial science and probability theory. In 1910 he accepted the position of director. In 1937 he resigned from all of his positions at the Academia at the age of 65. In 1908 Bronzin published hi''Theorie der Prämiengeschäfte''( German: "Theory of Premium Contracts") discussing a then current type of option contract. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russell Sage
Russell Risley Sage (August 4, 1816 – July 22, 1906) was an American financier, railroad executive and Whig Party (United States), Whig politician from New York (state), New York, who became one of the List of richest Americans in history, richest Americans of all time. As a frequent partner of Jay Gould in various transactions, he amassed a fortune. Margaret Olivia Slocum Sage, Olivia Slocum Sage, his second wife, inherited his fortune, which was unrestricted for her use. In his name she used the money for philanthropic purposes, endowing a number of buildings and institutions to benefit women's education: she established the Russell Sage Foundation in 1907 and founded the Russell Sage College for women in 1916. Early life and family Sage was born at Verona, New York, Verona in Oneida County, New York to Elisha Sage Jr. and Prudence Risley. His grandfather Elisha Yale Sr. was a construction contractor, and his uncle, Barzillai Sage, was the grandfather of railroad magnate Col. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equity Of Redemption
The equity of redemption refers to the right of a mortgagor to redeem his or her property once the debt secured by the mortgage has been discharged. Overview Historically, a mortgagor (the borrower) and a mortgagee (the lender) executed a conveyance of legal title to the property in favour of the mortgagee as security for the loan. If the loan was repaid, then the mortgagee would return the property; if the loan was not repaid, then the mortgagee would keep the property in satisfaction of the debt. The equity of redemption was the right to petition the courts of equity to compel the mortgagee to transfer the property back to the mortgagor once the secured obligation had been performed. Today, most mortgages are granted by statutory charge rather than by a formal conveyance, although theoretically there is usually nothing to stop two parties from executing a mortgage in the more traditional manner. Traditionally, the courts have been astute to ensure that the mortgagee did not i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bond (finance)
In finance, a bond is a type of Security (finance), security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor (e.g. repay the principal (i.e. amount borrowed) of the bond at the Maturity (finance), maturity date and interest (called the coupon (bond), coupon) over a specified amount of time.) The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. 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 Share capital, stocks are both Security (finance), securities, but the major difference between the two is that (capital) stockholders h ... [...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] |
Arbitrage-free
Arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more marketsstriking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which the unit is traded. Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge. When used by academics in economics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price. In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to ''expected'' profit, though losses may occur, and in practice, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Underlying
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements: # an item (the "underlier") that can or must be bought or sold, # a future act which must occur (such as a sale or purchase of the underlier), # a price at which the future transaction must take place, and # a future date by which the act (such as a purchase or sale) must take place. A derivative's value depends on the performance of the underlier, which can be a commodity (for example, corn or oil), a financial instrument (e.g. a stock or a bond), a price index, a currency, or an interest rate. Derivatives can be used to insure against price movements ( hedging), increase exposure to price movements for speculation, or get access to otherwise hard-to-trade assets or markets. Most derivatives are price guarantees. But some are based on an event or performance of an act rather than a pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Present Value
In economics and finance, present value (PV), also known as present discounted value (PDV), is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to Renting, rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force Of Interest
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower. Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period. Compounded interest depends on the simple interest rate applied and the frequency at which the interest is compounded. Compounding frequency The ''compounding frequency'' is the number of times per given unit of time the accumulated interest is capitalized, on a regular basis. The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, continuously, or not at all until maturity. For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in months. Annual equivalent rate To help consum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
