The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return; the formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is used, although with adjustments and corrections, by options market participants. Based on works developed by market researchers and practitioners, such as Louis Bachelier, Sheen Kassouf and Ed Thorp among others, Fischer Black and Myron Scholes demonstrated in the late 1960s that a dynamic revision of a portfolio removes the expected return of the security, thus inventing the risk neutral argument.
In 1970, after they attempted to apply the formula to the markets and incurred financial losses due to lack of risk management in their trades, they decided to focus in their domain area, the academic environment. After three years of efforts, the formula named in honor of them for making it public, was published in 1973 in an article entitled "The Pricing of Options and Corporate Liabilities", in the Journal of Political Economy. Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, coined the term "Black–Scholes options pricing model". Merton and Scholes received the 1997 Nobel Memorial Prize in Economic Sciences for their work, the committee citing their discovery of the risk neutral dynamic revision as a breakthrough that separates the option from the risk of the underlying security. Although ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish Academy; the key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk.
This type of hedging is called "continuously revised delta hedging" and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds. The model's assumptions have been relaxed and generalized in many directions, leading to a plethora of models that are used in derivative pricing and risk management, it is the insights of the model, as exemplified in the Black–Scholes formula, that are used by market participants, as distinguished from the actual prices. These insights include risk-neutral pricing. Further, the Black–Scholes equation, a partial differential equation that governs the price of the option, enables pricing using numerical methods when an explicit formula is not possible; the Black–Scholes formula has only one parameter that cannot be directly observed in the market: the average future volatility of the underlying asset, though it can be found from the price of other options. Since the option value is increasing in this parameter, it can be inverted to produce a "volatility surface", used to calibrate other models, e.g. for OTC derivatives.
The Black–Scholes model assumes that the market consists of at least one risky asset called the stock, one riskless asset called the money market, cash, or bond. Now we make assumptions on the assets: The rate of return on the riskless asset is constant and thus called the risk-free interest rate; the instantaneous log return of stock price is an infinitesimal random walk with drift. The stock does not pay a dividend. Assumptions on the market: There is no arbitrage opportunity, it is possible to borrow and lend any amount fractional, of cash at the riskless rate. It is possible to buy and sell any amount fractional, of the stock; the above transactions do not incur any costs. With these assumptions holding, suppose there is a derivative security trading in this market. We specify that this security will have a certain payoff at a specified date in the future, depending on the value taken by the stock up to that date, it is a surprising fact that the derivative's price is determined at the current time though we do not know what path the stock price will take in the future.
For the special case of a European call or put option and Scholes showed that "it is possible to create a hedged position, consisting of a long position in the stock and a short position in the option, whose value will not depend on the price of the stock". Their dynamic hedging strategy led to a partial differential equation which governed the price of the option, its solution is given by the Black–Scholes formula. Several of these assumptions of the original model have been removed in subsequent extensions of the model. Modern versions account for dynamic interest rates, transaction costs and taxes, dividend payout; the notation used throughout this page will be defined as follows: S, the price of the underlying asset at time t..
The secondary market called the aftermarket and follow on public offering is the financial market in which issued financial instruments such as stock, bonds and futures are bought and sold. Another frequent usage of "secondary market" is to refer to loans which are sold by a mortgage bank to investors such as Fannie Mae and Freddie Mac; the term "secondary market" is used to refer to the market for any used goods or assets, or an alternative use for an existing product or asset where the customer base is the second market. With primary issuances of securities or financial instruments, or the primary market, investors purchase these securities directly from issuers such as corporations issuing shares in an IPO or private placement, or directly from the federal government in the case of treasuries. After the initial issuance, investors can purchase from other investors in the secondary market; the secondary market for a variety of assets can vary from loans to stocks, from fragmented to centralized, from illiquid to liquid.
The major stock exchanges are the most visible example of liquid secondary markets - in this case, for stocks of publicly traded companies. Exchanges such as the New York Stock Exchange, London Stock Exchange and Nasdaq provide a centralized, liquid secondary market for the investors who own stocks that trade on those exchanges. Most bonds and structured products trade “over the counter,” or by phoning the bond desk of one’s broker-dealer. Loans sometimes trade online using a Loan Exchange. In the secondary market, securities are sold by and transferred from one investor or speculator to another, it is therefore important that the secondary market be liquid. As a general rule, the greater the number of investors that participate in a given marketplace, the greater the centralization of that marketplace, the more liquid the market. Fundamentally, secondary markets mesh the investor's preference for liquidity with the capital user's preference to be able to use the capital for an extended period of time.
Accurate share price allocates scarce capital more efficiently when new projects are financed through a new primary market offering, but accuracy may matter in the secondary market because: 1) price accuracy can reduce the agency costs of management, make hostile takeover a less risky proposition and thus move capital into the hands of better managers, 2) accurate share price aids the efficient allocation of debt finance whether debt offerings or institutional borrowing. The term may refer to markets in things of value other than securities. For example, the ability to buy and sell intellectual property such as patents, or rights to musical compositions, is considered a secondary market because it allows the owner to resell property entitlements issued by the government. Secondary markets can be said to exist in some real estate contexts as well; these have similar functions as secondary stock and bond markets in allowing for speculation, providing liquidity, financing through securitization.
It facilitates marketability of the long term instrument. It provides instant valuation of securities caused by changes in the environment. Private equity secondary market refers to the buying and selling of pre-existing investor commitments to private equity funds. Sellers of private equity investments sell not only the investments in the fund but their remaining unfunded commitments to the funds. Due to the increased compliance and reporting obligations enacted in the Sarbanes-Oxley Act of 2002, private secondary markets began to emerge, such as SecondMarket and SecondaryLink; these markets are only available to institutional or accredited investors and allow trading of unregistered and private company securities. Digital currency exchanges are being regarded as secondary markets. Aftermarket Clean Energy Bank Grey market Primary market Third market Fourth market Original equipment manufacturer Private equity secondary market Reseller
A stock exchange, securities exchange or bourse, is a facility where stock brokers and traders can buy and sell securities, such as shares of stock and bonds and other financial instruments. Stock exchanges may provide for facilities the issue and redemption of such securities and instruments and capital events including the payment of income and dividends. Securities traded on a stock exchange include stock issued by listed companies, unit trusts, pooled investment products and bonds. Stock exchanges function as "continuous auction" markets with buyers and sellers consummating transactions via open outcry at a central location such as the floor of the exchange or by using an electronic trading platform. To be able to trade a security on a certain stock exchange, the security must be listed there. There is a central location at least for record keeping, but trade is less linked to a physical place, as modern markets use electronic communication networks, which give them advantages of increased speed and reduced cost of transactions.
Trade on an exchange is restricted to brokers. In recent years, various other trading venues, such as electronic communication networks, alternative trading systems and "dark pools" have taken much of the trading activity away from traditional stock exchanges. Initial public offerings of stocks and bonds to investors is done in the primary market and subsequent trading is done in the secondary market. A stock exchange is the most important component of a stock market. Supply and demand in stock markets are driven by various factors that, as in all free markets, affect the price of stocks. There is no obligation for stock to be issued through the stock exchange itself, nor must stock be subsequently traded on an exchange; such trading may be off over-the-counter. This is the usual way that bonds are traded. Stock exchanges are part of a global securities market. Stock exchanges serve an economic function in providing liquidity to shareholders in providing an efficient means of disposing of shares.
The idea of debt dates back to the ancient world, as evidenced for example by ancient Mesopotamian city clay tablets recording interest-bearing loans. There is little consensus among scholars as to; some see the key event as the Dutch East India Company's founding in 1602, while others point to earlier developments. Economist Ulrike Malmendier of the University of California at Berkeley argues that a share market existed as far back as ancient Rome. One of Europe's oldest stock exchanges is the Frankfurt Stock Exchange established in 1585 in Frankfurt am Main. In the Roman Republic, which existed for centuries before the Empire was founded, there were societates publicanorum, organizations of contractors or leaseholders who performed temple-building and other services for the government. One such service was the feeding of geese on the Capitoline Hill as a reward to the birds after their honking warned of a Gallic invasion in 390 B. C. Participants in such organizations had partes or shares, a concept mentioned various times by the statesman and orator Cicero.
In one speech, Cicero mentions "shares that had a high price at the time". Such evidence, in Malmendier's view, suggests the instruments were tradable, with fluctuating values based on an organization's success; the societas declined into obscurity in the time of the emperors, as most of their services were taken over by direct agents of the state. Tradable bonds as a used type of security were a more recent innovation, spearheaded by the Italian city-states of the late medieval and early Renaissance periods. While the Italian city-states produced the first transferable government bonds, they did not develop the other ingredient necessary to produce a fully-fledged capital market: the stock market in its modern sense. In the early 1600s the Dutch East India Company became the first company in history to issue bonds and shares of stock to the general public; as Edward Stringham notes, "companies with transferable shares date back to classical Rome, but these were not enduring endeavors and no considerable secondary market existed."
The VOC, formed to build up the spice trade, operated as a colonial ruler in what is now Indonesia and beyond, a purview that included conducting military operations against the wishes of the exploited natives and of competing colonial powers. Control of the company was held by its directors, with ordinary shareholders not having much influence on management or access to the company's accounting statements. However, shareholders were rewarded well for their investment; the company paid an average dividend of over 16% per year from 1602 to 1650. Financial innovation in Amsterdam took many forms. In 1609, investors led by Isaac Le Maire formed history's first bear market syndicate, but their coordinated trading had only a modest impact in driving down share prices, which tended to remain robust throughout the 17th century. By the 1620s, the company was expanding its securities issuance with the first use of corporate bonds. Joseph de la Vega known as Joseph Penso de la Vega and by other variations of his name, was an Amsterdam trader from a Spanish Jewish family and a prolific writer as well as a successful businessman in 17th-century Amsterdam.
His 1688 book Confusion of Confusions explained the workings of the city's stock market. It was the earliest book about stock trading and inner workings of a stock market, taking the form of a dialogue between a merchant, a shareholder and a philosopher, the book described a market, sophisticated but prone to excesses, de la Vega of
A stock trader or equity trader or share trader is a person or company involved in trading equity securities. Stock traders may be an agent, arbitrageur, stockbroker; such equity trading in large publicly traded companies may be through one of the major stock exchanges, such as the New York Stock Exchange or the London Stock Exchange, which serve as managed auctions for stock trades. Stock shares in smaller public companies are sold in over-the-counter markets. Equity trading can be performed by the owner of the shares, or by an agent authorized to buy and sell on behalf of the share's owner. Proprietary trading is selling for the trader's own profit or loss. In this case, the principal is the owner of the shares. Agency trading is buying and selling by an agent a stockbroker, on behalf of a client. Agents are paid a commission for performing the trade. Major stock exchanges have market makers who help limit price variation by buying and selling a particular company's shares on their own behalf and on behalf of other clients.
Stock traders help manage portfolios. Traders engage in buying and selling bonds, stocks and shares in hedge funds. A stock trader conducts extensive research and observation of how financial markets perform; this is accomplished through microeconomic study. Other duties of a stock trader include comparison of financial analysis to current and future regulation of his or her occupation. Professional stock traders who work for a financial company, are required to complete an internship of up to four months before becoming established in their career field. In the United States, for example, internship is followed up by taking and passing a Financial Industry Regulatory Authority-administered Series 63 or 65 exam. Stock traders who pass demonstrate familiarity with U. S. Securities and Exchange Commission compliant practices and regulation. Stock traders with experience obtain a four-year degree in a financial, accounting or economics field after licensure. Supervisory positions as a trader may require an MBA for advanced stock market analysis.
The U. S. Bureau of Labor Statistics reported that growth for stock and commodities traders was forecast to be greater than 21% between 2006 and 2016. In that period, stock traders would benefit from trends driven by pensions of baby boomers and their decreased reliance on Social Security. U. S. Treasury bonds would be traded on a more fluctuating basis. Stock traders just entering the field suffer. While entry into this career field is competitive, increased ownership of stocks and mutual funds drive substantial career growth of traders. Banks were offering more opportunities for people of average means to invest and speculate in stocks; the BLS reported that stock traders had median annual incomes of $68,500. Experienced traders of stocks and mutual funds have the potential to earn more than $145,600 annually. Contrary to a stockbroker, a professional who arranges transactions between a buyer and a seller, gets a guaranteed commission for every deal executed, a professional trader may have a steep learning curve and his/her ultra-competitive performance based career may be cut short during generalized stock market crashes.
Stock market trading operations have a high level of risk and complexity for unwise and inexperienced stock traders/investors seeking an easy way to make money quickly. In addition, trading activities are not free. Stock speculators/investors face several costs such as commissions and fees to be paid for the brokerage and other services, like the buying/selling orders placed at the stock exchange. Depending on the nature of each national or state legislation involved, a large array of fiscal obligations must be respected, taxes are charged by jurisdictions over those transactions and capital gains that fall within their scope. However, these fiscal obligations will vary from jurisdiction to jurisdiction. Among other reasons, there could be some instances where taxation is incorporated into the stock price through the differing legislation that companies have to comply with in their respective jurisdictions. Beyond these costs are the opportunity costs of money and time, currency risk, financial risk, Internet and news agency services and electricity consumption expenses—all of which must be accounted for.
Jérôme Kerviel and Kweku Adoboli, two rogue traders, worked in the same type of position, the Delta One desk - a table where derivatives are traded, not single stocks or bonds. These types of operations are simple and reserved for novice traders who specialize in exchange-traded funds, financial products that mimic the performance of an index; as they are easy to use, they facilitate portfolio diversification through the acquisition of contracts backed by a stock index or industry. The two traders were familiar to control procedures, they worked in the back office, the administrative body of the bank that controls the regularity of operations, before moving to trading. According to the report of the Inspector General of Societe Generale, in 2005 and 2006 Kerviel "led" by taking 100 to 150 million-euro positions on the shares of Solarworld AG listed in Germany. Moreover, the "unauthorized trading" of Kweku Adoboli, similar to Kerviel, did not date back a long way. Adoboli h
The stock of a corporation is all of the shares into which ownership of the corporation is divided. In American English, the shares are known as "stocks." A single share of the stock represents fractional ownership of the corporation in proportion to the total number of shares. This entitles the stockholder to that fraction of the company's earnings, proceeds from liquidation of assets, or voting power dividing these up in proportion to the amount of money each stockholder has invested. Not all stock is equal, as certain classes of stock may be issued for example without voting rights, with enhanced voting rights, or with a certain priority to receive profits or liquidation proceeds before or after other classes of shareholders. Stock can be bought and sold or on stock exchanges, such transactions are heavily regulated by governments to prevent fraud, protect investors, benefit the larger economy; as new shares are issued by a company, the ownership and rights of existing shareholders are diluted in return for cash to sustain or grow the business.
Companies can buy back stock, which lets investors recoup the initial investment plus capital gains from subsequent rises in stock price. Stock options, issued by many companies as part of employee compensation, do not represent ownership, but represent the right to buy ownership at a future time at a specified price; this would represent a windfall to the employees if the option is exercised when the market price is higher than the promised price, since if they sold the stock they would keep the difference. A person who owns a specific percentage of the share has the ownership of the corporation proportional to his share; the shares together form stock. The stock of a corporation is partitioned into shares, the total of which are stated at the time of business formation. Additional shares may subsequently be authorized by the existing shareholders and issued by the company. In some jurisdictions, each share of stock has a certain declared par value, a nominal accounting value used to represent the equity on the balance sheet of the corporation.
In other jurisdictions, shares of stock may be issued without associated par value. Shares represent a fraction of ownership in a business. A business may declare different types of shares, each having distinctive ownership rules, privileges, or share values. Ownership of shares may be documented by issuance of a stock certificate. A stock certificate is a legal document that specifies the number of shares owned by the shareholder, other specifics of the shares, such as the par value, if any, or the class of the shares. In the United Kingdom, Republic of Ireland, South Africa, Australia, stock can refer to different financial instruments such as government bonds or, less to all kinds of marketable securities. Stock takes the form of shares of either common stock or preferred stock; as a unit of ownership, common stock carries voting rights that can be exercised in corporate decisions. Preferred stock differs from common stock in that it does not carry voting rights but is entitled to receive a certain level of dividend payments before any dividends can be issued to other shareholders.
Convertible preferred stock is preferred stock that includes an option for the holder to convert the preferred shares into a fixed number of common shares any time after a predetermined date. Shares of such stock are called "convertible preferred shares". New equity issue may have specific legal clauses attached that differentiate them from previous issues of the issuer; some shares of common stock may be issued without the typical voting rights, for instance, or some shares may have special rights unique to them and issued only to certain parties. New issues that have not been registered with a securities governing body may be restricted from resale for certain periods of time. Preferred stock may be hybrid by having the qualities of bonds of fixed returns and common stock voting rights, they have preference in the payment of dividends over common stock and have been given preference at the time of liquidation over common stock. They have other features of accumulation in dividend. In addition, preferred stock comes with a letter designation at the end of the security.
B, whereas Class "A" shares of ORION DHC, Inc will sell under ticker OODHA until the company drops the "A" creating ticker OODH for its "Common" shares only designation. This extra letter does not mean that any exclusive rights exist for the shareholders but it does let investors know that the shares are considered for such, these rights or privileges may change based on the decisions made by the underlying company. "Rule 144 Stock" is an American term given to shares of stock subject to SEC Rule 144: Selling Restricted and Control Securities. Under Rule 144, restricted and controlled securities are acquired in unregistered form. Investors either purchase or take ownership of these securities through private sales from the issuing company or from an affiliate of the issuer. Investors wishing to sell these securities are subject to different rules than those selling traditional common or preferred stock; these individuals will only be allowed to liquidate their securities after meeting the specific conditions set forth by SEC Rule 144.
Capital market line
Capital market line is the tangent line drawn from the point of the risk-free asset to the feasible region for risky assets. The tangency point M represents the market portfolio, so named since all rational investors should hold their risky assets in the same proportions as their weights in the market portfolio. C M L: σ p ↦ R f + σ p ⋅ E − R f σ M The CML results from the combination of the market portfolio and the risk-free asset. All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier, with the exception of the Market Portfolio, the point on the efficient frontier to which the CML is the tangent. From a CML perspective, the portfolio M is composed of the risky asset, the market, has no holding of the risk free asset, i.e. money is neither invested in, nor borrowed from the money market account. Points to the left of and above the CML are infeasible, whereas points to the right/below are attainable but inefficient. Addition of leverage creates levered portfolios that are on the CML.
All of the portfolios on the CML have the same Sharpe ratio as that of the market portfolio, i.e. E − R f σ = E − R f σ M. In fact, the slope of the CML is the Sharpe ratio of the market portfolio. A stock picking rule of thumb is to buy assets whose Sharpe ratio will be above the CML and sell those whose Sharpe ratio will be below. Indeed, from the efficient market hypothesis it follows. Therefore, all portfolios should equal to the market's. In consequence, if there is a portfolio whose Sharpe ratio will be bigger than the market's this portfolio has a higher return per unit of risk, which contradicts the efficient market hypothesis; this abnormal extra return over the market's return at a given level of risk is what is called the alpha. Capital allocation line Efficient frontier Modern portfolio theory Security characteristic line Security market line Capital Market Line - CML
Market capitalization is the market value of a publicly traded company's outstanding shares. Market capitalization is equal to the share price multiplied by the number of shares outstanding; as outstanding stock is bought and sold in public markets, capitalization could be used as an indicator of public opinion of a company's net worth and is a determining factor in some forms of stock valuation. Market cap reflects only the equity value of a company, it is important to note that a firm's choice of capital structure has a significant impact on how the total value of a company is allocated between equity and debt. A more comprehensive measure is enterprise value, which gives effect to outstanding debt, preferred stock, other factors. For insurance firms, a value called. Market capitalization is used by the investment community in ranking the size of companies, as opposed to sales or total asset figures, it is used in ranking the relative size of stock exchanges, being a measure of the sum of the market capitalizations of all companies listed on each stock exchange.
In performing such rankings, the market capitalizations are calculated at some significant date, such as June 30 or December 31. The total capitalization of stock markets or economic regions may be compared with other economic indicators; the total market capitalization of all publicly traded companies in the world was US$51.2 trillion in January 2007 and rose as high as US$57.5 trillion in May 2008 before dropping below US$50 trillion in August 2008 and above US$40 trillion in September 2008. In 2014 and 2015, global market capitalization was US$68 trillion and US$67 trillion, respectively. Market cap is given by the formula MC = N × P, where MC is the market capitalization, N is the number of shares outstanding, P is the closing price per share. For example, if a company has 4 million shares outstanding and the closing price per share is $20, its market capitalization is $80 million. If the closing price per share rises to $21, the market cap becomes $84 million. If it drops to $19 per share, the market cap falls to $76 million.
This is in contrast to mercantile pricing where purchase price, average price and sale price may differ due to transaction costs. Not all of the outstanding shares trade on the open market; the number of shares trading on the open market is called the float. It is equal to or less than N; the free-float market cap uses just the floating number of shares in the calculation resulting in a smaller number. Traditionally, companies were divided into large-cap, mid-cap, small-cap; the terms mega-cap and micro-cap have since come into common use, nano-cap is sometimes heard. Different numbers are used by different indexes; the cutoffs may be defined as percentiles rather than in nominal dollars. The definitions expressed in nominal dollars need to be adjusted over decades due to inflation, population change, overall market valuation, market caps are to be different country to country. List of corporations by market capitalization List of finance topics List of stock exchanges London Stock Exchange Market price Market trend Middle-market company NASDAQ New York Stock Exchange Public float Shares authorized Treasury stock How to Value Assets – from the Washington State government web site Year-end market capitalization by country – World Bank, 1988–2010