Asset values are assumed to be constant throughout the time of the option.?In this formula, the interest rate R and standard deviation To facilitate the calculation of this formula have developed a table of values of N (d) for various d. Black-Scholes formula is often used by those attempting to detect the situation when the market price of the option is seriously different from its actual price. Option, which is sold at a significantly lower price than that obtained by the formula, is a candidate for purchase, and vice versa – one that is sold at a considerably higher price – a candidate for sale [7. 185-224 p.].
Binomial model of Cox, Ross and Rubinstein used to estimate the premium American options, first of all put option. Entire period of the option contract is divided into several time intervals. It is believed that within each of them, the underlying price can go up or down with a certain probability. Get the value of the underlying asset price for each time interval, given the data on the standard deviation of its course (build distribution tree for sale), also determine the likelihood of rising and falling exchange value of the asset at each interval time interval. Possible option price at a given time determined based on the value price of an asset on the expiry of the option.
After that, consistent discounting price option (based on the likelihood of increasing and decreasing value of the asset at each time interval) get the value of its price at the conclusion of the contract. Any buyer of an option would have a guarantee that the seller fulfills its obligations when the options are exercised. The buyer of a call option wants a guarantee that the seller is able to deliver the required action, and the buyer of the put option “wants to have guarantees that the seller is able to pay the necessary sum of money.Therefore birzhi set in options trading margin requirements – the system of protection from the actions of the seller, known as “margin”. Brokerage firms are allowed to install on their desire even more stringent requirements for their clients.
Many tools have the features of options, especially the call option. Consider some of them. Stock warrant (or warrants) – a call option issued by a firm on its shares. Warrants usually are issued for a longer period (five years or more) than the typical call option. Also issued perpetual warrants. Exercise price can be fixed or changed during the term of the warrants, usually upward. The initial exercise price at the time of issue the warrant, usually set well above the market price of the underlying asset. One of the differences warrant from the call option is to limit the number of warrants. Always produced only a certain number of warrants particular type.
Total number usually can not be increased, and it declines as performance warrants.Execution of the warrant has a positive impact on the corporation – a corporation gets more funds, increasing the number of issued shares and reduced the number of warrants. The right seems to warrant, in the sense that it also represents a call option issued by the company on its shares. The right is also called subscription warrant.
They give shareholders pre-emptive rights in respect of subscription for new ordinary shares in issue prior to their public offering. Each share outstanding, gets one right. One share purchased for a certain amount of human, plus the amount of money equal to the subscription price. To ensure that the sale of new shares, subscription price is usually set below the market rate of shares at the time of registration rights. Rights normally have a short period (two to ten weeks from the date of issue) and are free to apply before they are executed. Up until a certain date the old stocks are sold together with the rights. This means that the buyer receives the shares and rights when they are released. After this, the shares are sold without a license at a lower cost [1. 583-624 p.]
Forward contract is usually in order to implement a real sale or purchase of these assets and the insurance provider or purchaser of the possible adverse price changes. It is true that contractors can not also take advantage of favorable conditions possible. Forward contract involves enforceable, but the parties are not immune from its failure in the event of bankruptcy or bad faith of one of the parties to the transaction. Secondary market of forward contracts on most of the assets is underdeveloped because of their characteristics forward contract – a contract individual. An exception is the forward exchange market.
By entering into a forward contract, the parties agree on the price at which the transaction will be executed. This price is called the cost of delivery. There are two approaches to determining the forward price. According to the first forward price occurs as a consequence of expectations of the derivatives market on the future price of the swap. The second approach – Arbitration – based on the technical relationship between forward and current spot prices, which is determined by the current market rate without the risk.
Moreover, it is assumed that the investor indifferent whether to acquire the asset in the spot market now or in a forward contract in the future. As part of the arbitration approach is also distinguished: 1) the forward leg price of the asset on which no income is paid and 2) the forward leg of the asset price at which the income is paid. For the first case of formula for determining the forward price can be represented as follows:
Forward leg price of an asset that pays income to determine a bit more complicated. If the per share dividend paid during the term of the forward contract, the price of the forward leg should be adjusted to its size, since purchasing the contract, the investor does not receive the dividend [14. 180-196 p.]. For the simplest case, when the dividend is paid just before the expiry of the contract, the formula is: If the dividend is paid at some time during the term of the contract, the buyer will lose not only the dividend but also the interest of its reinvestment before the expiry of the contract. In this case, the previous formula becomes: where: T – is the term of the contract; t – the date of payment of dividends; r – interest rate risk-free for the time period T; rate without risk for the period Tt;
There are several varieties of short-term forward contracts, among them – the repo and reverse repo. Repo – is an agreement between counterparties, whereby one party sells securities with the obligation to redeem them from her after a while at a higher price. The operation resulted in the first party actually obtains a loan secured by securities. Income in the second part is formed by the difference between prices at which she first buys and then sells the paper.
Reverse repurchase agreement – an agreement to purchase securities with the obligation of selling them later at a lower price. In this transaction the person purchasing the securities at a higher price actually gets them into a loan secured by the money. The second person who provides credit in the form of securities, receives the income (interest on a loan) in the amount of difference between selling price and the repurchase of securities [2. 171-185p.].
A futures contract is an agreement between the parties on the purchase or sale of a certain quantity of goods on the date fixed for an agreed price.Although such a contract is determined by purchase price, but an asset to the delivery date is not paid. Participants in the transaction are liable for compulsory execution of the contract. Futures contracts are concluded on assets such as agricultural products, raw materials, foreign currency, securities and fixed income market indices, bank deposits. Futures contracts are made only on the exchange. Consider more currency futures [6. 193-201p.].
The U.S. trade currency futures contracts carried in the international monetary market (IMM), Division of the Chicago Mercantile Exchange (CME). In Rossi’s futures are trading at the moment only on the Stock Exchange “Saint Petersburg”. Currency futures, like forward contracts fix the price of any currency up to the date of delivery in a certain period of time in the future. Unlike forward contracts, futures contracts are standardized, and trading operations shall be implemented on an organized exchange. The advantage of futures contracts to forwards is their market liquidity, ie, the possibility of selling or buying in the stock market.
Futures contracts provide the necessary services to participants of the foreign exchange market.These services include: 1) determine the price, ie market participants are conducting hedging and speculators react to determine the future price of any currency, 2) liquidity, the ability of market participants to buy and sell at any time when the market opened for trading, and 3) the protection of the client, which is implemented by the introduction of compulsory exchangerules. To ensure a high level of customer protection on the CME uses the following measures: the margin requirements, protection from bankruptcy protection by default; clearing system.
The first level of protection to trade currency futures – is the initial margin (initial margin). Exchange sets margin requirements for each firm a member of the clearing. In turn, the company sets the standards for the client (buyer or seller of a futures contract). These requirements minimize the potential damage that can be applied to the client in the event of bankruptcy or insolvency of the member firms clearing system. In addition to the initial margin requirements, there are maintenance margin (maintenance margin).They are based on the daily increase or decrease in value of the futures contract.
Clearing system exchanges only work with its member firms and not to individual market participants. Exchange performs calculations directly with members of the clearing system. Clearing house acts as a guarantor of the implementation of futures and options contracts. Standardized futures contracts have a number of features, which are set by the exchange. These standardized elements of the currency futures include: 1) the unit or the amount of the contract and 2) the method of price quotations, and 3) the minimum price change, and 4) limits the price, 5) deadlines, 6) a predetermined end date of trade; 7) The estimated date, 8 ) provision or margin requirements [6. 193-201p.].
All foreign exchange contracts that are sold or bought in the IMM, are estimated in U.S. dollars. IMM contracts have a standard period of performance. Currency futures contracts are paid on the third Wednesday of the month expiry of the contract. Trade contracts IMM ends two business days prior to the medium in which the term expires on them. This is usually the Monday before the environment.
Purchase of foreign currency futures provide the buyer “a long position (futures position when the game does not rise) and can be used to hedge against the future payment obligation in the same currency. Sales of foreign currency futures provides the seller “short position (short position) in this currency. One of the most popular futures transactions are transactions in the indices.They constitute a contract for the sale of imaginary securities package assembled from the largest shares of companies whose market value in the summation determines the value of market indexes such as the RTS in Russia, “Nikkey” in Japan, “Dow-Jones”