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Forward Price
The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the spot price and any dividends. For forwards on non-tradeables, pricing the forward may be a complex task. Forward price formula If the underlying asset is tradable and a dividend exists, the forward price is given by: : F = S_0 e^ - \sum_^N D_i e^ \, where :F is the forward price to be paid at time T :e^x is the exponential function (used for calculating continuous compounding interests) :r is the risk-free interest rate :q is the convenience yield :S_0 is the spot price of the asset (i.e. what it would sell for at time 0) :D_i is a dividend that is guaranteed to be paid at time t_i where 0< t_i < T. Proof of the forward price formula The two questions here are what price the short position ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Rate
The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a ''forward rate''.. Forward rate calculation To extract the forward rate, we need the zero-coupon yield curve. We are trying to find the future interest rate r_ for time period (t_1, t_2), t_1 and t_2 expressed in years, given the rate r_1 for time period (0, t_1) and rate r_2 for time period (0, t_2). To do this, we use the property that the proceeds from investing at rate r_1 for time period (0, t_1) and then reinvesting those proceeds at rate r_ for time period (t_1, t_2) is equal to the proceeds from investing at rate r_2 for time period (0, t_2). r_ depends on the rate calculation mode (simple, yearly compounded or continuously compounded), which yields three different results. Mathematically it reads as follows: Simple rate : (1+r_1t_1)(1+ r_(t_2-t_1)) = 1+r_2t_2 Solving for r_ yields: Thus r_ = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martingale (probability Theory)
In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal to the most recent value. In other words, the conditional expectation of the next value, given the past, is equal to the present value. Martingales are used to model fair games, where future expected winnings are equal to the current amount regardless of past outcomes. History Originally, ''martingale (betting system), martingale'' referred to a class of betting strategy, betting strategies that was popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins their stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double their bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake. As the gambler's wealth and available time jointly approach infinity, their pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contango
Contango is a situation in which the futures contract, futures price (or forward contract, forward price) of a commodity is higher than the spot price. In a contango situation, arbitrageurs or speculators are "willing to pay more for a commodity [to be received] at some point in the future than to purchase the commodity immediately. This may be due to people's desire to pay a premium to have the commodity in the future rather than paying the costs of storage and carry costs of buying the commodity today." On the other side of the trade, Hedge (finance), hedgers (commodity producers and commodity holders) are happy to sell futures contracts and accept the higher-than-expected returns. A contango market is also known as a ''normal market'' or ''carrying cost, carrying-cost market''. The opposite market condition to contango is known as backwardation. "A market is 'in backwardation' when the futures price is below the spot price for a particular commodity. This is favorable for inves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backwardation
Normal backwardation, also sometimes called backwardation, is the market condition where the price of a commodity's forward contract, forward or futures contract is trading below the ''expected'' spot price at contract maturity. The resulting futures or forward curve would ''typically'' be downward sloping (i.e. "inverted"), since contracts for further dates would typically trade at even lower prices. In practice, the expected future spot price is unknown, and the term "backwardation" may refer to "positive basis", which occurs when the current spot price exceeds the price of the future. The opposite market condition to normal backwardation is known as contango. Contango refers to "negative basis" where the future price is trading above the expected spot price. Note: In industry parlance backwardation may refer to the situation that futures prices are below the ''current'' spot price. Backwardation occurs when the difference between the forward price and the spot price is less ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cost Of Carry
The cost of carry or carrying charge is the cost of holding a security or a physical commodity over a period of time. The carrying charge includes insurance, storage and interest on the invested funds as well as other incidental costs. In interest rate futures markets, it refers to the differential between the yield on a cash instrument and the cost of the funds necessary to buy the instrument. If long, the cost of carry is the cost of interest paid on a margin account. Conversely, if short, the cost of carry is the cost of paying dividends, or rather the opportunity cost; the cost of purchasing a particular security rather than an alternative. For most investments, the cost of carry generally refers to the risk-free interest rate that could be earned by investing currency in a theoretically safe investment vehicle such as a money market account minus any future cash flows that are expected from holding an equivalent instrument with the same risk (generally expressed in percentag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convenience Yield
A convenience yield is an implied return on holding inventories. It is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints. Let F_ be the forward price of an asset with initial price S_t and maturity T. Suppose that r is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be F_ = S_t \cdot e^ However, this relationship does not hold in most commodity markets, partly because of the inability of investors and speculators to short the underlying asset, S_t. Instead, there is a correction to the forward pricing formula given by the convenience yield c. Hence F_ = S_t \cdot e^ This makes it possible for backwardation Normal backwardation, also sometimes called backwardation, is the market condition where the price of a commodity's forward contract, forward or futures contract is trading below the ''expected'' spot price at contract maturity. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Measure
In finance, a ''T''-forward measure is a pricing measure equivalent to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity ''T''. The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds. Mathematical definition Let : B(T) = \exp\left(\int_0^T r(u)\, du\right) be the bank account or money market account numeraire and : D(T) = 1/B(T) = \exp\left(-\int_0^T r(u)\, du\right) be the discount factor in the market at time 0 for maturity ''T''. If Q_* is the risk neutral measure, then the forward measure Q_T is defined via the Radon–Nikodym derivative given by :\frac = \frac = \frac. Note that this implies that the forward measure and the risk neutral measure coincide when interest rates are deterministic. Also, this is a particular form of the change of numeraire formula by changing the numeraire from the money market or bank accou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Rate
The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a ''forward rate''.. Forward rate calculation To extract the forward rate, we need the zero-coupon yield curve. We are trying to find the future interest rate r_ for time period (t_1, t_2), t_1 and t_2 expressed in years, given the rate r_1 for time period (0, t_1) and rate r_2 for time period (0, t_2). To do this, we use the property that the proceeds from investing at rate r_1 for time period (0, t_1) and then reinvesting those proceeds at rate r_ for time period (t_1, t_2) is equal to the proceeds from investing at rate r_2 for time period (0, t_2). r_ depends on the rate calculation mode (simple, yearly compounded or continuously compounded), which yields three different results. Mathematically it reads as follows: Simple rate : (1+r_1t_1)(1+ r_(t_2-t_1)) = 1+r_2t_2 Solving for r_ yields: Thus r_ = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk-neutral Measure
In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or '' equivalent martingale measure'') is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free. A risk-neutral measure is a probability measure The easiest way to remember what the risk-neutral measure is, or to explain it to a probability generalist who might not know much about finance, is to realize that it is: # The probability measure of a transformed random variable. Typically this transformation is the utility function of the payoff. The risk-neutral measure would be the measure co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Measure
In finance, a ''T''-forward measure is a pricing measure equivalent to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity ''T''. The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds. Mathematical definition Let : B(T) = \exp\left(\int_0^T r(u)\, du\right) be the bank account or money market account numeraire and : D(T) = 1/B(T) = \exp\left(-\int_0^T r(u)\, du\right) be the discount factor in the market at time 0 for maturity ''T''. If Q_* is the risk neutral measure, then the forward measure Q_T is defined via the Radon–Nikodym derivative given by :\frac = \frac = \frac. Note that this implies that the forward measure and the risk neutral measure coincide when interest rates are deterministic. Also, this is a particular form of the change of numeraire formula by changing the numeraire from the money market or bank accou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asset
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can be converted into cash (although cash itself is also considered an asset). The balance sheet of a firm records the monetaryThere are different methods of assessing the monetary value of the assets recorded on the Balance Sheet. In some cases, the ''Historical Cost'' is used; such that the value of the asset when it was bought in the past is used as the monetary value. In other instances, the present fair market value of the asset is used to determine the value shown on the balance sheet. value of the assets owned by that firm. It covers money and other valuables belonging to an individual or to a business. ''Total assets'' can also be called the ''balance sheet total''. Assets can be grouped into two major classes: Tangible property, tangib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
