Stochastic volatilityIn statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others.
Yield to maturityThe yield to maturity (YTM), book yield or redemption yield of a bond or other fixed-interest security, such as gilts, is an estimate of the total rate of return anticipated to be earned by an investor who buys a bond at a given market price, holds it to maturity, and receives all interest payments and the capital redemption on schedule. It is the (theoretical) internal rate of return (IRR, overall interest rate): the discount rate at which the present value of all future cash flows from the bond (coupons and principal) is equal to the current price of the bond.
United States Treasury securityUnited States Treasury securities, also called Treasuries or Treasurys, are government debt instruments issued by the United States Department of the Treasury to finance government spending in addition to taxation. Since 2012, U.S. government debt has been managed by the Bureau of the Fiscal Service, succeeding the Bureau of the Public Debt. There are four types of marketable Treasury securities: Treasury bills, Treasury notes, Treasury bonds, and Treasury Inflation Protected Securities (TIPS).
Forward rate agreementIn finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular it is a linear IRD with strong associations with interest rate swaps (IRSs). A forward rate agreement's (FRA's) effective description is a cash for difference derivative contract, between two parties, benchmarked against an interest rate index. That index is commonly an interbank offered rate (-IBOR) of specific tenor in different currencies, for example LIBOR in USD, GBP, EURIBOR in EUR or STIBOR in SEK.
Bond optionIn finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC. A European bond option is an option to buy or sell a bond at a certain date in future for a predetermined price. An American bond option is an option to buy or sell a bond on or before a certain date in future for a predetermined price. Generally, one buys a call option on the bond if one believes that interest rates will fall, causing an increase in bond prices.
Arbitrage pricing theoryIn finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, it is widely believed to be an improved alternative to its predecessor, the Capital Asset Pricing Model (CAPM). APT is founded upon the law of one price, which suggests that within an equilibrium market, rational investors will implement arbitrage such that the equilibrium price is eventually realised.
Swap (finance)In finance, a swap is an agreement between two counterparties to exchange financial instruments, cashflows, or payments for a certain time. The instruments can be almost anything but most swaps involve cash based on a notional principal amount. The general swap can also be seen as a series of forward contracts through which two parties exchange financial instruments, resulting in a common series of exchange dates and two streams of instruments, the legs of the swap.
Currency swapIn finance, a currency swap (more typically termed a cross-currency swap, XCS) is an interest rate derivative (IRD). In particular it is a linear IRD, and one of the most liquid benchmark products spanning multiple currencies simultaneously. It has pricing associations with interest rate swaps (IRSs), foreign exchange (FX) rates, and FX swaps (FXSs). A cross-currency swap's (XCS's) effective description is a derivative contract, agreed between two counterparties, which specifies the nature of an exchange of payments benchmarked against two interest rate indexes denominated in two different currencies.
Futures contractIn finance, a futures contract (sometimes called futures) is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price of the contract is known as the forward price. The specified time in the future when delivery and payment occur is known as the delivery date.
Hilbert spaceIn mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space.
