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Applying the HJM-approach when volatility is stochastic

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Corporate bond

A corporate bond is a bond issued by a corporation in order to raise financing for a variety of reasons such as to ongoing operations, M&A, or to expand business. The term is usually applied to longer-term debt instruments, with maturity of at least one year. Corporate debt instruments with maturity shorter than one year are referred to as commercial paper. The term "corporate bond" is not strictly defined. Sometimes, the term is used to include all bonds except those issued by governments in their own currencies.

Bond option

In 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.

Forward exchange rate

The forward exchange rate (also referred to as forward rate or forward price) is the exchange rate at which a bank agrees to exchange one currency for another at a future date when it enters into a forward contract with an investor. Multinational corporations, banks, and other financial institutions enter into forward contracts to take advantage of the forward rate for hedging purposes.

Bond convexity

In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller.

Volatility risk

Volatility risk is the risk of a change of price of a portfolio as a result of changes in the volatility of a risk factor. It usually applies to portfolios of derivatives instruments, where the volatility of its underlying is a major influencer of prices. A measure for the sensitivity of a price of a portfolio (or asset) to changes in volatility is vega, the rate of change of the value of the portfolio with respect to the volatility of the underlying asset.

Term (logic)

In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variables and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.

Contingent claim

In finance, a contingent claim is a derivative whose future payoff depends on the value of another “underlying” asset, or more generally, that is dependent on the realization of some uncertain future event. These are so named, since there is only a payoff under certain contingencies. Any derivative instrument that is not a contingent claim is called a forward commitment. The prototypical contingent claim is an option, the right to buy or sell the underlying asset at a specified exercise price by a certain expiration date; whereas (vanilla) swaps, forwards, and futures are forward commitments, since these grant no such optionality.

Bond market index

A bond index or bond market index is a method of measuring the investment performance and characteristics of the bond market. There are numerous indices of differing construction that are designed to measure the aggregate bond market and its various sectors (government, municipal, corporate, etc.) A bond index is computed from the change in market prices and, in the case of a total return index, the interest payments, associated with selected bonds over a specified period of time.

Forward contract

In finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on at the time of conclusion of the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into.

Electronic trading platform

In finance, an electronic trading platform also known as an online trading platform, is a computer software program that can be used to place orders for financial products over a network with a financial intermediary. Various financial products can be traded by the trading platform, over a communication network with a financial intermediary or directly between the participants or members of the trading platform.