Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Bootstrapping (finance)In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. A bootstrapped curve, correspondingly, is one where the prices of the instruments used as an input to the curve, will be an exact output, when these same instruments are valued using this curve. Here, the term structure of spot returns is recovered from the bond yields by solving for them recursively, by forward substitution: this iterative process is called the bootstrap method.
Lattice model (finance)In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date.
Spot contractIn finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the trade date. The settlement price (or rate) is called spot price (or spot rate). A spot contract is in contrast with a forward contract or futures contract where contract terms are agreed now but delivery and payment will occur at a future date.
Interest rate derivativeIn finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates.
Option (finance)In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction.
Risk-neutral measureIn 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.
Bond (finance)In finance, a bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor (e.g. repay the principal (i.e. amount borrowed) of the bond at the maturity date as well as interest (called the coupon) over a specified amount of time). The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds.
Interest rateAn interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized.
ArbitrageIn economics and finance, arbitrage (ˈɑːrbᵻtrɑːʒ, -trɪdʒ) is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs.
