Volatility (finance)In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option).
Brownian model of financial marketsThe Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes. Under this model, these assets have continuous prices evolving continuously in time and are driven by Brownian motion processes.
Forward contractIn 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.
Implied volatilityIn financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security.
Option time valueIn finance, the time value (TV) (extrinsic or instrumental value) of an option is the premium a rational investor would pay over its current exercise value (intrinsic value), based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market, thus an option is always worth more than its current exercise value. As an option can be thought of as 'price insurance' (e.g.
Exotic optionIn finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic option may also include a non-standard underlying instrument, developed for a particular client or for a particular market. Exotic options are more complex than options that trade on an exchange, and are generally traded over the counter.
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.
Option-adjusted spreadOption-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security's payments to match its market price, using a dynamic pricing model that accounts for embedded options. OAS is hence model-dependent. This concept can be applied to a mortgage-backed security (MBS), or another bond with embedded options, or any other interest rate derivative or option. More loosely, the OAS of a security can be interpreted as its "expected outperformance" versus the benchmarks, if the cash flows and the yield curve behave consistently with the valuation model.
Call optionIn finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at or before a certain time (the expiration date) for a certain price (the strike price). This effectively gives the owner a long position in the given asset.
Expiration (options)In finance, the expiration date of an option contract (represented by Greek letter tau, τ) is the last date on which the holder of the option may exercise it according to its terms. In the case of options with "automatic exercise", the net value of the option is credited to the long and debited to the short position holders. Typically, exchange-traded option contracts expire according to a pre-determined calendar. For instance, for U.S.
