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.
Volatility smileVolatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.
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).
Autoregressive conditional heteroskedasticityIn econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.
Options strategyOption strategies are the simultaneous, and often mixed, buying or selling of one or more options that differ in one or more of the options' variables. Call options, simply known as Calls, give the buyer a right to buy a particular stock at that option's strike price. Opposite to that are Put options, simply known as Puts, which give the buyer the right to sell a particular stock at the option's strike price. This is often done to gain exposure to a specific type of opportunity or risk while eliminating other risks as part of a trading strategy.
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 (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.
Binomial options pricing modelIn finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (), and formalized by Cox, Ross and Rubinstein in 1979 and by Rendleman and Bartter in that same year.
Local volatilityA local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the current asset level and of time . As such, it is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of and ). Local volatility models are often compared with stochastic volatility models, where the instantaneous volatility is not just a function of the asset level but depends also on a new "global" randomness coming from an additional random component.
Employee stock optionEmployee stock options (ESO) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options. Employee stock options are commonly viewed as an internal agreement providing the possibility to participate in the share capital of a company, granted by the company to an employee as part of the employee's remuneration package. Regulators and economists have since specified that ESOs are compensation contracts.
