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The Black formula. The Black formula is similar to the Black–Scholes formula for valuing stock options except that the spot price of the underlying is replaced by a discounted futures price F. Suppose there is constant risk-free interest rate r and the futures price F (t) of a particular underlying is log-normal with constant volatility σ.
The Black–Scholes / ˌblæk ˈʃoʊlz / [1] or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives ...
In 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.
Price index numbers are usually defined either in terms of (actual or hypothetical) expenditures (expenditure = price * quantity) or as different weighted averages of price relatives ( ). These tell the relative change of the price in question. Two of the most commonly used price index formulae were defined by German economists and ...
The equation states that over any infinitesimal time interval the loss from theta and the gain from the gamma term must offset each other so that the result is a return at the riskless rate. From the viewpoint of the option issuer, e.g. an investment bank, the gamma term is the cost of hedging the option.
Implied volatility. In 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 (usually Black–Scholes ), will return a theoretical value equal to the price of the option. A non-option financial instrument that has ...
Zazzle. Zazzle is an American online marketplace that allows designers and customers to create their own products with independent manufacturers (clothing, posters, etc.), as well as use images from participating companies. Zazzle has partnered with many brands to amass a collection of digital images from companies like Disney, Warner Brothers ...
Chemical plant cost indexes are dimensionless numbers employed to updating capital cost required to erect a chemical plant from a past date to a later time, following changes in the value of money due to inflation and deflation.
The simplest formulation of the Vanna–Volga method suggests that the Vanna–Volga price of an exotic instrument is given by. where by denotes the Black–Scholes price of the exotic and the Greeks are calculated with ATM volatility and. These quantities represent a smile cost, namely the difference between the price computed with/without ...
The Black–Scholes formula (hereinafter, "BS Formula") provides an explicit equation for the value of a call option on a non-dividend paying stock. In case the stock pays one or more discrete dividend (s) no closed formula is known, but several approximations can be used, or else the Black–Scholes PDE will have to be solved numerically. One such approximation is described here. See also ...