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In finance, Black's approximation is an approximate method for computing the value of an American call option on a stock paying a single dividend. It was described by Fischer Black in 1975. [1] 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 ...
In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put—the binary options are easier to analyze, and correspond to the two terms in the Black–Scholes formula.
The options trader makes a profit of $200, or the $400 option value (100 shares * 1 contract * $4 value at expiration) minus the $200 premium paid for the call.
Option values vary with the value of the underlying instrument over time. The price of the call contract must act as a proxy response for the valuation of: the expected intrinsic value of the option, defined as the expected value of the difference between the strike price and the market value, i.e., max[S−X, 0]. [3]
As the seller of a call option, you hope the stock price stays below the strike price, so that the option expires worthless and you keep the option premium received as your profit.
%If Unchanged Potential Return = (call option price - put option price) / [stock price - (call option price - put option price)] For example, for stock JKH purchased at $52.5, a call option sold for $2.00 with a strike price of $55 and a put option purchased for $0.50 with a strike price of $50, the %If Unchanged Return for the collar would be:
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.
In finance, a price (premium) is paid or received for purchasing or selling options.This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling § Quantitative finance generally.
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