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Black and Scholes' insight was that the portfolio represented by the right-hand side is riskless: thus the equation says that the riskless return over any infinitesimal time interval can be expressed as the sum of theta and a term incorporating gamma.
Nikolay Borisovich Sukhomlin (Russian: Николай Борисович Сухомлин; April 1945, in Leningrad – 12 January 2010, in Haiti) was a Russian scientist who discovered new solutions and symmetry for the Black-Scholes equation.
Fischer Sheffey Black (January 11, 1938 – August 30, 1995) was an American economist, best known as one of the authors of the Black–Scholes equation. Working variously at the University of Chicago, the Massachusetts Institute of Technology, and at Goldman Sachs, Black died two years before the Nobel Memorial Prize in Economic Sciences (which is not given posthumously) was awarded to his ...
If we know that (,) satisfies an equation (like the Black–Scholes equation) we are guaranteed that we can make good use of the equation in the derivation of the equation for a new function (,) defined in terms of the old if we write the old V as a function of the new v and write the new and x as functions of the old t and S.
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 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.
Birch–Murnaghan equation of state: Continuum mechanics: Francis Birch and Francis D. Murnaghan: Birkhoff–Rott equation [4] [5] Fluid dynamics: Garrett Birkhoff: Black's equation: Electronics: James R. Black: Black–Scholes equation: Mathematical finance: Fischer Black and Myron Scholes: Blaney–Criddle equation: Agronomy: Blaney and ...
Most quantum option pricing research typically focuses on the quantization of the classical Black–Scholes–Merton equation from the perspective of continuous equations like the Schrödinger equation. Emmanuel Haven builds on the work of Zeqian Chen and others, [1] but considers the market from the perspective of the Schrödinger equation. [2]