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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.
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.
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.
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.
Photosynthesis usually refers to oxygenic photosynthesis, a process that produces oxygen. Photosynthetic organisms store the chemical energy so produced within intracellular organic compounds (compounds containing carbon) like sugars, glycogen , cellulose and starches .
The discrete difference equations may then be solved iteratively to calculate a price for the option. [4] The approach arises since the evolution of the option value can be modelled via a partial differential equation (PDE), as a function of (at least) time and price of underlying; see for example the Black–Scholes PDE. Once in this form, a ...
Itô's lemma can be used to derive the Black–Scholes equation for an option. [2] Suppose a stock price follows a geometric Brownian motion given by the stochastic differential equation dS = S(σdB + μ dt). Then, if the value of an option at time t is f(t, S t), Itô's lemma gives
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 ...