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  2. Black–Scholes model - Wikipedia

    en.wikipedia.org/wiki/BlackScholes_model

    In fact, the BlackScholes 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 BlackScholes formula.

  3. Implied volatility - Wikipedia

    en.wikipedia.org/wiki/Implied_volatility

    Using a standard BlackScholes pricing model, the volatility implied by the market price is 18.7%, or: ¯ = (¯,) = % To verify, we apply implied volatility to the pricing model, f , and generate a theoretical value of $2.0004:

  4. Black–Scholes equation - Wikipedia

    en.wikipedia.org/wiki/BlackScholes_equation

    In mathematical finance, the BlackScholes equation, also called the BlackScholes–Merton equation, is a partial differential equation (PDE) governing the price evolution of derivatives under the BlackScholes model. [1]

  5. The Most Valuable Formula Ever Created - AOL

    www.aol.com/news/2013-05-09-the-most-valuable...

    The Black-Scholes option-pricing model, first published in 1973 in a paper titled "The Pricing of Options and Corporate Liabilities," was delivered in complete form for publication to.

  6. Local volatility - Wikipedia

    en.wikipedia.org/wiki/Local_volatility

    The starting point is the basic Black Scholes formula, coming from the risk neutral dynamics = +, with constant deterministic volatility and with lognormal probability density function denoted by ,. In the Black Scholes model the price of a European non-path-dependent option is obtained by integration of the option payoff against this lognormal ...

  7. Volatility (finance) - Wikipedia

    en.wikipedia.org/wiki/Volatility_(finance)

    Although the Black-Scholes equation assumes predictable constant volatility, this is not observed in real markets. Amongst more realistic models are Emanuel Derman and Iraj Kani 's [ 5 ] and Bruno Dupire 's local volatility , Poisson process where volatility jumps to new levels with a predictable frequency, and the increasingly popular Heston ...

  8. Moneyness - Wikipedia

    en.wikipedia.org/wiki/Moneyness

    This measure does not account for the volatility σ of the underlying asset. Unlike previous inputs, volatility is not directly observable from market data, but must instead be computed in some model, primarily using ATM implied volatility in the BlackScholes model. Dispersion is proportional to volatility, so standardizing by volatility ...

  9. Geometric Brownian motion - Wikipedia

    en.wikipedia.org/wiki/Geometric_Brownian_motion

    A straightforward extension of the Black Scholes GBM is a local volatility SDE whose distribution is a mixture of distributions of GBM, the lognormal mixture dynamics, resulting in a convex combination of Black Scholes prices for options.