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Black-Scholes model

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Black-Scholes model
The original Closed-form solution to Option pricing developed by Fischer Black and Myron Scholes in 1973. In its simplest form it offers a solution to pricing European-style options on assets with interim Cash pay-outs over the life of the Option. The model calculates the theoretical, or fair value for the Option by constructing an instantaneously riskless Hedge: that is, one whose performance is the mirror image of the Option pay-out. The Portfolio of Option and Hedge can then be assumed to earn the Risk-free rate of return. Central to the model is the assumption that market returns are normally distributed (ie have lognormal prices), that there are no transaction costs, that Volatility and Interest rates remain constant throughout the life of the Option, and that the market follows a Diffusion process. The model has five major inputs: the Risk-free Interest rate, the Option’s Strike Price, the price of the Underlying, the Option’s maturity, and the Volatility assumed. Since the first four are usually determined by the market, options traders tend to trade the Implied volatility of the Option.
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