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Stochastic volatility

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Stochastic volatility
One of the key assumptions of the Black-Scholes model is that the stock price follows Geometric Brownian motion with constant Volatility and Interest rates. However, in real markets, Volatility is far from constant. If Volatility is assumed to be driven by some Stochastic process, however, the Black-Scholes model no longer describes a complete market, since there is NOW another source of uncertainty in the Option pricing model. A variety of approaches have been attempted to resolve this difficulty since the mid-1980s, most notably the Heath-Jarrow-Morton framework.
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