ABSTRACT
One way to eliminate the problem of constant volatility inherent in the Black-Scholes model is to assume that the daily log-returns Xi = ln(Si/Si−1) are modeled by
Xi = μi + σiεi, i > r, (7.1)
for some integer r ≥ 1, where μi and σi depend on Fi−1 = σ{Hi, X1, . . . , Xi−1}, where Hi is a random vector containing possibly exogenous variables. In addition, (εi)i>r are independent and identically distributed with mean zero and variance one. Moreover, εi is independent of Fi−1, for all i > r. The εis are called the innovations.
