Suppose that a stock price, S, follows geometric Brownian motion with expected return μ and volatility σ, i.e., dS = μS dt + σS dz. Consider the function f(t,S) = ln(S), what is df(t,S) in terms of dt and dz?
a. df = μ dt + σ dz
b. df = (μ - ½ σ²) dt + σ dz
c. df = μf dt + σf dz
d. df = (μ - σ²) dt + σ dz