Suppose that the daily price S of an asset satisfies the Black-Scholes model with parameters and

Suppose that the daily price S of an asset satisfies the Black-Scholes model with parameters μ and σ (on a daily time scale). With the daily data, we first compute the log-returns xt, t = 1, . . . , 506. Then with the MATLAB function fminunc, we find the following estimations for θ = (μ, ln(σ)).

theta =

0.0029 -3.9769 hessian =

1.0e+006 *

1.4404 -0.0007

-0.0007 0.0010

(a) Compute 95% confidence intervals for μ and σ.

(b) Compute 95% confidence intervals for the mean and volatility per annum.