b.

$E\left[\mathrm{ln}\frac{{S}_{52}}{{S}_{0}}\right]=\left[\left(0.001-\frac{{0.02}^{2}}{2}\right)0.52\right]=0.0416$

$\mathrm{Var}\left[\mathrm{ln}\frac{{S}_{52}}{{S}_{0}}\right]={\sigma}^{2}T={0.02}^{2}\cdot 52=0.0208$

6.23. First, divide both sides of the differential by *M*−*S*_{t} to obtain:

$\frac{\mathrm{d}{S}_{t}}{M-{S}_{t}}=\mu \mathrm{d}t+\sigma \mathrm{d}{Z}_{t}$

Since the integral of d*S*_{t}*/*(*M*−*S*_{t}) for real-valued functions *S*_{t} equals −ln(*M*−*S*_{t}), we will use the expression ln(*M*−*S*_{t}) to obtain the correct solution for the stochastic process *S*_{t}

Get *Risk Neutral Pricing and Financial Mathematics: A Primer* now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.