Trailing stops

(a) Prove Proposition 4A.11: derive the exponential law of the peak $M_\tau-x_0$ for a trailing stop of distance $d$ under Brownian motion with drift $\mu$. (b) Nifty futures, daily volatility 250 points, drift $+10$ points a day, trailing distance 350 points, continuous monitoring. Compute the expected peak gain, expected P&L, probability of a loss, and expected holding time. (c) Compute the expected holding time with no drift. (d) If the stop is checked only on daily closes, what effective distance does the continuity correction give, and what expected P&L does the corrected formula predict?