Learning outcomes

After this module you should be able to:

1. Write any candle, bar aggregation, swing pivot, support/resistance cluster, gap, relative-volume or VWAP rule as an explicit, look-ahead-free function of OHLCV data, and state the null distribution it must beat under a random walk.
2. Derive, by optional stopping and the scale function, the probability that a price hits a target before a stop, with and without drift, and the expected time to exit (Propositions 4A.6–4A.8).
3. Prove that for a driftless price no combination of stop, target, trailing stop or scaling rule has non-zero expectancy, and that with drift $\mu$ the expectancy equals $\mu$ times expected exposure-time (Propositions 4A.9 and 4A.12).
4. Compute stop-out probabilities over a horizon by the reflection principle, correct them for discrete (closing-basis) monitoring, and size stops in ATR units so that the probability is the same across stocks.
5. Derive the law of the peak and the expected give-back of a trailing stop under Brownian motion (Proposition 4A.11), and check it by simulation.
6. Explain with a model why widening a stop after entry is negative-expectancy behaviour when the adverse move carries information, and connect it to prospect theory (M14).
7. Read NSE breadth, participant-wise open interest, delivery and bulk/block-deal data, and say exactly what each can and cannot tell you.
8. Lay out a pre-market routine and an event calendar for the Indian market, with the session times and rules in force on 6 Nov 2026, and estimate how event days change volatility.