Exam questions on trees, Americans, and barriers rarely ask for a one-line formula — they ask for a complete algorithm written in full, with the calibration check, the for early exercise, or the bridge survival weights stated explicitly. This note collects the markable templates for European and American binomial pricing, knock-out barriers on trees and in Monte Carlo, and a hand-executed Longstaff–Schwartz regression (the standard long question when Monte Carlo replaces the lattice). Each template lists steps in the order an examiner expects; the worked example shows where regression coefficients and exercise decisions earn partial credit.
Learning objectives. By the end of this note you should be able to:
- write the European and American binomial algorithms from inputs to output, including the no-arbitrage check and cost quote;
- modify the backward pass for a knock-out barrier and explain barrier-node alignment;
- state the bridge-corrected down-and-out Monte Carlo estimator and justify the bias direction of the uncorrected version;
- carry out the Longstaff–Schwartz backward induction on a small path table, regressing only over ITM paths;
- quote the quick-recall facts (CRR calibration, in–out parity, smooth pasting, bridge formula) under time pressure.
In this lesson
- Template: European option by binomial tree
- Template: American option by binomial tree
- Template: knock-out barrier on a binomial tree
- Template: down-and-out barrier by Monte Carlo with bridge correction
- Worked example: Longstaff–Schwartz American put
- Quick-recall facts
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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