Binomial / American Pricer
Build a Cox-Ross-Rubinstein lattice, confirm it converges to Black-Scholes, then price an American put and report the early-exercise premium.
The scenario
You've joined a quant-dev desk. Before the closed-form work, they want to see you can build a lattice pricer from scratch and handle early exercise. Implement a Cox-Ross-Rubinstein binomial tree, price a European option and confirm it converges to Black-Scholes, then price an American put and show the early-exercise premium.
Where this shows up
A binomial tree with early exercise is the canonical quant-dev pricing warm-up and a common take-home at firms of this type.
Firms such as Bank of America, Barclays, IMC.
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Task brief
# Binomial / American Pricer **Role relevance:** Quant developer take-home **Estimated time:** 55 minutes **Difficulty:** Intermediate **Format:** Python (.py) ## What you are given - binomial_pricer_starter.py with the function signatures stubbed and a self-check harness - A closed-form Black-Scholes function, for the convergence check only ## What you must deliver 1. CRR tree parameters with a guard on the risk-neutral probability 2. European call and put by backward induction, converging to Black-Scholes 3. An American put via max(continuation, intrinsic) at each node 4. The early-exercise premium, and a comment on when it is largest ## Constraints & assumptions Standard library only - math and statistics, no numpy or scipy. Non-dividend-paying stock. One rolling array is enough storage; do not build the full tree. ## Submission note Complete the starter file, then compare your work against the mark scheme.
Your tasks
- 01Build a CRR binomial tree with n steps: u = exp(sigma sqrt(dt)), d = 1/u, risk-neutral p = (exp(r dt) - d) / (u - d).
- 02Price a European call and put by backward induction and confirm they converge to the Black-Scholes price as n grows.
- 03Price an American put by taking max(continuation value, intrinsic value) at each node.
- 04Report the early-exercise premium (American minus European put) and comment on when it is largest.
How you're assessed
The full points-based mark scheme is included with the pack.
What you'll learn
- How backward induction prices any option on a lattice.
- Why American puts can be worth exercising early, and calls on a non-dividend stock are not.
- How the tree converges to Black-Scholes as the step count grows.