Black-Scholes Pricer
Complete a European option pricer and return the Greeks for a given parameter set.
The scenario
You've joined the options desk at a derivatives market maker. Before you can be trusted to quote, the desk wants to see you can price a vanilla European option from first principles and explain how its risk moves. Your first task is to build a clean, correct Black-Scholes pricer and the core Greeks the desk watches all day.
Where this shows up
Pricing a vanilla option and reasoning about its Greeks is the canonical warm-up for quant-dev and options-trading assessments at firms such as these.
Firms such as Mako, IMC, Optiver.
DeskPrep is not affiliated with, endorsed by, or sponsored by any named firm. Firm names are used for illustrative, educational purposes only and do not imply that these materials are official assessments of, or are connected with, those firms.
Task brief
# Black-Scholes Pricer **Role relevance:** Quant research take-home **Estimated time:** 40 minutes **Difficulty:** Beginner **Format:** Python (.py) ## What you are given - bs_pricer_starter.py with the function signatures stubbed - A small set of test parameters in params.csv ## What you must deliver 1. Implement bs_call and bs_put using the Black-Scholes formula 2. Return a dict of the four primary Greeks 3. Verify put-call parity holds to 1e-8 ## Constraints & assumptions Assume continuous compounding and no dividends. Use scipy.stats.norm only. ## Submission note Complete the starter file, then compare your work against the mark scheme.
Your tasks
- 01Implement d1 and d2 and the European call and put price under Black-Scholes-Merton.
- 02Add the five core Greeks: delta, gamma, vega, theta and rho.
- 03Verify your prices satisfy put-call parity, and that an at-the-money 1Y option (S=K=100, r=2%, σ=20%) returns the expected values.
- 04Briefly comment on how delta and gamma behave as the option moves in- and out-of-the-money.
How you're assessed
The full points-based mark scheme is included with the pack.
What you'll learn
- How the Black-Scholes price decomposes into the two probability-weighted terms.
- What each Greek measures and why desks hedge delta and watch gamma.
- How to sanity-check a pricer with parity and limiting cases — a habit interviewers look for.