Price a Barrier Option

Problem Statement#

The Question#

Interview question: "Price a down-and-out call option. Walk me through the closed-form solution under Black-Scholes, then tell me how you'd price it numerically and where the analytical formula breaks down."

This question shows up at Goldman Sachs Strats, JP Morgan Quant Research, Citadel's derivatives desk, and Barclays Quantitative Analytics. You'll also see it in...