How do I price a barrier option using Monte Carlo simulation?

Question

AcadiFi · Accepted Answer

Barrier options pay only if the underlying hits or avoids a trigger during life. For a down-and-out call on Larimer Robotics at $72, strike $70, barrier $62, 6-month maturity, you simulate thousands of paths under GBM with daily or continuous monitoring. At each time step t, update S(t+dt) = S(t)*exp((r - q - 0.5*sigma^2)*dt + sigma*sqrt(dt)*Z), check if S(t+dt) <= 62, and if so, set the path payoff to zero. Otherwise, terminal payoff = max(S(T) - 70, 0). Discount and average across paths. A critical issue: discrete monitoring overstates survival probability because between observations the path can breach and recover. Broadie-Glasserman-Kou correction shifts the barrier by exp(-beta*sigma*sqrt(dt)) where beta = 0.5826, accounting for the expected maximum between discrete points. Without this correction, you systematically overprice down-and-out calls by 2-5% for weekly monitoring. ```mermaid graph LR A[Simulate
path] --> B{Hit barrier?} B -->|Yes| C[Payoff=0] B -->|No| D[Vanilla
payoff] ``` Explore our exotic derivatives lessons for more path-dependent pricing.

How do I price a barrier option using Monte Carlo simulation?

Master Part I with our FRM Course

Related Questions

Practice Questions