Barrier Option Pricer
Price knock-in and knock-out options with the Reiner-Rubinstein closed form, and see how the barrier reshapes the payoff.
A barrier option only pays off if the underlying does — or does not — touch a barrier level before expiry. This barrier option calculator prices all eight European variants — down/up × in/out × call/put — using the Reiner-Rubinstein closed-form solution under Black-Scholes, and returns the price, the greeks and the knock probability.
Knock-in vs knock-out
A knock-out option dies the moment the barrier is touched; a knock-in only comes to life once the barrier is hit. Because a vanilla option equals a knock-in plus a knock-out with the same barrier, the in-out parity holds — a useful sanity check, and a classic interview question. Barriers are cheaper than the equivalent vanilla (you give up some scenarios), which is exactly why they show up inside structured products and cheap directional trades.
What to watch
Near the barrier the greeks misbehave: delta and gamma can spike and even flip sign, which makes knock-out books notoriously hard to hedge — the source of "barrier pin risk". Move the spot toward the barrier on the price-vs-spot curve to see it. For the structured-product side, the same maths powers the bonus certificate (a down-and-out put) — try the Structured Products pricer next.
Frequently asked questions
What is a barrier option?
A barrier option only pays out (knock-in) or stops existing (knock-out) once the underlying touches a preset barrier level during its life. That path-dependence makes it cheaper than a vanilla — you give up payoff in exchange for the barrier condition.
Which barrier variants can it price?
All eight: down-and-in, down-and-out, up-and-in and up-and-out, each as a call or a put, using the Reiner-Rubinstein (1991) closed-form formulas — the same analytics a structuring desk uses for turbos and barrier certificates.
What is in-out parity?
A knock-in plus the matching knock-out equals the plain vanilla option: buying both barriers reconstructs the unconditional payoff. The tool checks this identity so you can see the pricing is internally consistent.
Why do the greeks blow up near the barrier?
Close to the barrier a tiny move in spot flips whether the option survives, so delta and gamma spike and can change sign — the source of barrier pin risk and why knock-out books are hard to hedge on a gap.