Down-and-Out Barrier Call
Computes the price of a down-and-out barrier call: an option that ceases to exist if the asset touches a barrier below the current price before expiry. Because of that knockout risk, it costs less than a plain call, and the difference is exactly the value of the down-and-in version. The Reiner-Rubinstein closed form holds for a barrier at or below the strike. Enter the spot price, the strike, the barrier, the interest rate, the term and the volatility.
Result
—
Down-and-Out Barrier Call
Computes the price of a down-and-out barrier call: an option that ceases to exist if the asset touches a barrier below the current price before expiry. Because of that knockout risk, it costs less than a plain call, and the difference is exactly the value of the down-and-in version. The Reiner-Rubinstein closed form holds for a barrier at or below the strike. Enter the spot price, the strike, the barrier, the interest rate, the term and the volatility.
The option that can vanish before its time
A plain call exists until expiry, come what may. The down-and-out call has a sudden-death condition: if the asset touches a barrier set below the current price, the option evaporates at once, paying nothing. In exchange for that risk, it costs less than a plain call, which appeals to those who want to bet on the upside while spending less premium.
There's a beautiful relationship behind this. The value of a plain call is exactly the sum of a down-and-out and a down-and-in, the version that only comes into existence if the barrier is touched. The Reiner-Rubinstein closed form, from 1991, prices these options elegantly when the barrier is at or below the strike.
Enter the spot price, the strike, the barrier (below spot), the interest rate, the term and the volatility. The tool returns the down-and-out call premium. Remember the calculation assumes continuous barrier monitoring; barriers observed only at each day's close are worth slightly more and require a separate adjustment.
Related Tools
Down-and-Out Barrier Option (Put)
Computes the price of a down-and-out barrier put option. It's a knock-out barrier option: it works like a normal put, but is cancelled the moment the asset price touches a barrier below the current level. Because it disappears precisely when the put would be gaining the most value, it's usually worth much less than a plain put, making it cheaper for those betting on moderate declines. The pricing uses the Reiner-Rubinstein formulas. Enter price, strike, barrier, rate, dividend, volatility and term.
Up-and-In Barrier Option (Call)
Computes the price of an up-and-in barrier call option. It's a knock-in barrier option: it only comes to life if the asset price touches a barrier above the current level before expiry; if it never touches, it expires worthless, however deep in the money it might have been. Because of that extra condition, it costs less than a plain call. The pricing uses the Reiner-Rubinstein closed-form formulas. Enter price, strike, barrier, rate, dividend, volatility and term.
Contingent-Premium Call Option
Computes the fair premium of a contingent-premium call option, also called pay-later. The buyer pays nothing upfront: the premium is only due at expiry, and even then only if the option finishes in the money. For the deal to be fair, that deferred premium must be larger than a plain call's, compensating for the risk the seller receives nothing. The formula divides the Black-Scholes value by the exercise probability. Enter price, strike, rate, dividend, volatility and term.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.