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.
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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.
The call that's only born if the price climbs enough
An up-and-in barrier option carries a birth condition. It's a plain call in almost everything, except that it only comes into existence if the asset price touches a barrier set above the current level at some point before expiry. If that barrier is never touched, the option expires worthless, even if it would have finished deep in the money.
That extra condition makes it cheaper than a standard call, since there are scenarios where it simply never activates. It makes sense for those with a specific view: they believe that if the asset is going to rise enough for the option to pay, it will first cross the barrier. The pricing uses the Reiner-Rubinstein closed-form formulas, which decompose the value into analytic terms based on the normal distribution.
Enter the asset price, the strike, the barrier, the rate, the dividend, the volatility and the term. The tool returns the price of the up-and-in call. Note the parity relationship: the value of an option that knocks in on the way up plus that of its sibling that knocks out on the way up, with the same barrier, equals a plain call, since together they cover every scenario.
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.
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.
Up-and-Out Barrier Call
Computes the price of an up-and-out barrier call: an option that ceases to exist if the asset touches a barrier above the current price before expiry. It's a curious case — the option is a bet on the upside, but it dies if the price rises too far, which makes it cheap when the barrier is close. The Reiner-Rubinstein formula holds for a barrier above the strike. Enter the spot price, the strike, the barrier, the rate, the term and the volatility.
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.