Down-and-In Barrier Call
Computes the price of a down-and-in barrier call: an option that only comes into existence if the asset touches a barrier below the current price before expiry. It's the counterpart of the down-and-out, and the sum of the two is exactly a plain call: either the barrier is touched (activating the in) or it isn't (keeping the out). Because it depends on a trigger, it costs less than a plain call. Enter the spot price, the strike, the barrier, the rate, the term and the volatility.
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Down-and-In Barrier Call
Computes the price of a down-and-in barrier call: an option that only comes into existence if the asset touches a barrier below the current price before expiry. It's the counterpart of the down-and-out, and the sum of the two is exactly a plain call: either the barrier is touched (activating the in) or it isn't (keeping the out). Because it depends on a trigger, it costs less than a plain call. Enter the spot price, the strike, the barrier, the rate, the term and the volatility.
The option that only is born if the price falls
The down-and-in call is the mirror image of the down-and-out. Instead of dying when it touches a barrier, it's born: the option only comes into existence if the asset falls to touch a barrier set below the current price. Before that, it's just a promise; afterward, it becomes a plain call.
Its relationship with the down-and-out is elegant and exact. The sum of a down-and-in and a down-and-out, with the same barrier, is precisely a plain call: either the price touches the barrier at some point (and the in activates) or it doesn't (and the out survives). One of the two always happens, so the two together are worth the same as a barrier-free option.
Enter the spot price, the strike, the barrier, the interest rate, the term and the volatility. The tool returns the down-and-in call premium. Anyone who buys this type of option bets the price will fall first, activating it, and then rise — a specific scenario that justifies the discount versus a plain call.
Related Tools
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.
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.
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.
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.
Compound Option (Call-on-Call, Geske)
Computes the price of a compound call-on-call option with the Geske (1979) model: a call option whose underlying is, itself, another call option. It's the structure behind many real-world contracts — an option to extend a project, for example, is an option on an option. The calculation requires finding the critical price at which exercising the first option is worthwhile and uses the bivariate normal. Enter the spot price, the two strikes, the two expiries, the rate and the volatility.
Floating-Strike Lookback Call
Computes the price of a floating-strike lookback call with the Goldman-Sosin-Gatto formula: an option that pays the difference between the final price and the lowest price observed during the contract's life. In practice, it's like buying at the best possible price in hindsight, which makes it expensive but eliminates the risk of mistiming the purchase. It requires a positive interest rate. Enter the spot price, the observed minimum, the interest rate, the volatility and the 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.