Gap Option
Computes the price of a gap call, where the strike that triggers exercise differs from the strike that sets the payoff. The option pays (S − K1) when the price exceeds K2, and that separation creates a jump (gap) in the payoff exactly at K2: the option can start paying with a positive or negative value. It's the theoretical basis of many discontinuous-payoff options. Enter the spot price, the payment strike, the trigger strike, the rate, the volatility and the term.
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Gap Option
Computes the price of a gap call, where the strike that triggers exercise differs from the strike that sets the payoff. The option pays (S − K1) when the price exceeds K2, and that separation creates a jump (gap) in the payoff exactly at K2: the option can start paying with a positive or negative value. It's the theoretical basis of many discontinuous-payoff options. Enter the spot price, the payment strike, the trigger strike, the rate, the volatility and the term.
Trigger and payment live at different strikes
A plain option uses the same strike for two things: deciding whether to exercise and computing how much it pays. The gap option splits those two functions across distinct strikes. One strike, the trigger, decides whether the option pays; another, the payment strike, sets the value. That creates a jump, a gap, in the payoff diagram exactly at the trigger level.
The effect is curious: the option can start paying with a negative value the instant the trigger is crossed, if the payment strike is above the trigger. The formula is almost identical to Black-Scholes, with the twist that the trigger strike enters the d1 and d2 terms, while the payment strike appears only in the cash term. It's the theoretical basis of several discontinuous-payoff options.
Enter the spot price, the payment strike, the trigger strike, the interest rate, the volatility and the term. The tool returns the gap call premium. When the two strikes coincide, the gap option becomes a plain call, which is a good way to check the calculation.
Related Tools
Gap Put Option
Computes the price of a gap put, where the strike that triggers exercise differs from the strike that sets the payoff. The option pays (K1 − S) when the price falls below K2, creating a jump in the payoff exactly at K2. It's the downside version of the gap option, the theoretical basis of many discontinuous-payoff contracts. Enter the spot price, the payment strike, the trigger strike, the rate, the volatility and the term.
Power Option
Computes the price of a power call option, whose payoff is the asset price raised to a power, minus the strike: max(S^n − K, 0). Raising the price to a power hugely amplifies the moves, so these options have explosive payoffs and high premiums. They're used for leveraged bets on volatility and in structured products. The growth prefactor already incorporates the discounting, with no double counting. Enter the spot price, the strike, the power, the rate, the volatility and the term.
Supershare Option
Computes the price of a supershare option (Hakansson): it pays a fraction of the asset if the price finishes within a band between a lower and an upper bound, and nothing outside it. It was proposed as the building block of a state-contingent mutual fund system, and is an elegant example of a range-dependent option. The price is the asset fraction multiplied by the probability of landing in the band. Enter the spot price, the lower and upper bounds, the 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.