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.
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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.
When the payoff is squared
A plain option pays in proportion to the difference between the price and the strike. The power option goes further: it raises the asset price to a power before comparing it with the strike. Squaring, for example, turns a 10% rise in the asset into a 21% rise in the powered term, hugely amplifying both gains and premiums.
That amplification makes power options aggressive leverage instruments, used in structured products and concentrated volatility bets. The price has an important subtlety: the growth factor multiplying the first term already carries the interest-rate discount embedded, and multiplying it again by e^(−rT) is a common error that underestimates the premium.
Enter the spot price, the strike, the power, the interest rate, the volatility and the term. The tool returns the power option premium, using the correct formula with no double-counting of the discount. Note the strike must be on the same scale as the powered price, so it tends to be a large number when the power is greater than one.
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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.
Chooser Option
Computes the price of a simple chooser option with the Rubinstein formula: an option that lets the holder decide, on a future date, whether it will be a call or a put, both with the same strike and expiry. It's the ideal bet for someone expecting a big move but not yet knowing the direction, costing more than a plain option and less than buying a call and a put separately. Enter the spot price, the strike, the interest rate, the volatility, the expiry and the choice date.
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.
Contingent-Premium Put Option
Computes the fair premium of a contingent-premium (pay-later) put option. As in the call version, the buyer pays only at expiry and only if the put finishes in the money. It's an attractive structure for those wanting protection with no upfront outlay, at the cost of a higher premium if the insurance is actually triggered. The price comes from the Black-Scholes put value divided by the exercise probability. Enter price, strike, rate, dividend, volatility and 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.
Option Lambda (Elasticity)
Computes the lambda of a call option, also called omega or elasticity: the percentage change in the premium for each one-percent change in the underlying's price. It's the delta times S/C, and it measures the leverage built into the option. A lambda of 6, for instance, means the option moves, in percentage terms, about six times faster than the stock, which is why options amplify gains and losses. Enter the spot price, the strike, the interest rate, the term in years 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.