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.
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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.
Buy at the best price, in hindsight
Every investor dreams of buying at the low. The floating-strike lookback option turns that dream into a contract: at expiry, it pays the difference between the final price and the lowest price the asset reached over the option's entire life. It's as if you could go back in time and pick the best moment to buy, with no chance of getting it wrong.
That power has a price, and it's high. The lookback costs far more than a plain option, precisely because it eliminates the timing risk all others carry. The Goldman, Sosin and Gatto formula, from 1979, prices this option in closed form, with an extra term that captures the value of remembering the minimum. It requires positive rates to make mathematical sense.
Enter the spot price, the lowest price observed so far, the interest rate, the volatility and the term. The tool returns the lookback call premium. If the option is new, the observed minimum is usually the starting price itself; if it's already running, use the lowest value recorded so far.
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Floating-Strike Lookback Put
Computes the price of a floating-strike lookback put with the Goldman-Sosin-Gatto formula: an option that pays the difference between the highest price observed during the contract's life and the final price. It's like always selling at the top, in hindsight, eliminating the risk of mistiming the sale. It's the counterpart of the lookback call, and the high price reflects that power to pick the best moment. Enter the spot price, the observed maximum, the rate, the cost of carry, the volatility and the 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.
Call Dual Delta
Computes the dual delta of a call option: the premium's sensitivity to the strike price, that is, dC/dK. While ordinary delta measures the reaction to the underlying's price, dual delta measures how much the option would change if the strike were slightly different. For a call it equals −e^(−rT)·N(d2) and has a practical reading: in absolute terms it approximates the risk-neutral probability of the option finishing in the money. 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.