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.
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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.
Selling at the top, in hindsight
If the lookback call fulfills the dream of buying at the low, the floating-strike lookback put fulfills that of selling at the high. At expiry, it pays the difference between the highest price the asset reached during the option's entire life and the final price. It's as if you could look back and pick the best moment to sell, with no chance of mistiming it.
That power to sell at the top, guaranteed by contract, costs dearly. The lookback put is worth far more than a plain put, because it completely eliminates the risk of choosing the wrong time to sell. The Goldman, Sosin and Gatto formula, from 1979, prices this option in closed form, with an extra term that carries the value of remembering the observed maximum.
Enter the spot price, the highest price observed so far, the interest rate, the cost of carry, the volatility and the term. The tool returns the lookback put premium. If the option is new, the observed maximum is usually the starting price itself; if it's already running, use the highest value recorded so far.
Related Tools
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.
Cash-or-Nothing Put
Computes the price of a cash-or-nothing put: it pays a fixed amount if the asset finishes below the strike, and nothing otherwise. It's the downside version of the digital option, the complement of the cash-or-nothing call. The price is the payout discounted and multiplied by the risk-neutral probability of the asset finishing below the strike, Q·e^(−rT)·N(−d2). Enter the spot price, the strike, the interest rate, the term, the volatility and the payout.
Black-76 Put Price (Options on Futures)
Works out the premium of a European put option on futures with the Black-76 model, the Black-Scholes version for when the underlying is a future or forward contract. The price is e^(−rT)·[K·N(−d2) − F·N(−d1)], where d1 and d2 come from the futures price, the strike, the volatility and the term. The future already carries the cost of carry, so the discount factor multiplies both terms and interest does not enter d1. It applies to puts on commodities, indices and rates. Enter the futures price, the strike, the risk-free rate, the term in years and the annual 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.