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.
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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.
All or nothing, now betting on the fall
The cash-or-nothing put is the pessimistic sibling of the digital call. Its verdict at expiry is equally binary: if the asset finishes below the strike, you receive a fixed agreed amount; if it finishes above, you receive nothing. It's the purest possible bet that the price will fall below a certain level.
The price has the same elegance as the call version. It's the payout, brought to present value and multiplied by the risk-neutral probability of the asset finishing below the strike, which is N(−d2). Together, cash-or-nothing calls and puts with the same payout always sum to the present value of the payout, because one or the other always happens.
Enter the spot price, the strike, the interest rate, the term, the volatility and the payout. The tool returns the cash-or-nothing put price. Like every digital option, the discontinuous payoff at the strike makes hedging hard near expiry, when a small price move decides everything.
Related Tools
Asset-or-Nothing Put
Computes the price of an asset-or-nothing put: it delivers the asset itself if the price finishes below the strike, and nothing otherwise. It's the downside counterpart of the asset-or-nothing call, and together they always sum to the asset's value, because one or the other always pays. The price is simply S·N(−d1). Enter the spot price, the strike, the interest rate, the volatility and the term.
Digital Call (Cash-or-Nothing)
Computes the price of a cash-or-nothing digital call option: it pays a fixed amount if the asset finishes above the strike, and nothing otherwise. The price is the discounted payout multiplied by the risk-neutral probability of finishing in the money, Q·e^(−rT)·N(d2). It's the purest form of a binary bet and the building block of many exotic structures. Enter the spot price, the strike, the interest rate, the term, the volatility and the payout.
Asset-or-Nothing Call
Computes the price of an asset-or-nothing call: it delivers the asset itself if the price finishes above the strike, and nothing otherwise. It's the sibling of the cash-or-nothing option, and together they decompose the plain Black-Scholes call — a call equals exactly an asset-or-nothing minus a strike's worth of cash-or-nothing. The price is simply S·N(d1). Enter the spot price, the strike, the interest rate, the volatility and the term.
Two-Asset Correlation Binary
Computes the price of a two-asset binary option: it pays a fixed amount if and only if the first asset finishes above its strike AND the second asset finishes above its own. It's a conditional double bet whose price depends critically on the correlation between the assets — the more correlated, the more likely both conditions happen together. It uses the bivariate normal. Enter the two prices, the two strikes, the two volatilities, the correlation, the rate, the term 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.
Garman-Kohlhagen FX Put Price
Prices an FX put option with the Garman-Kohlhagen model, the currency-market version of Black-Scholes. As with the call, the foreign interest rate enters as a continuous dividend on the base currency: the premium is K·e^(−rd·T)·N(−d2) − S·e^(−rf·T)·N(−d1). The strike term is discounted by the domestic rate and the spot term by the foreign one. It's used to hedge against a currency falling or to speculate in that direction. Enter the spot rate, the strike, the domestic and foreign rates, 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.