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.
Result
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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.
All or nothing at expiry
The digital option, also called binary, is the cleanest bet there is in derivatives: either the asset finishes above the strike and you receive a fixed amount, or it finishes below and you receive nothing. There's no middle ground, no proportional payoff. It's a yes or no with a set date.
Because of that simplicity, the price has a beautiful interpretation: it's the payout, brought to present value and multiplied by the risk-neutral probability of the option finishing in the money. That N(d2) is exactly the same probability that appears in the second term of Black-Scholes. Digital options are also the bricks from which more complex exotic structures are built.
Enter the spot price, the strike, the interest rate, the term, the volatility and the payout on exercise. The tool returns the digital call price. Remember the discontinuous payoff at the strike makes hedging these options notoriously hard near expiry, when a small price move changes everything.
Related Tools
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.
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.
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.
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.