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.
Result
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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.
The payout that hinges on two bets
A plain binary option pays a fixed amount if one condition happens. The two-asset version raises the stakes: it only pays if two conditions occur at the same time, the first asset above its strike AND the second above its own. It's a double, all-or-nothing bet, where just one of the two failing means you get nothing.
Here the correlation between the assets is everything. If they tend to rise together, the probability of both conditions hitting at once is high, and the option is worth more. If they move in opposite directions, getting both right is rare, and the price plunges. The bivariate normal distribution is exactly the tool that computes that joint probability, and it's the heart of the calculation.
Enter the prices and strikes of the two assets, the two volatilities, the correlation, the interest rate, the term and the payout. The tool returns the two-asset binary price. This kind of structure appears in products that pay only when two markets rise together, and the price is highly sensitive to the correlation entered.
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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.
Rainbow Option on the Minimum (Stulz)
Computes the price of a call on the minimum of two assets with the Stulz (1982) formula: the option pays based on the worse performer of two assets, minus the strike. It's the more conservative option of the rainbow pair, valuable when you want both assets to perform. An elegant identity holds: the sum of the call on the maximum and the call on the minimum equals the sum of two plain calls. It uses the bivariate normal. Enter the two prices, the strike, the two volatilities, the correlation, the rate and the term.
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.
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.