Rainbow Option on the Maximum (Stulz)
Computes the price of a call on the maximum of two assets with the Stulz (1982) formula: the option pays based on the better performer of two correlated assets, minus the strike. It's a bet on the winner of a race between two assets, and its price depends heavily on the correlation between them — the less correlated, the more valuable, because there's a greater chance at least one takes off. It uses the bivariate normal. Enter the two prices, the strike, the two volatilities, the correlation, the rate and the term.
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Rainbow Option on the Maximum (Stulz)
Computes the price of a call on the maximum of two assets with the Stulz (1982) formula: the option pays based on the better performer of two correlated assets, minus the strike. It's a bet on the winner of a race between two assets, and its price depends heavily on the correlation between them — the less correlated, the more valuable, because there's a greater chance at least one takes off. It uses the bivariate normal. Enter the two prices, the strike, the two volatilities, the correlation, the rate and the term.
Betting on the best of two assets
What if you could buy an option whose performance always tracked the winner between two assets? That's exactly what a rainbow on the maximum does: at expiry, it pays based on the asset that rose more, minus the strike. Robert Stulz priced this structure in 1982, and it's the basis of products that promise the best of two references.
The decisive ingredient is correlation. If the two assets always move together, having two is almost like having one, and the option is worth little more than a plain call. But if they move independently or oppositely, the chance of at least one taking off rises sharply, and the value of the option on the maximum grows. The bivariate normal is what mathematically captures that interaction.
Enter the prices of the two assets, the strike, the two volatilities, the correlation, the interest rate and the term. The tool returns the call-on-the-maximum premium. It's worth checking against its sibling, the option on the minimum: the sum of the two always equals the sum of two plain calls on each asset.
Related Tools
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.
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.
Margrabe Exchange Option
Computes the price of an exchange option with the Margrabe formula: the right to exchange one asset for another at expiry. It's the generalization of Black-Scholes to two risky assets, where the strike stops being fixed and becomes the price of a second asset. The relevant volatility is that of the ratio between the two, combining the individual volatilities and the correlation. It shows up in mergers, spread options and executive compensation. Enter the two prices, the two volatilities, the correlation 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.