Market Presets:
Rainbow Option Price
$0.00
Call on Max (Best-Of)
Asset 1 Delta ($\Delta_1$)
0.000
Spot $S_1 = $100
Asset 2 Delta ($\Delta_2$)
0.000
Spot $S_2 = $100
Correlation Sensitivity ($d V / d\rho$)
$0.00
Corr $\rho = 0.50$Contract & Asset Parameters
Rainbow Parity Breakdown
Vanilla Call $S_1$ ($C_1$):
$0.00
Vanilla Call $S_2$ ($C_2$):
$0.00
Call on Maximum ($C_{\max}$):
$0.00
Call on Minimum ($C_{\min}$):
$0.00
Sum: $C_{\max} + C_{\min}$:
$0.00
Vanilla Basket Sum: $C_1 + C_2$:
$0.00
Parity Difference: $0.00 (Identity holds)
Multi-Asset Visualizer
Option value sweep across correlation $\rho \in [-0.95, +0.95]$. Note diverging behavior between Best-Of ($C_{\max}$) and Worst-Of ($C_{\min}$).
Option price as Asset 1 ($S_1$) varies with Asset 2 fixed at its current spot level.
Asset 1 Delta ($\Delta_1$) and Asset 2 Delta ($\Delta_2$) as $S_1$ ranges from deep OTM to deep ITM.
Cross-Asset Risk Greeks Suite
| Greek | Value | Unit / Scale | Hedging Interpretation |
|---|---|---|---|
| Asset 1 Delta ($\Delta_1$) | 0.000 | $\partial V / \partial S_1$ | Shares of Asset 1 required for instantaneous delta hedge |
| Asset 2 Delta ($\Delta_2$) | 0.000 | $\partial V / \partial S_2$ | Shares of Asset 2 required for instantaneous delta hedge |
| Cross-Gamma ($\Gamma_{12}$) | 0.0000 | $\partial^2 V / (\partial S_1 \partial S_2)$ | Sensitivity of Asset 1 Delta to price moves in Asset 2 |
| Asset 1 Vega ($\nu_1$) | $0.00 | per 1% $\sigma_1$ | Price change per 100 bps shift in Asset 1 volatility |
| Asset 2 Vega ($\nu_2$) | $0.00 | per 1% $\sigma_2$ | Price change per 100 bps shift in Asset 2 volatility |
| Cross-Rho ($\partial V / \partial \rho$) | $0.00 | per 0.10 $\Delta \rho$ | Option sensitivity to a 10% shift in correlation |
| Theta ($\Theta$) | $0.00 | per day ($1/365$) | Time decay per calendar day elapsed |
5x5 Matrix: Spot $S_1$ vs Correlation $\rho$
5x5 Matrix: Volatility $\sigma_1$ vs Volatility $\sigma_2$
Rainbow Option Mastery Quiz
1. For a Call Option on the Maximum of two assets (Best-Of Call), what is the effect of increasing cross-asset correlation from -0.80 to +0.80?
Frequently Asked Questions
A rainbow option is an exotic derivative whose payoff is contingent on the performance of two or more underlying assets. Named after the multiple 'colors' of market risk, popular configurations include options on the maximum (Best-of: max[max(S1, S2) - K, 0]), options on the minimum (Worst-of: max[min(S1, S2) - K, 0]), and outperformance spreads.
Correlation drives the joint probability distribution. For a Call on the Maximum, lower or negative correlation expands the spread of possible outcomes, increasing the likelihood that at least one asset experiences a strong upside gain, making the option more valuable. For a Call on the Minimum (Worst-of), higher positive correlation is beneficial because both assets must stay above the strike for the option to finish in-the-money.
Johnson (1987) established that a European call on max is evaluated using bivariate normal cumulative distributions: C_max = S1 * exp(-q1*T) * M(d1_1, y1; rho1) + S2 * exp(-q2*T) * M(d1_2, y2; rho2) - K * exp(-r*T) * [1 - M(-d2_1, -d2_2; rho)], where y1 and y2 relate to the Margrabe exchange option spread variance sigma_spread^2 = sigma1^2 + sigma2^2 - 2*rho*sigma1*sigma2, and M(a, b; rho) is the bivariate normal CDF.
Because max(S1, S2) + min(S1, S2) = S1 + S2 holds identically at any point in time, the sum of a call on max and a call on min equals the sum of two standard single-asset vanilla calls with the same strike: Call_max(K) + Call_min(K) = Call_vanilla1(K) + Call_vanilla2(K). This exact no-arbitrage identity provides an indispensable consistency benchmark.