Market Presets:
Basket Option Price
$0.00
Call Option
Effective Basket Volatility
0.0%
Diversification Dampening
Diversification Discount
$0.00
0.0% vs sum of vanillas
Correlation Sensitivity ($d V / d\rho$)
$0.00
per 0.10 shift in $\rho$Basket Parameters
Diversification Breakdown
Current Basket Spot ($B_0$):
$100.00
Forward Basket Price ($F_B$):
$103.50
Weighted Sum of Single Options:
$0.00
Basket Option Price:
$0.00
Diversification Savings:
$0.00 (0.0%)
Jensen's Inequality: $V_{\text{basket}} \le \sum w_i V_i$ Holds
Basket Visualizer
Basket Option Price and Sum of Vanillas vs Pairwise Correlation $\rho \in [-0.4, 0.99]$. As $\rho \to 1$, basket discount vanishes.
Basket Option valuation curve across portfolio index levels vs terminal intrinsic payoff $\max(B_T - K, 0)$.
Component hedge ratios: dollar and share Deltas per constituent asset in the basket portfolio.
Component Greeks & Risk Sensitivities
| Component | Weight ($w_i$) | Delta ($\Delta_i = \partial V / \partial S_i$) | Dollar Delta ($S_i \Delta_i$) | Vega ($\partial V / \partial \sigma_i$) |
|---|
5x5 Matrix: Correlation $\rho$ vs Strike $K$
5x5 Matrix: Basket Spot $B_0$ vs Maturity $T$
Basket Option Mastery Quiz
1. What happens to the price of an arithmetic basket call option as pairwise correlation between all constituent stocks decreases towards zero or negative values?
Frequently Asked Questions
A basket option is an exotic multi-asset derivative whose payoff is contingent on the weighted sum or arithmetic average of two or more underlying assets. Rather than exercising individual options on each stock, the investor exercises once against the composite portfolio index value.
By Jensen's inequality and the convexity of option payoffs, an option on an average is never more expensive than the average of the options: max(sum(w_i * S_i) - K, 0) ≤ sum(w_i * max(S_i - K_i, 0)). Offsetting cross-asset price movements cancel each other out, compressing composite portfolio volatility and reducing the probability of deep in-the-money outcomes. This pricing difference is known as the diversification discount.
In standard continuous-time financial engineering, individual equity prices are modeled as geometric Brownian motions, resulting in marginal lognormal distributions. However, the sum of correlated lognormal variables has no closed-form analytical probability density function. Quantitative analysts rely on moment-matching techniques (such as Ju 2002 Taylor expansions or Turnbull-Wakeman lognormal matching) to approximate the distribution of the sum with high precision.
Dispersion trading is an institutional volatility arbitrage strategy that capitalizes on the difference between implied index correlation and realized correlation. Hedge funds sell an index or basket option (which is short correlation) and buy single-stock options on the index constituents (which are long individual volatilities). If stocks move independently or correlation falls, the single-stock options gain more from idiosyncratic moves than the basket option loses.