Volatility Trading and Arbitrage Strategies › Key Parameters
Michael BrenndoerferDecember 30, 20252 min read
Quantitative FinanceAll chapters Part 11 of 15Quantitative Trading Strategies
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The key parameters for dispersion trading are:
- w_i: Weight of each constituent in the index.
- σ_index: Volatility of the index. Lower than average constituent volatility due to diversification.
- σ_constituent: Volatility of individual stocks in the index.
- ρ (rho): Pairwise correlation between constituents. The primary driver of the spread between index and constituent volatility.
In[28]:
Codedef implied_correlation(index_vol, constituent_vols, weights):
"""
Calculate implied correlation from index and constituent volatilities.
"""
n = len(weights)
# Variance terms
index_var = index_vol**2
weighted_var_sum = np.sum(weights**2 * constituent_vols**2)
# Cross terms (denominator)
cross_term = 0
for i in range(n):
for j in range(n):
if i != j:
cross_term += (
weights[i]
* weights[j]
* constituent_vols[i]
* constituent_vols[j]
)
# Implied correlation
if cross_term > 0:
impl_corr = (index_var - weighted_var_sum) / cross_term
return np.clip(impl_corr, 0, 1) # Ensure valid correlation
return 0.0
# Calculate implied correlation
impl_corr = implied_correlation(index_implied, constituent_implied, weights)Out[29]:
ConsoleIndex Implied Volatility: 22.0% Average Constituent Implied Vol: 27.2% Implied Correlation: 0.57
The implied correlation of 0.25 indicates that the market is pricing in a relatively low level of co-movement between stocks. If you believe actual correlation will be higher, you might sell dispersion (buy index options, sell constituent options).