Implied basket correlation dynamics
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Wolfgang Karl Härdle
Abstract
Equity basket correlation can be estimated both using the physical measure from stock prices, and also using the risk neutral measure from option prices. The difference between the two estimates motivates a so-called “dispersion strategy”. We study the performance of this strategy on the German market and propose several profitability improvement schemes based on implied correlation (IC) forecasts. Modelling IC conceals several challenges. Firstly the number of correlation coefficients would grow with the size of the basket. Secondly, IC is not constant over maturities and strikes. Finally, IC changes over time. We reduce the dimensionality of the problem by assuming equicorrelation. The IC surface (ICS) is then approximated from the implied volatilities of stocks and the implied volatility of the basket. To analyze the dynamics of the ICS we employ a dynamic semiparametric factor model.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: CRC 649 “Economic Risk”
Funding statement: The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft through CRC 649 “Economic Risk”.
A Switch point selection for correlation regimes
The dependence of ρ and
Segmented linear regression of
| τ | Slope 1 | Slope 2 | ||
|---|---|---|---|---|
| 0.083 | 20.24 | 0.5917 | 0.0361 | 0.0085 |
| 0.25 | 20.34 | 0.5728 | 0.0336 | 0.0093 |
| 0.5 | 22.42 | 0.6008 | 0.0286 | 0.0094 |
| Average | 21.00 | 0.5884 | 0.0328 | 0.0091 |
B Smoothing parameters selection
For both (3.5) and (3.6) kernel bandwidths
with the Akaike (1970) information criterion (AIC) as penalizing function
for every
Since the distribution of the observations is very uneven, we use the weighted version of the criterion with weights
The bandwidth
Acknowledgements
Thanks go to L. Udvarhelyi for editorial assistance.
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