Joint risk-neutral laws and hedging

Dilip Madan

IISE Transactions, 2011, vol. 43, issue 12, 840-850

Abstract: Complex positions on multiple underliers are hedged using the options surface of all underliers. Hedging objectives minimize ask prices for which post-hedge residual risks are acceptable at prespecified levels. It is shown that such hedges require the use of a risk-neutral law on the set of underlying risks. A joint risk-neutral law for multiple underliers is proposed and estimated from multiple option surfaces. Under the proposed joint law, asset returns are a linear mixture of independent Lévy components. Data on the independent components are estimated by an application of independent components analysis on time series data for the underlying returns. A comparison of the the risk-neutral law with the statistical law shows that risk neutral correlations dominate their statistical counterparts. Hedges significantly reduce ask prices.

Date: 2011
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DOI: 10.1080/0740817X.2010.541179

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