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Replicating a Basket of Options with Self-Financing Portfolios

Article Quant Q&A · Author: novice
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Summary

The document considers how to form a self-financing portfolio of bonds and stocks to replicate a basket of options, with each option written on a different underlying stock. It suggests constructing a replicating portfolio for each option separately and then summing those portfolios. The accepted response endorses this as the simpler method for assembling the basket replication.

Attempting to replicate the basket directly as a single position would require handling relationships among the underlying stocks, including their correlations and covariances. The discussion gives no explicit portfolio weights, financing dynamics, or assumptions about market completeness, and it does not show that a direct basket replication is impossible. Its practical point is that individual option replication can be combined by addition, while a joint approach introduces dependence considerations.

Key ideas

  • A basket of options can be approached by replicating each option individually.
  • The individual replicating portfolios can then be added to form the combined portfolio.
  • Direct replication of the basket involves correlations and covariances among underlying stocks.
  • The document provides no explicit hedge weights or detailed self-financing construction.

Tags

OptionsEquitiesPortfolio constructionDerivatives pricing
Full text
# Self financing portfolio for a basket of options


# Self financing portfolio for a basket of options












How do I create a self financing portfolio consisting of bonds and stocks, for a portfolio of options?

My thoughts are that we would need multiple stocks to do so, since the payoff need not be binary, or we can take individual options, create each one's portfolio and then sum it up to get one final self financing portfolio.

Each option is written on one underlying stock.

## Answer by phdstudent (score 4, accepted)

https://quant.stackexchange.com/a/40184

Yes. The simpler approach is to take each call/put option create the replicating portfolio for that individual security and then add them up. Otherwise you get into issues of correlations and covariances if you want to replicate the basked in one go.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.