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Why Vanilla Options Cannot Replicate Pure Correlation Exposure

Article Quant Q&A · Author: zuhao
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Summary

The document asks whether vanilla options on two assets, together with the assets themselves, can create insurance that costs money when correlation is high and pays when correlation falls. The motivation is to hedge a strategy that benefits from the assets moving together, while avoiding an over-the-counter correlation swap.

The main response says a portfolio of ordinary options and underlyings cannot replicate pure correlation exposure because those instruments do not have correlation sensitivity on their own. A second response notes that listed options on spreads can provide exposure to multiple factors in some markets, such as energy spread products. Index options may also be relevant when the holdings approximate the index composition. These are qualified alternatives rather than a general replication recipe; the document offers no payoff construction or quantitative analysis, and whether spread or index options fit depends on available listings and the portfolio.

Key ideas

  • The proposed hedge would pay when the relationship between two assets weakens.
  • A portfolio of vanilla options on each asset and the underlying assets does not provide pure correlation exposure.
  • Listed options on spreads can create joint-factor exposure in some markets.
  • Index options may be relevant when a portfolio closely resembles the underlying index.
  • The alternatives discussed are contingent on available products and portfolio composition.

Tags

OptionsDerivatives pricingVolatility
Full text
# How to replicate a correlation swap using only vanilla options and underlying


# How to replicate a correlation swap using only vanilla options and underlying












Assume I have two assets A and B that are positively correlated most of the time. I'm trading a strategy based on this correlation. Is there a way to protect myself in the event that the correlation tears?

After some googling I found there are OTC correlation swaps for the purpose. However, there seems to be no similar exchange-traded products.

I do not have access to the OTC market and therefore I'm wondering if I can replicate a similar portfolio using vanilla options of A and B, as well as the underlyings, to achieve:

- When correlation is positive & high, I'm paying "premium" for the insurance.

- When correlation is low or even negative, my insurance pays off.

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/27854

That's impossible. Since neither the vanilla options nor the underlyings have any exposure to the correlation, no portfolio of these instruments can either.

## Answer by RiskyScientist (score 0)

https://quant.stackexchange.com/a/27858

Exchanges list some options on spreads, such as crack spreads, spark spreads, etc, so that could provide with you a two factor correlation exposure. But if you are long only two underlyings, it is unlikely you will find an option on the sum of the two. If you happen to have an approximately index weighted portfolio of stocks, then of course index options would be useful, but it doesn't sound like you are looking for this.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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