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Monte Carlo Pricing of Multi-Asset Barrier Options and Correlation

Article Quant Q&A · Author: SVIJW
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Summary

The document raises a question about pricing barrier options on multiple correlated assets. It describes a result from a cited paper: for a barrier option on two assets, two biased estimators can act as upper and lower bounds, with their average used as a price estimate. The author asks how to extend pricing to the general multi-asset case and whether correlation can be inferred from vanilla option prices or an index.

A proposed baseline is Monte Carlo simulation using asset-specific local volatility models and correlated increments. The document does not give a complete pricing procedure, calibration method, or evidence beyond the referenced result for two assets. It is therefore best read as an open modeling question: the role of dependence assumptions and how to estimate correlation remain unresolved, especially when moving beyond the two-asset setting.

Key ideas

  • For a two-asset barrier option, biased estimators may provide bounds whose average estimates the price.
  • Monte Carlo simulation with calibrated local volatility models and correlated increments is proposed for multiple assets.
  • The document leaves open how to estimate asset correlation, including whether vanilla option prices or an index can help.
  • The described bounds concern a two-asset setting and are not shown to generalize to arbitrary multi-asset options.

Tags

OptionsMulti-assetDerivatives pricingStatistics
Full text
# Monte-Carlo method for multi-asset pricing


# Monte-Carlo method for multi-asset pricing












As I was working on this paper https://hal.science/hal-00319947/document by Emmanuel Gobet, I came across this paragraph that says to price a barrier option on (for example) two correlated assets, you can derive two biased estimators that acts like bounds and average them to estimate the price of the option. This looks amazing since you do not really need to quantify the correlation between the two assets, but how would one price a multi-asset option in the general case? As I only have experience with pricing for a single asset, I was wondering what would be the industry standard in this regard. My first idea would be to use MC simulations with (for example again) local vol models calibrated on each of the assets and using correlated increments. But how could one estimate the correlation here ? Could you use vanilla prices to estimate a sort of implied correlation between the two assets? Or using an index ? I would be happy to discuss this or if you could provide me with some references. Thanks for your time !

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