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American Monte Carlo for Exposure and CVA Across Trade Types

Article Quant Q&A · Author: jambodev
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Summary

The document asks about using American Monte Carlo (AMC) to simulate exposure for credit valuation adjustment across a portfolio containing different trade types. Its central question is how the method can estimate the distribution of positive portfolio value without implementing each product’s usual valuation model at every simulation step. The portfolio examples include European foreign exchange options, vanilla swaps, and Bermudan swaptions, which differ in payoff structure and exercise features.

The author wonders whether AMC can handle these products through payoff functions as part of a combined pricing and exposure calculation, and asks about the mathematical basis, assumptions, and limitations. A presentation by Giovanni Cesari is cited as a possible explanation, but the document itself does not provide the method’s equations or answer the question. It therefore offers a topic for further study rather than evidence that AMC is faster, more consistent, or suitable for every trade type.

Key ideas

  • The question concerns using American Monte Carlo to simulate counterparty exposure across varied products.
  • The portfolio examples include European FX options, vanilla swaps, and Bermudan swaptions.
  • The author asks whether payoff functions can replace product-specific valuation models in the exposure calculation.
  • The document raises questions about AMC’s mathematical foundation, assumptions, and limitations.
  • It cites a presentation as a possible source but provides no explanation or results itself.

Tags

OptionsForexFixed incomeDerivatives pricingRisk management
Full text
# using AMC across the board (for all trade types) for calculating CVA


# using AMC across the board (for all trade types) for calculating CVA












I know that some banks use AMC (american monte-carlo) to calculate exposure simulation (for CVA) across the board (for all trade types, not just american style option trade types) instead of implementing each trade type's own valuation model, perhaps this is for consistency or speed. I was wondering if someone could briefly explain the mathematical foundation for doing that. what are the assumptions or limitations of that approach. (And a link to a paper would be nice too).

thanks

https://www.epfl.ch/schools/cdm/wp-content/uploads/2019/02/Cesari_talk.pdf

I think, above presentation from Giovanni Cesari is explaining this (He's got a book on the subject too, i think), although I think I still need to think about it to understand it.

My confusion is about, how do we construct the V+ itself (the distribution of prices for the counterparty portfolio)? In that portfolio we have, say, European FX options, vanilla swaps and Bermudan swaptions. I think for all those products, we only need their payoff function. i.e. even for the European option, we won't implement the BS formula(?). The bit that talks about solving the pricing and the exposure calculation in one step.

I'd still welcome more explanation on this please.

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