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Assume I have implemented a solution of the Libor Market model PDE in terms of the Finite Difference method. What is a good strategy for validating and benchmarking the results of this implementation?

  • Against which analytical formula or numerical method can I compare my simulation results?
  • Which instruments should be reasonably considered for the validation?
  • How to choose the model parameters of the LMM?

I assume there is no definite answer to these questions, so I'd also be interested in your experiences.

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1 Answer 1

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Answering versus your specific queries

  • Against which analytical formula or numerical method can I compare my simulation results?

Basic would be to benchmark the accuracy against European Swaptions as priced ATM,and ITM/OTM versus the SABR-zero-shift model. Ths is fundamental to make sure the LMM can properly re-price basic Options and the hedges.

  • Which instruments should be reasonably considered for the validation?

LMM generally are used for Bermudans and American Options. Hence, logically, should be used for checking versus these product types

  • How to choose the model parameters of the LMM?

It should be based on the product-types calibrated. Assuming the Bermudans being priced are (for example) on the diagonals of the vol-grid, the global mean-reversion parameters should be calibrated/chosen such that the pricing errors of the Bermudan portfolio is minimized.

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