Benchmark a Libor Market Model implementation

Question

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.

Answer 1

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.