Validating a Libor Market Model with Swaptions and Bermudan Options
Summary
The document outlines a validation approach for a finite-difference implementation of the Libor Market Model. It recommends comparing European swaption prices across at-the-money and in-the-money or out-of-the-money strikes with prices from a zero-shift SABR model. This provides a basic check that the model can reprice standard options and their hedges.
It also suggests validating against Bermudan or American-style options, since these products are common uses of the LMM. Model parameters should reflect the products being priced: for a Bermudan portfolio concentrated on a particular part of the volatility grid, choose global mean-reversion parameters to reduce pricing errors for that portfolio. The guidance is qualitative and gives no benchmark data, parameter values, or detailed calibration procedure. Its recommendations therefore serve as a starting point, and the appropriate tests depend on the target products and calibration setup.
Key ideas
- Compare European swaption prices at different moneyness levels with a zero-shift SABR benchmark.
- Include Bermudan or American-style options in validation because the LMM is often used for these products.
- Choose mean-reversion parameters to reduce pricing errors for the portfolio being valued.
- Treat the suggested comparisons as a starting point because no numerical benchmarks or calibration details are provided.
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Full text
# Benchmark a Libor Market Model implementation # Benchmark a Libor Market Model implementation 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 by Kiann (score 1, accepted) https://quant.stackexchange.com/a/69774 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.