Frozen Drift in the LIBOR Market Model and Exotic Derivative Pricing

Summary

The document introduces the frozen-drift approximation in the LIBOR Market Model (also called the LIBOR Forward Model). Freezing drift can make calculations more efficient and treats swap rates as approximately lognormal, but it may distort the terminal correlation structure calibrated to current market data. That distortion can create pricing errors in exotic interest-rate derivatives that depend strongly on correlations among forward rates.

It proposes Monte Carlo simulation under a hypothetical forward measure as a way to compare frozen-drift results with dynamics that retain the exact forward-rate behavior. The document then asks which other derivative classes are most exposed, what model risk the approximation creates, and which market conditions cause it to fail. It does not answer these questions or report numerical results, so it serves as a framing of the model issue rather than a complete assessment. Any conclusions about affected products or market regimes would require further analysis.

Key ideas

• Freezing drift in the LIBOR Market Model can reduce computational effort.
• The approximation treats swap rates as approximately lognormal.
• Frozen drift may distort terminal correlations calibrated from current market observables.
• Correlation distortion can lead to pricing error in correlation-sensitive exotic derivatives.
• Monte Carlo simulation under a forward measure is proposed to assess the approximation against exact forward-rate dynamics.

Tags

# Impact of Freezing the Drift in LFM on Exotic Interest Rate Derivatives


# Impact of Freezing the Drift in LFM on Exotic Interest Rate Derivatives












Freezing the drift in the LIBOR Market Model (LFM/LMM) provides computational advantages and enables efficient pricing of various fixed-income products. Under this assumption, swap rates are approximately lognormal, but the terminal correlation structure—calibrated from today's market observables—may be distorted. This can lead to pricing errors, particularly for exotic derivatives.

Monte Carlo simulation under a hypothetical forward measure $Q^\gamma$ can be used to assess these errors, as it captures the exact forward-rate dynamics without the frozen drift assumption.

Question: Other than exotics that heavily rely on the terminal correlations of forward rates, what classes of interest rate derivatives are most affected by the frozen drift approximation in LFM? What specific model risk does this introduce, and under what market conditions does the approximation break down?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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