Advanced Interest Rate Models (HJM and LMM) › Key Parameters
Michael BrenndoerferDecember 7, 20251 min read
Quantitative FinanceAll chapters Part 7 of 15Interest Rate Models and Derivatives
Advanced Interest Rate Models (HJM and LMM) › Key ParametersOne section · Sections in this chapter5 / 13 ↓
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The key parameters for the LIBOR Market Model are:
- L_i(0): Initial forward LIBOR rates. Observable directly from the current yield curve, these provide the starting point for all simulations and ensure the model fits today's market prices exactly.
- σ_i: Volatility of the i-th forward rate. Determines the width of the distribution for each rate and is typically calibrated to cap volatility data.
- ρ_ij: Correlation between forward rates L_i and L_j. It determines how the rates co-move and therefore affects the volatility of rate combinations used to price multi-rate products such as swaptions.
- δ: Accrual period (tenor spacing). Typically 0.25 (3 months) or 0.5 (6 months), matching the conventions of the underlying interest rate contracts.
- β: Correlation decay parameter. Controls how quickly correlation decreases as the distance between rate maturities increases, with higher values producing faster decay.