Yield Curve Simulation with Historical Copulas

I present a procedure for yield curve simulation using historical copulas to model the curve dynamics (bending and steepening). This separates the modelling of curve dynamics from that of individual tenor points. Using this, the model is able to capture a swaption volatility surface across all three dimensions (expiry, tenor, strike) whilst also producing sensible curve shapes. A summary of the steps is: 1) Use an established model to simulate individual curve points at individual horizons. For the examples here I use the market-standard SABR model. 2) Combine the horizons using a common set of standard-normal driving variables. 3) Combine the tenor points using historical copulas. 4) Apply adjustments to put all simulations in the same risk-neutral measure.This is very different from common curve simulation models such as the LIBOR Market Model (LMM) where the curve is simulated jointly and measure consistency is achieved through drift adjustments. The model is a practical approach to yield curve simulation, an easy way to capture a volatility surface and produce sensible curve shapes. It is not mathematically rigorous or strictly arbitrage-free, though for the examples tested the output is arbitrage-free within simulation error. If required, the model could also be adjusted to produce given correlations between yield curve points or forward rates.A possible application of the method is XVA calculation, where risk-neutral simulation and curve dynamics are both important features. In this regard, the approach could be extended from a single curve to a large set of rates across multiple currencies