Scenario Generation for Time Series and Curves: A Comparison of Nonparametric and Semiparametric Bootstrap

Abstract

Generating stochastic trajectories for asset classes is an increasingly relevant task in quantitative finance. Traditional approaches, such as the stationary bootstrap, preserve by construction the empirical distribution of asset-class returns, but do not ensure that each individual simulated path is economically realistic: scenarios may be valid in distribution while single trajectories fail to represent plausible states of the world. To address this limitation, we review semiparametric simulation methodologies that combine a parametric structure, which enforces realistic dynamics, with the resampling of model residuals, which preserves the stochastic component observed in historical data. The issue is particularly acute for interest rates, where direct resampling of rate changes may produce implausible yield-curve evolutions despite correct distributional properties. Our empirical analysis shows the effectiveness of semiparametric bootstrap methods based on autoregressive or mean-reverting specifications. In the fixed-income setting, combining these methods with fully parametric term-structure models yields more coherent and realistic simulations of yield-curve dynamics.