标题： Heath-Jarrow-Morton 在能源市场中与提升的Heston模型相遇，用于联合历史和隐含校准 显示英文标题

标题： Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration

摘要： 在能源市场中，联合历史校准与隐含校准对从业者而言至关重要，但由于需要使期货合约的历史相关性与期权市场的隐含波动率微笑相一致，这一问题也极其棘手。 我们通过一种简洁的多因子 Heath-Jarrow-Morton（HJM）前向曲线模型以及来自提升的 Heston 模型的随机波动率因子来解决这个关键问题。 我们开发了一种基于 Kemna-Vorst 近似法的快速顺序校准程序：(i) 历史相关性和方差互换（VS）波动率期限结构通过水平、斜率和曲率因子捕捉，(ii) 随后可通过固定点算法对 VS 波动率期限结构进行修正以实现完美匹配，(iii) 使用基于傅里叶的方法校准隐含波动率微笑。 我们的模型在德电市场和 TTF 天然气市场中展现了卓越的联合历史和隐含校准拟合能力，并能够在隐含波动率超立方体内实现现实的插值。 显示英文摘要

摘要： In energy markets, joint historical and implied calibration is of paramount importance for practitioners yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from the option market. We address this crucial problem with a parsimonious multiplicative multi-factor Heath-Jarrow-Morton (HJM) model for forward curves, combined with a stochastic volatility factor coming from the Lifted Heston model. We develop a sequential fast calibration procedure leveraging the Kemna-Vorst approximation of futures contracts: (i) historical correlations and the Variance Swap (VS) volatility term structure are captured through Level, Slope, and Curvature factors, (ii) the VS volatility term structure can then be corrected for a perfect match via a fixed-point algorithm, (iii) implied volatility smiles are calibrated using Fourier-based techniques. Our model displays remarkable joint historical and implied calibration fits - to both German power and TTF gas markets - and enables realistic interpolation within the implied volatility hypercube.