Long-Term Yield in an Affine HJM Framework on Sd+

作者：Biagini Francesca^*; Gnoatto Alessandro; Härtel Maximilian

来源：Applied Mathematics and Optimization, 2018, 77(3): 405-441.

DOI：10.1007/s00245-016-9379-8

• Affine process
• Explicit representation
• Forward rate
• Long-term yields
• Model parameters
• Positive semidefinite matrices
• Wishart
• Yield curve

We develop the HJM framework for forward rates driven by affine processes on the state space of symmetric positive semidefinite matrices. In this setting we find an explicit representation for the long-term yield in terms of the model parameters. This generalises the results of El Karoui et al. (Rev Deriv Res 1(4):351–369, 1997) and Biagini and Härtel (Int J Theor Appl Financ 17(3):1–24, 2012), where the long-term yield is investigated under no-arbitrage assumptions in a HJM setting using Brownian motions and Lévy processes respectively.