A stochastic spread HJM model with stochastic volatility

We present an interest rate model incorporating stochasticity on spreadson the OIS rate, employing a Trolle--Schwartz model for the OIS rate and aTrolle--Schwartz commodity model for the spreads, both facilitating stochastic... [ view full abstract ]

We present an interest rate model incorporating stochasticity on spreads
on the OIS rate, employing a Trolle--Schwartz model for the OIS rate and a
Trolle--Schwartz commodity model for the spreads, both facilitating stochastic volatility. We describe the model's basic
properties and derive necessary drift conditions following the works of Grbac and Rungaldier to ensure
arbitrage-free-ness under the OIS numéraire. Moreover, we provide a
simulation scheme for the hypothetical spread bonds and derive a
semi-closed-form solution based on Fourier pricing methods for bond options on
spread-bearing zero bonds.