Heat modulated affine stochastic volatility models for forward curve dynamics

We present a function-valued stochastic volatility model designed to capture the continuous-time evolution of forward curves in fixed-income or commodity markets.

The dynamics of the (logarithmic) forward curves are defined by a Heath-Jarrow-Morton-Musiela stochastic partial differential equation modulated by an instantaneous volatility process that describes the second-order moment structure of forwards with different time-to-maturity.

We propose to model the operator-valued instantaneous covariance by an affine process on the cone of positive trace-class operators with drift given by the Lyapunov operator of the Laplacian.

The so defined infinite-rank stochastic volatility model is analytically tractable due to its affine structure and allows to model maturity specific risk and volatility clustering in forward markets.

Furthermore, we introduce a numerically feasible spectral Galerkin approximation of the associated operator-valued generalized Riccati equations and study the robustness of the model with respect to finite-rank approximations by providing explicit error bounds on the approximation error.