Emahoy Tsegue-Maryam Guebrou is a 98-year-old Ethiopian nun whose solo piano music came to prominence in 2006 as part of the Ethiopiques collection. She was trained in the western classical tradition though her music has been described as bluesy, freewheeling waltzes with the influence of the chants of the Orthodox Church. It might all sound a bit obscure, but it is well worth a listen.
In order for one to infer reasonable predictions from a model, it must be calibrated to reproduce observations in the market. We use the semimartingale optimal transport methodology to formulate this calibration problem into a constrained optimisation problem, with our model calibrated using a finite number of European options observed in the market as constraints. Given such a PDE formulation, we are able to then derive a dual formulation involving an HJB equation which we can numerically solve. We focus on two cases: (1) The stochastic interest rate is known and perfectly matches the observed term structure in the market, however the asset local volatility and correlation are not known and must be calibrated; (2) The dynamics of both the stochastic interest rate and the underlying asset are unknown, and we must jointly calibrate both to European options on the interest rate and on the asset.