Stabilizing Log-Normal Diffusion in View of Compounding Swaps Funding Risk Credit Valuation Adjustment (FRCVA)

We discuss several methodologies for stabilizing the diffusion of compounding instruments modeled by means of lognormal instantaneous interest rate models. We first delve into alternative mathematical and numerical methodologies before showing that the latter suffer from a high seed sensitivity which makes them difficult to apply in practice. We consequently resort to a fine-tune capping of the maximal value of the interest rate which ensures stabilization without altering the main diffusion moments characteristics. We illustrate our approach by examining the funding loss, the Funding Risk Adjustment (FRA) and the Funding Risk Credit Valuation Adjustment (FRCVA) of a compounding swap along the lines of a preceding paper where we advocate the benefit, when funding cannot be hedged, of examining funding risk in an actuarial setting.