The standard market formula used to price cash-settled swaptions is a copy of the physical delivery Black formula, where the classical annuity term is replaced with a single-factor one (discounting on the underlying swap rate fixing at maturity).
As reported in Mercurio and OpenGamma notes, this formula is not arbitrage-free. In order to get a proper pricing, one has to take into account the convexity between the swap rate and the ratio cash settled vs. physical annuity.
Cash-settled European Swaptions