Title: Adapting the CVA model to Leland's framework,
Abstract: We consider the framework proposed by Burgard and Kjaer (2011) that derives
the PDE which governs the price of an option including bilateral counterparty
risk and funding. We extend this work by relaxing the assumption of absence of
transaction costs in the hedging portfolio by proposing a cost proportional to
the amount of assets traded and the traded price. After deriving the nonlinear
PDE, we prove the existence of a solution for the corresponding
initial-boundary value problem. Moreover, we develop a numerical scheme that
allows to find the solution of the PDE by setting different values for each
parameter of the model. To understand the impact of each variable within the
model, we analyze the Greeks of the option and the sensitivity of the price to
changes in all the risk factors.