We demonstrate how to compute first- and second-order sensitivities of portfolio credit derivatives such as synthetic collateralized debt obligation (CDO) tranches using algorithmic Hessian methods developed in Joshi and Yang (2010) in a single-factor Gaussian copula model. Our method is correct...

We incorporate a simple and effective control-variate into Fourier inversion formulas for vanilla option prices. The control-variate used in this paper is the Black-Scholes formula whose volatility parameter is determined in a generic non-arbitrary fashion. We analyze contour dependence both in...

We present a fast method to price and hedge CMS spread options in the displaced-diffusion co-initial swap market model. Numerical tests demonstrate that we are able to obtain sufficiently accurate prices and Greeks with computational times measured in milliseconds. Further, we find that CMS...

We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the...