We propose a simple computational method for constructing an arbitrage-free CDO pricing model which matches a pre-specified set of CDO tranche spreads. The key ingredient of the method is a formula for computing the local default intensity function of a portfolio from its expected tranche...

We introduce a reduced basis method for the efficient numerical solution of partial integro-differential equations which arise in option pricing theory. Our method uses a basis of functions constructed from a sequence of Black-Scholes solutions with different volatilities. We show that this...

We present a pathwise approach to continuous-time finance, based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous-time self-financing portfolios which does not rely on any integration concept and show that the value...