Abstracts

This article presents lower and upper bounds for the basket option price, assuming very general dynamics for the n underlings. The only quantity we need to know explicitly is the joint characteristic function of the log-returns of the assets. All the bounds are general and do not require any additional assumption on the characteristic function specification. In particular, no affinity restriction on the characteristic function structure is made. Our procedure allows the computation for a very large class of stochastic dynamics like mean reverting and non-affine models. Moreover, the basket weights are not required to be positive. Our bounds involve the computation of a univariate Fourier inversion, hence they do not suffer from the curse of dimensionality. This makes our methodology particularly appealing for higher dimensional problems. We test the bounds on different models, including non Gaussian settings. Numerical examples are discussed and benchmarked against Monte Carlo simulations.