We provide new closed-form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, i.e., when log-returns are modeled as Brownian motions (Black-Scholes model), Variance Gamma processes (VG model) or Normal Inverse Gaussian processes (NIG...

Tankov (2011) improves the Fréchet bounds for a bivariate copula when its values on a compact subset of the unit square are given. He shows that the best possible bounds are quasi-copulas and gives a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient...

Albrecher et al. (2008) have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with...