  In this paper we consider the problem of finding bounds on the prices of
options depending on multiple assets without assuming any underlying model on
the price dynamics, but only the absence of arbitrage opportunities. We
formulate this as a generalized moment problem and utilize the well-known
Moment-Sum-of-Squares (SOS) hierarchy of Lasserre to obtain bounds on the range
of the possible prices. A complementary approach (also due to Lasserre) is
employed for comparison. We present several numerical examples to demonstrate
the viability of our approach. The framework we consider makes it possible to
incorporate different kinds of observable data, such as moment information, as
well as observable prices of options on the assets of interest.
