  Advertisement (abbreviated ad) options are a recent development in online
advertising. Simply, an ad option is a first look contract in which a publisher
or search engine grants an advertiser a right but not obligation to enter into
transactions to purchase impressions or clicks from a specific ad slot at a
pre-specified price on a specific delivery date. Such a structure provides
advertisers with more flexibility of their guaranteed deliveries. The valuation
of ad options is an important topic and previous studies on ad options pricing
have been mostly restricted to the situations where the underlying prices
follow a geometric Brownian motion (GBM). This assumption is reasonable for
sponsored search; however, some studies have also indicated that it is not
valid for display advertising. In this paper, we address this issue by
employing a stochastic volatility (SV) model and discuss a lattice framework to
approximate the proposed SV model in option pricing. Our developments are
validated by experiments with real advertising data: (i) we find that the SV
model has a better fitness over the GBM model; (ii) we validate the proposed
lattice model via two sequential Monte Carlo simulation methods; (iii) we
demonstrate that advertisers are able to flexibly manage their guaranteed
deliveries by using the proposed options, and publishers can have an increased
revenue when some of their inventories are sold via ad options.
