A Lattice Framework for Pricing Display Ad Options with the Stochastic Volatility Model. Working Paper (2014

Ad options are a recent development in online advertising which provide advertis-ers with greater flexibility related to buying their guaranteed deliveries in the future. In short, an ad option is a contract in which an online publisher (or search engine) grants an advertiser the right but not obligation to enter into transactions to purchase impressions or clicks from a specific online ad slot at a pre-specified price on a specific delivery date. Previous studies on the ad option pricing models are mostly restricted to the situation where the underlying price follows a geometric Brownian motion (GBM). However, it has been shown that GBM only happens in less than 20 % of the stochastic movements of ad auction prices. In this paper, we address this issue by employing a stochastic volatility (SV) model to describe the evolution of the underlying price which does not rely on the assumption of GBM. The computational tractability is solved by approximating the SV model with a proposed censored binomial lattice. Our develop-ments are validated by experiments with the real advertising data. We find that the SV model has a better fitness to the real adverting data; with the real data, we demonstrate that advertisers are able flexibly to manage their guaranteed deliveries by using the pro-posed options. We also demonstrate that publishers will have increased revenue when some of their inventories are sold via ad options