Pricing average price advertisement options when underlying spot market prices are discontinuous

摘要

Advertisement (ad) options have been recently studied as a novel guaranteeddelivery (GD) system in online advertising. In essence, an ad option is acontract that gives an advertiser a right but not obligation to enter intotransactions to purchase ad inventories such as page views or link clicks froma specific slot at one or multiple pre-specified prices in a specific futureperiod. Compared to guaranteed contracts, the advertiser pays a lower upfrontfee but can have greater flexibility and more control in advertising. So far adoption studies have been restricted to the situations where the option payoffis determined by the underlying auction payment price at a specific time pointand the price evolution over time is assumed to be continuous. The former leadsto a biased option payoff calculation and the latter is invalid empirically formany ad slots. This paper discusses a new option pricing framework which can beapplied to a general situation. The option payoff is calculated based on theaverage price over a specific future period. As we use the general mean, ourframework contains different payoff functions as special cases. Further, we usejump-diffusion stochastic models to describe the auction payment pricemovement, which have Markov and price discontinuity properties, and thoseproperties are validated by our statistical investigation of ad auctions fromdifferent datasets. In the paper, we propose a general option pricing solutionbased on Monte Carlo simulation and also give an explicit pricing formula for aspecial case. The latter is also a generalisation of the option pricing modelsin some other recent developments.