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Advertising options have been recently studied as a special type ofguaranteed contracts in online advertising, which are an alternative salesmechanism to real-time auctions. An advertising option is a contract whichgives its buyer a right but not obligation to enter into transactions topurchase page views or link clicks at one or multiple pre-specified prices in aspecific future period. Different from typical guaranteed contracts, the optionbuyer pays a lower upfront fee but can have greater flexibility and morecontrol of advertising. Many studies on advertising options so far have beenrestricted to the situations where the option payoff is determined by theunderlying spot market price at a specific time point and the price evolutionover time is assumed to be continuous. The former leads to a biased calculationof option payoff and the latter is invalid empirically for many onlineadvertising slots. This paper addresses these two limitations by proposing anew advertising option pricing framework. First, the option payoff iscalculated based on an average price over a specific future period. Therefore,the option becomes path-dependent. The average price is measured by the powermean, which contains several existing option payoff functions as its specialcases. Second, jump-diffusion stochastic models are used to describe themovement of the underlying spot market price, which incorporate severalimportant statistical properties including jumps and spikes, non-normality, andabsence of autocorrelations. A general option pricing algorithm is obtainedbased on Monte Carlo simulation. In addition, an explicit pricing formula isderived for the case when the option payoff is based on the geometric mean.This pricing formula is also a generalized version of several other optionpricing models discussed in related studies.

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