  Advertising options have been recently studied as a special type of
guaranteed contracts in online advertising, which are an alternative sales
mechanism to real-time auctions. An advertising option is a contract which
gives its buyer a right but not obligation to enter into transactions to
purchase page views or link clicks at one or multiple pre-specified prices in a
specific future period. Different from typical guaranteed contracts, the option
buyer pays a lower upfront fee but can have greater flexibility and more
control of advertising. Many studies on advertising options so far have been
restricted to the situations where the option payoff is determined by the
underlying spot market price at a specific time point and the price evolution
over time is assumed to be continuous. The former leads to a biased calculation
of option payoff and the latter is invalid empirically for many online
advertising slots. This paper addresses these two limitations by proposing a
new advertising option pricing framework. First, the option payoff is
calculated based on an average price over a specific future period. Therefore,
the option becomes path-dependent. The average price is measured by the power
mean, which contains several existing option payoff functions as its special
cases. Second, jump-diffusion stochastic models are used to describe the
movement of the underlying spot market price, which incorporate several
important statistical properties including jumps and spikes, non-normality, and
absence of autocorrelations. A general option pricing algorithm is obtained
based on Monte Carlo simulation. In addition, an explicit pricing formula is
derived for the case when the option payoff is based on the geometric mean.
This pricing formula is also a generalized version of several other option
pricing models discussed in related studies.

Computer Science and Game Theory