The Design of Arbitrage-Free Data Pricing Schemes

Motivated by a growing market that involves buying and selling data over the web, we study pricing schemes that assign value to queries issued over a database. Previous work studied pricing mechanisms that compute the price of a query by extending a data seller's explicit prices on certain queries, or investigated the properties that a pricing function should exhibit without detailing a generic construction. In this work, we present a formal framework for pricing queries over data that allows the construction of general families of pricing functions, with the main goal of avoiding arbitrage. We consider two types of pricing schemes: instance-independent schemes, where the price depends only on the structure of the query, and answer-dependent schemes, where the price also depends on the query output. Our main result is a complete characterization of the structure of pricing functions in both settings, by relating it to properties of a function over a lattice. We use our characterization, together with information-theoretic methods, to construct a variety of arbitrage-free pricing functions. Finally, we discuss various tradeoffs in the design space and present techniques for efficient computation of the proposed pricing functions.Comment: full pape

A Theory of Pricing Private Data

Personal data has value to both its owner and to institutions who would like to analyze it. Privacy mechanisms protect the owner's data while releasing to analysts noisy versions of aggregate query results. But such strict protections of individual's data have not yet found wide use in practice. Instead, Internet companies, for example, commonly provide free services in return for valuable sensitive information from users, which they exploit and sometimes sell to third parties. As the awareness of the value of the personal data increases, so has the drive to compensate the end user for her private information. The idea of monetizing private data can improve over the narrower view of hiding private data, since it empowers individuals to control their data through financial means. In this paper we propose a theoretical framework for assigning prices to noisy query answers, as a function of their accuracy, and for dividing the price amongst data owners who deserve compensation for their loss of privacy. Our framework adopts and extends key principles from both differential privacy and query pricing in data markets. We identify essential properties of the price function and micro-payments, and characterize valid solutions.Comment: 25 pages, 2 figures. Best Paper Award, to appear in the 16th International Conference on Database Theory (ICDT), 201

Multi-keyword multi-click advertisement option contracts for sponsored search

In sponsored search, advertisement (abbreviated ad) slots are usually sold by a search engine to an advertiser through an auction mechanism in which advertisers bid on keywords. In theory, auction mechanisms have many desirable economic properties. However, keyword auctions have a number of limitations including: the uncertainty in payment prices for advertisers; the volatility in the search engine's revenue; and the weak loyalty between advertiser and search engine. In this paper we propose a special ad option that alleviates these problems. In our proposal, an advertiser can purchase an option from a search engine in advance by paying an upfront fee, known as the option price. He then has the right, but no obligation, to purchase among the pre-specified set of keywords at the fixed cost-per-clicks (CPCs) for a specified number of clicks in a specified period of time. The proposed option is closely related to a special exotic option in finance that contains multiple underlying assets (multi-keyword) and is also multi-exercisable (multi-click). This novel structure has many benefits: advertisers can have reduced uncertainty in advertising; the search engine can improve the advertisers' loyalty as well as obtain a stable and increased expected revenue over time. Since the proposed ad option can be implemented in conjunction with the existing keyword auctions, the option price and corresponding fixed CPCs must be set such that there is no arbitrage between the two markets. Option pricing methods are discussed and our experimental results validate the development. Compared to keyword auctions, a search engine can have an increased expected revenue by selling an ad option.Comment: Chen, Bowei and Wang, Jun and Cox, Ingemar J. and Kankanhalli, Mohan S. (2015) Multi-keyword multi-click advertisement option contracts for sponsored search. ACM Transactions on Intelligent Systems and Technology, 7 (1). pp. 1-29. ISSN: 2157-690

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

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.Comment: IEEE Transactions on Knowledge and Data Engineering, 201

Quantum computational finance: martingale asset pricing for incomplete markets

A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for the model from the given asset prices, and using that probability measure to price the derivative. When the number of underlying assets and/or the number of market outcomes in the model is large, pricing can be computationally demanding. We show that a variety of quantum techniques can be applied to the pricing problem in finance, with a particular focus on incomplete markets. We discuss three different methods that are distinct from previous works: they do not use the quantum algorithms for Monte Carlo estimation and they extract the martingale measure from market variables akin to bootstrapping, a common practice among financial institutions. The first two methods are based on a formulation of the pricing problem into a linear program and are using respectively the quantum zero-sum game algorithm and the quantum simplex algorithm as subroutines. For the last algorithm, we formalize a new market assumption milder than market completeness for which quantum linear systems solvers can be applied with the associated potential for large speedups. As a prototype use case, we conduct numerical experiments in the framework of the Black-Scholes-Merton model.Comment: 31 pages, 6 figure