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

A lattice framework for pricing display advertisement options with the stochastic volatility underlying model

Advertisement (abbreviated ad) options are a recent development in online advertising. Simply, an ad option is a first look contract in which a publisher or search engine grants an advertiser a right but not obligation to enter into transactions to purchase impressions or clicks from a specific ad slot at a pre-specified price on a specific delivery date. Such a structure provides advertisers with more flexibility of their guaranteed deliveries. The valuation of ad options is an important topic and previous studies on ad options pricing have been mostly restricted to the situations where the underlying prices follow a geometric Brownian motion (GBM). This assumption is reasonable for sponsored search; however, some studies have also indicated that it is not valid for display advertising. In this paper, we address this issue by employing a stochastic volatility (SV) model and discuss a lattice framework to approximate the proposed SV model in option pricing. Our developments are validated by experiments with real advertising data: (i) we find that the SV model has a better fitness over the GBM model; (ii) we validate the proposed lattice model via two sequential Monte Carlo simulation methods; (iii) we demonstrate that advertisers are able to flexibly manage their guaranteed deliveries by using the proposed options, and publishers can have an increased revenue when some of their inventories are sold via ad options.Comment: Bowei Chen and Jun Wang. A lattice framework for pricing display advertisement options with the stochastic volatility underlying model. Electronic Commerce Research and Applications, 2015, Volume 14, Issue 6, pages 465-479, ISSN: 1567-422

A dynamic pricing model for unifying programmatic guarantee and real-time bidding in display advertising

There are two major ways of selling impressions in display advertising. They are either sold in spot through auction mechanisms or in advance via guaranteed contracts. The former has achieved a significant automation via real-time bidding (RTB); however, the latter is still mainly done over the counter through direct sales. This paper proposes a mathematical model that allocates and prices the future impressions between real-time auctions and guaranteed contracts. Under conventional economic assumptions, our model shows that the two ways can be seamless combined programmatically and the publisher's revenue can be maximized via price discrimination and optimal allocation. We consider advertisers are risk-averse, and they would be willing to purchase guaranteed impressions if the total costs are less than their private values. We also consider that an advertiser's purchase behavior can be affected by both the guaranteed price and the time interval between the purchase time and the impression delivery date. Our solution suggests an optimal percentage of future impressions to sell in advance and provides an explicit formula to calculate at what prices to sell. We find that the optimal guaranteed prices are dynamic and are non-decreasing over time. We evaluate our method with RTB datasets and find that the model adopts different strategies in allocation and pricing according to the level of competition. From the experiments we find that, in a less competitive market, lower prices of the guaranteed contracts will encourage the purchase in advance and the revenue gain is mainly contributed by the increased competition in future RTB. In a highly competitive market, advertisers are more willing to purchase the guaranteed contracts and thus higher prices are expected. The revenue gain is largely contributed by the guaranteed selling.Comment: Chen, Bowei and Yuan, Shuai and Wang, Jun (2014) A dynamic pricing model for unifying programmatic guarantee and real-time bidding in display advertising. In: The Eighth International Workshop on Data Mining for Online Advertising, 24 - 27 August 2014, New York Cit

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

Trading Behavior in a Marginal Organized Market

As increasingly more transactions occur away from open markets, the so-called "thin" market issues arise. This paper analyzes unpublished transaction data from Egg Clearinghouse, Inc. (ECI), a marginal marketplace for eggs that trades 4% of all eggs (80% of eggs available for open trading). Results suggest that marginalized markets can serve as an inventory adjustment mechanism while maintaining the role of price discovery as a check for non-market prices. At ECI, most firms both buy and sell regardless of operational types, participation is balanced across all types of firms in the industry, and sellers in general yield to buyers' preferred terms of trade.eggs, inventory adjustment, organized market, price discovery, thin market, Agribusiness,

Pricing of Warrants with Stock Price Dependent Threshold Conditions

Warrants with stock price dependent threshold conditions give the right to buy specially issued stocks, if the performance of the stock price satisfies some requirements. Existence of these derivatives changes the price process of the underlying. We show that in the presence of such warrants one cannot assume that the stock market is arbitrage free and that the stock is tradeable at every time moment with the same price for buying and selling. This means that the usual methods for deriving fair prices for such warrants cannot be used. We start from a simple model for the firm's value process and discuss some ways to specify a related model for the stock price process in the presence of warrants with threshold conditions. We also discuss how indifference pricing approach can be used for pricing such warrants

Confessions of an Internet Monopolist: Demand Estimation for a Versioned Information Good

We investigate profit-maximizing versioning plans for an information goods monopolist. The analysis employs data obtained from a web-based field experiment in which potential buyers were offered information goods in varied price-quality configurations. Maximum simulated likelihood (MSL) methods are used to estimate parameters describing the distribution of utility function parameters across potential buyers of the good. The resulting estimates are used to examine the impact of versioning on seller profits and market efficiency.Versioning, price discrimination, field experiment, maximum simulated likelihood

Some numerical methods for solving stochastic impulse control in natural gas storage facilities

The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP

Different Prices for Identical Products? Market Efficiency and the Virtual Location in B2C E-Commerce

This paper analyses market efficiency and the role of the virtual location in digital markets using a data set containing more than 23,000 price observations from the online market for contact lenses as well as detailed information about online retailer and product characteristics. The data allow to implement and test the concept of virtual location. The empirical results reveal evidence for lower prices and less price dispersion among e-retailers in comparison to hybrid retailers, which supports the hypothesis of enhanced market efficiency in electronic markets. Furthermore, the results show that an online shop?s virtual location influences its prices and that differences in prices are partially driven by differentiation in retailer service. A decomposition of the price differential reveals that there may indeed be a competition effect. --electronic markets,efficiency,virtual location,pricing