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

Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction

In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.Comment: 8 pages, SIGKDD 202

Risk-aware dynamic reserve prices of programmatic guarantee in display advertising

Display advertising is one important online advertising type where banner advertisements (shortly ad) on websites are usually measured by how many times they are viewed by online users. There are two major channels to sell ad views. They can be auctioned off in real time or be directly sold through guaranteed contracts in advance. The former is also known as real-time bidding (RTB), in which media buyers come to a common marketplace to compete for a single ad view and this inventory will be allocated to a buyer in milliseconds by an auction model. Unlike RTB, buying and selling guaranteed contracts are not usually programmatic but through private negotiations as advertisers would like to customise their requests and purchase ad views in bulk. In this paper, we propose a simple model that facilitates the automation of direct sales. In our model, a media seller puts future ad views on sale and receives buy requests sequentially over time until the future delivery period. The seller maintains a hidden yet dynamically changing reserve price in order to decide whether to accept a buy request or not. The future supply and demand are assumed to be well estimated and static, and the model's revenue management is using inventory control theory where each computed reverse price is based on the updated supply and demand, and the unsold future ad views will be auctioned off in RTB to the meet the unfulfilled demand. The model has several desirable properties. First, it is not limited to the demand arrival assumption. Second, it will not affect the current equilibrium between RTB and direct sales as there are no posted guaranteed prices. Third, the model uses the expected revenue from RTB as a lower bound for inventory control and we show that a publisher can receive expected total revenue greater than or equal to those from only RTB if she uses the computed dynamic reserves prices for direct sales

MM2RTB: bringing multimedia metrics to real-time bidding

In display advertising, users' online ad experiences are important for the advertising effectiveness. However, users have not been well accommodated in real-time bidding (RTB). This further influences their site visits and perception of the displayed banner ads. In this paper, we propose a novel computational framework which brings multimedia metrics, like the contextual relevance, the visual saliency and the ad memorability into RTB to improve the users' ad experiences as well as maintain the benefits of the publisher and the advertiser. We aim at developing a vigorous ecosystem by optimizing the trade-offs among all stakeholders. The framework considers the scenario of a webpage with multiple ad slots. Our experimental results show that the benefits of the advertiser and the user can be significantly improved if the publisher would slightly sacrifice his short-term revenue. The improved benefits will increase the advertising requests (demand) and the site visits (supply), which can further boost the publisher's revenue in the long run

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

Entanglement Entropy in Timelike Slices: a Free Fermion Study

We define the entanglement entropy of a quantum state in a discrete set of points in an arbitrary spacetime slice, and give the explicit formula for free fermions. We investigate timelike (causal) slices specifically. For 1D lattice free fermions, we calculated the time-direction entanglement entropy in a set of times $t_n=n\tau$ ($1\le n\le K$) on the same site, and identified a stabilizing transition at $\tau=\tau_0=2\pi/E_0$, where $E_0$ is the energy range of single-fermion spectrum. At zero temperature, the time-like entanglement entropy of the lattice fermion with $\tau<\tau_0$ resembles the Cardy formula for one flavor of chiral fermion. For generic slices, the entanglement entropy shows a clear transition between spacelike and timelike slices. We conjecture $\tau_0$ is the upper bound of time period for consecutive local observations to retrieve information from a quantum state, and conjecture a similar $\tau_0$ exists in interacting models

Karma: Adaptive Video Streaming via Causal Sequence Modeling

Optimal adaptive bitrate (ABR) decision depends on a comprehensive characterization of state transitions that involve interrelated modalities over time including environmental observations, returns, and actions. However, state-of-the-art learning-based ABR algorithms solely rely on past observations to decide the next action. This paradigm tends to cause a chain of deviations from optimal action when encountering unfamiliar observations, which consequently undermines the model generalization. This paper presents Karma, an ABR algorithm that utilizes causal sequence modeling to improve generalization by comprehending the interrelated causality among past observations, returns, and actions and timely refining action when deviation occurs. Unlike direct observation-to-action mapping, Karma recurrently maintains a multi-dimensional time series of observations, returns, and actions as input and employs causal sequence modeling via a decision transformer to determine the next action. In the input sequence, Karma uses the maximum cumulative future quality of experience (QoE) (a.k.a, QoE-to-go) as an extended return signal, which is periodically estimated based on current network conditions and playback status. We evaluate Karma through trace-driven simulations and real-world field tests, demonstrating superior performance compared to existing state-of-the-art ABR algorithms, with an average QoE improvement ranging from 10.8% to 18.7% across diverse network conditions. Furthermore, Karma exhibits strong generalization capabilities, showing leading performance under unseen networks in both simulations and real-world tests