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

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

Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines

We consider the pricing of American bond options in a Heath-Jarrow-Morton framework in which the forward rate volatility is a function of time to maturity and the instantaneous spot rate of interest. We have shown in Chiarella and El-Hassan (1996) that the resulting pricing partial differential operators are two dimensional in the spatial variables. In this paper we investigate an efficientnumerical method to solve there partial differential equations for American option prices and the corresponding free exercise surface. We consider in particular the method of lines which other investigators (eg Carr and Faguet (1994) and Van der Hoek and Meyer (1997)) have found to be efficient for American option pricing when there is one spatial variable. In extending this method for the two dimensional case, we solve the pricing equation by discretising the time variable and one state varialbe and using the spot rate of interest as a continuous variable. We compare our method with the lattice method of Li, Ritchken and Sankarasubramanian (1995).

Financial Methods for Online Advertising

Online advertising, a form of advertising that reaches consumers through the World Wide Web, has become a multi-billion dollar industry. Using the state of the art computing technologies, online auctions have become an important sales mechanism for automating transactions in online advertising markets, where advertisement (shortly ad) inventories, such as impressions or clicks, are able to be auctioned off in milliseconds after they are generated by online users. However, with providing non-guaranteed deliveries, the current auction mechanisms have a number of limitations including: the uncertainty in the winning payment prices for buyers; the volatility in the seller’s revenue; and the weak loyalty between buyer and seller. To address these issues, this thesis explores the methods and techniques from finance to evaluate and allocate ad inventories over time and to design new sales models. Finance, as a sub-field of microeconomics, studies how individuals and organisations make decisions regarding the allocation of resources over time as well as the handling of risk. Therefore, we believe that financial methods can be used to provide novel solutions to the non-guaranteed delivery problem in online advertising. This thesis has three major contributions. We first study an optimal dynamic model for unifying programmatic guarantee and real-time bidding in display advertising. This study solves the problem of algorithmic pricing and allocation of guaranteed contracts. We then propose a multi-keyword multi-click ad option. This work discusses a flexible way of guaranteed deliveries in the sponsored search context, and it’s evaluation is under the no arbitrage principle and is based on the assumption that the underlying winning payment prices of candidate keywords for specific positions follow a geometric Brownian motion. However, according to our data analysis and other previous research, the same underlying assumption is not valid empirically for display ads. We therefore study a lattice framework to price an ad option based on a stochastic volatility underlying model. This research extends the usage of ad options to display advertising in a more general situation

Pricing executive stock options under employment shocks

We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Within this setup,we obtain the executive's optimal exercise policy which allows us to analyze the determinants of both, the subjective valuation by executives and the objective valuation by firms. The perpetual ESO is compared with the more realistic finite maturity ESO finding that the approximation is reasonably good. We also use the objective valuation's results for accounting purposes. Further,we analyze the objective valuation distribution when there is uncertainty about the employment shock parameter. Finally, the role of ESOs in the design of executive's incentives is also discussed.ESO, Risk Aversion, Undiversification, Incentives, FAS 123R.

Attaining Knowledge Workforce Agility in a Product Life Cycle Environment using Real Options

The product life cycle (PLC) phenomenon has placed significant pressures on high-tech industries which rely heavily on the knowledge workforce in transferring cutting-edge technologies into products. This thesis examines systems where market changes and production technology advances happen frequently and unpredictably during the PLC, causing difficulties in predicting an appropriate demand on the knowledge workforce and in maintaining reliable performance. Knowledge workforce agility (KWA) is identified as a desirable means for addressing the difficulties, and yet previous work on KWA is incomplete. This thesis accomplishes several critical tasks for realizing the benefits of KWA in a representative PLC environment, semiconductor manufacturing. Real options (RO) is chosen as the approach towards exploiting KWA, since RO captures the essence of KWA-options in manipulating knowledge capacity, a human asset, or a self-cultivated organizational capability for pursuing interests associated with change. Accordingly, market demand change and workforce knowledge (WK) dynamics in adoption of technology advances are formulized as underlying stochastic processes during the PLC. This thesis models KWA as capacity options in a knowledge workforce and develops a RO approach of workforce training, either initial or continuous, for generating options. To quantify the elements of KWA that impact production, the role of the knowledge workforce in production and costs in obtaining KWA are characterized mathematically. It creates necessary RO valuation methods and techniques to optimize KWA. An analytical examination of the PLC models identifies that KWA has potential to reduce negative impacts and generate opportunities in an environment of volatile demand, and to compensate unreliable performance of knowledge workforce in adoption of technology advances. The benefits of KWA are especially important when confronting highly volatile demand, a low initial adoption level, shrinking PLCs, a growing market size, intense and frequent WK dynamics, insufficient learning capability of employees, or diminishing returns from investments in learning. The thesis further assesses RO, as an agility-driven approach, by comparing it to a chase-demand heuristic and to the Bass forecasting model under demand uncertainty. The assessment demonstrates that the KWA attained from the RO approach, termed RO-based KWA, leads to a stably higher yield, to a persistently larger net present value (NPV), and to a NPV distribution that is more robust to highly volatile demand. Subsequently, a quantitative evaluation of KWA value shows that the RO-based KWA creates a considerable profit growth, either with uncertainty in demand or in the WK dynamics. In evaluation, RO modeling and the RO valuation are identified to be useful in creation of KWA value especially in highly uncertain PLC environments. This thesis illustrates the effectiveness of the numerical methods used for solving the dynamic system problem. This research demonstrates an approach for optimizing KWA in PLC environments using RO. It provides an innovative solution for knowledge workforce planning in rapidly changing and highly unexpected environments. The work of this thesis is representative of studying KWA using quantitative techniques, where there is a dearth of quantitative studies in the literature

Pricing of credit risk and credit risk derivatives : from theory to implementation

Includes abstract. Includes bibliographical references (leaves 223-230)

Predictable dynamics in the S&P 500 index options implied volatility surface

One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the S&P 500 index options IVS. In the first stage we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas et al. (1998). In the second-stage we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models. We find that not only the S&P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic significance of this statistical predictability with mixed findings. Whereas profitable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this profitability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the time-varying S&P 500 implied volatility surface may be not inconsistent with market efficiency.Assets (Accounting) ; Prices

Default risk and the effective duration of bonds

Basis risk is the risk attributable to uncertain movements in the spread between yields associated with a particular financial instrument or class of instruments, and a reference interest rate over time. There are seven types of basis risk: Yields on 1) Long-term versus short-term financial instruments, 2) Domestic currency versus foreign currencies, 3) Liquid versus illiquid investments, 4) Bonds with higher or lower sensitivity to changes in interest rate volatility, 5) Taxable versus tax-free instruments, 6) Spot versus futures contracts and 7) Default-free versus non-default-free securities. Basis risk makes it difficult for the fixed-income portfolio manager to measure the portfolio's exposure to interest rate risk, heightens the anxiety of traders and arbitrageurs who are hedging their investments, and compounds the financial institution's problem of matching assets and liabilities. Much attention has been paid to the first type of basis risk. In recent years, attention has turned toward understanding the relation between credit risk and duration. The authors focus on that, emphasizing the importance of taking credit risk into account when computing measures of duration. The consensus of all work in this area is that credit risk shortens the effective duration of corporate bonds. The authors estimate how much durations shorten because of credit risk, basing their estimates on observable data and easily estimated bond pricing parameters.Banks&Banking Reform,Payment Systems&Infrastructure,International Terrorism&Counterterrorism,Economic Theory&Research,Insurance&Risk Mitigation,Environmental Economics&Policies,Strategic Debt Management,Economic Theory&Research,Banks&Banking Reform,Insurance&Risk Mitigation