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

Can standard preferences explain the prices of out-of-the-money S&P 500 put options?

The 1987 stock market crash occurred with minimal impact on observable economic variables (e.g., consumption), yet dramatically and permanently changed the shape of the implied volatility curve for equity index options. Here, we propose a general equilibrium model that captures many salient features of the U.S. equity and options markets before, during, and after the crash. The representative agent is endowed with Epstein-Zin preferences and the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. In reaction to a market crash, the agent updates her beliefs about the distribution of the jump component. We identify a realistic calibration of the model that matches the prices of shortmaturity at-the-money and deep out-of-the-money S&P 500 put options, as well as the prices of individual stock options. Further, the model generates a steep shift in the implied volatility ‘smirk’ for S&P 500 options after the 1987 crash. This ‘regime shift’ occurs in spite of a minimal impact on observable macroeconomic fundamentals. Finally, the model’s implications are consistent with the empirical properties of dividends, the equity premium, as well as the level and standard deviation of the risk-free rate. Overall, our findings show that it is possible to reconcile the stylized properties of the equity and option markets in the framework of rational expectations, consistent with the notion that these two markets are integrated.Money ; Macroeconomics ; Pricing

Efficient Monte Carlo methods for pricing of electricity derivatives

>Magister Scientiae - MScWe discuss efficient Monte Carlo methods for pricing of electricity derivatives. Electricity derivatives are risk management tools used in deregulated electricity markets. In the past,research in electricity derivatives has been dedicated in the modelling of the behaviour of electricity spot prices. Some researchers have used the geometric Brownian motion and the Black Scholes formula to offer a closed-form solution. Electricity spot prices however have unique characteristics such as mean-reverting, non-storability and spikes that render the use of geometric Brownian motion inadequate. Geometric Brownian motion assumes that changes of the underlying asset are continuous and electricity spikes are far from being continuous. Recently there is a greater consensus on the use of Mean-Reverting Jump-Diffusion (MRJD) process to describe the evolution of electricity spot prices. In this thesis,we use Mean-Reverting Jump-Diffusion process to model the evolution of electricity spot prices. Since there is no closed-form technique to price these derivatives when the underlying electricity spot price is assumed to follow MRJD, we use Monte Carlo methods to value electricity forward contracts. We present variance reduction techniques that improve the accuracy of the Monte Carlo Method for pricing electricity derivatives

Stochastic volatility

Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.Stochastic analysis

Estimating Dynamic Models of Imperfect Competition

We describe a two-step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov Perfect Equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including I.O. models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors, and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).

Mystery shopping: demand-side phenomena in markets for personal plight legal services

“Personal plight” is the sector of the legal services industry in which the clients are individuals, and the legal needs arise from disputes. This article proposes that competition among personal plight law firms is suppressed by three demand-side phenomena. First, consumers confront high search costs. Identifying competing law firms willing and able to provide the needed services often requires significant expenditure of temporal and psychological resources. Second, comparable price and quality information about firms is scarce for consumers. Both of these factors impede comparison shopping and reduce competitive pressure on firms. A third competition-suppressing factor is observed in tort legal service markets, where offerings are typically priced on a contingency basis. Contingency fees have relatively low salience to consumers, and this reduces consumers’ willingness to negotiate and comparison-shop on the basis of price. This analysis is supported by the author’s empirical research with Ontario personal plight lawyers as well as the existing literature. The article concludes by suggesting possible consequences of this analysis for regulatory policy

A Framework for Applied Dynamic Analysis in I.O.

This paper outlines a framework which computes and analyzes the equilibria from a class of dynamic games. The framework dates to Ericson and Pakes (1995), and allows for a finite number of heterogeneous firms, sequential investments with stochastic outcomes, and entry and exit. The equilibrium analyzed is a Markov Perfect equilibrium in the sense of Maskin and Tirole (1988). The simplest version of the framework is supported by a publically accessible computer program which computes equilibrium policies for user-specified primitives, and then analyzes the evolution of the industry from user-specified initial conditions. We begin by outlining the publically accessible framework. It allows for three types of competition in the spot market for current output (specified up to a set of parameter values set by the user), and has modules which allow the user to compare the industry structures generated by the Markov Perfect equilibrium to those that would be generated by a social planner and to those that would be generated by prefect collusion.' Next we review extensions that have been made to the simple framework. These were largely made by other authors who needed to enrich the framework so that it could be used to provide a realistic analysis of particular applied problems. The third section provides a simple way of evaluating the computational burden of the algorithm for a given set of primitives, and then shows that computational constraints are still binding in many applied situations. The last section reviews two computational algorithms designed to alleviate this computational constraint; one of which is based on functional form approximations and the other on learning techniques similar to those used in the artificial intelligence literature.

Three Essays on Sharing Economy

Overview The sharing economy for services like Uber and Airbnb has grown significantly. The growth is driven by technology that “whittled down the barriers to the formation and functioning of sharing markets by lowering or eliminating frictions in the identification, search, match, verification, and exchange” (Narasimhan et al 2017). Reductions in friction in steps to consummate transactions offer two types of savings to consumers. One, monetary savings, results from lower prices typically offered by sharing economy providers (SEP’s) relative to legacy providers (LP’s). The second type of savings results from reduced effort and/or time that consumers need to search, identify, and transact with providers. Thus, a consumer does not have to wait for a taxi to pass by and can instead hail a ride on Uber. A traveler can find an accommodation at a preferred spot in a city easily even in the absence of traditional hotels at that spot. Such reductions in the time and/ or effort needed to locate desired services result in what we label as hassle savings. While they may not be able to compete on monetary savings, LP’s can still provide hassle savings. For instance, although they may cost more, by being more readily available, traditional cabs in a city like New York can help riders save the time to hail and wait for Uber. Whether consumers weigh monetary or hassle savings more may, however, vary with the consumption context. For instance, avoiding the wait time for an Uber ride by taking a passing by taxi may weigh more if the ride is short and the savings are not substantial. The opposite may be true, however, for long rides where the difference in the cost of Uber and traditional taxis could be quite large. Monetary and/or hassle savings can, therefore, be strategic variables for LP’s and SEP’s. I examine if this is the case empirically in my dissertation through three essays on the sharing economy. Essay 1: Monetary and Hassle Savings as Strategic Variables in the Ride-Sharing Market The setting for my first essay is the ride-sharing market where I examine consumers’ choices between Yellow Taxi and Uber in New York City. Specifically, I assume that consumers will weigh monetary savings less than hassle savings if the former is below a threshold but that the opposite will be true for larger savings. I investigate if this is the case using data on paid rides on Yellow Taxi and Uber in New York City. The period of my investigation lies between April 1, 2014 and September 30, 2014, during which data on all rides taken on Yellow Taxi’s and Uber is available from the city. I focus my investigation on the hundred most frequently occurring latitude, longitude, combinations from where rides on Yellow Taxis originate in the city. I then relate the odds of riders in these neighborhoods choosing Uber over Yellow Taxi for a ride on different days of the week and at different times of the day to my primary variable of interest - the availability of Yellow Taxis. I operationalize availability as a one-week lagged proportion of the total of rides on Yellow Taxis from the neighborhood to the total rides on Yellow Taxi in NYC. I also consider other factors like the intrinsic preference for Uber in that neighborhood and in New York City as a whole, weather, time of day, and type of neighborhood. If my assumption about the relative importance of monetary and hassle savings is valid, there should be a ride distance below which Yellow Taxis should be preferred for the hassle savings and above which Uber should be preferred for the monetary savings. I find this indeed to be the case at a threshold of 6.64 miles. Given the potential endogeneity of availability of Yellow Taxis, I take two approaches to assess the reliability of my finding. First, I assume that the availability of Yellow Taxis in each neighborhood could be endogenous with the demand for and availability of paid transportation in the neighborhood. Specifically, I recalibrate my model including two additional covariates as proxies for demand and availability of paid transportation: number of rides taken on subways closest to the neighborhood at the time of the ride and the distance to the nearest subway station. Two, I jointly estimate a supply side equation for the availability of Yellow Taxis in the neighborhood at the time of the ride as a function of a 1-week lagged availability of Yellow Taxis in the same neighborhood at the time of the ride and the demand for and availability of public transportation. I include the residual from this equation as an additional covariate in the log-odds model. Findings from both models are very similar to and consistent with those from the proposed model and confirm that there is a threshold distance below (above) which Yellow Taxis (Uber) is the preferred option. Essay 2: Variations in the Strategic Value of Hassle Savings The accommodation sharing market is the setting for my second and third essays. Accommodations are experience goods because amenities and the quality of services may vary from provider to provider, increasing consumers’ uncertainty. Consumers, therefore, seek information on the features of accommodations before choosing one. Standardization mostly provides this information in the case of legacy providers like branded hotels. Sharing economy providers, however, cannot rely on standardization since the rented personal accommodations do vary across providers. Consumers, therefore, need to rely on alternative sources of information like user-generated ratings and reviews. Ratings and Reviews thus provide hassle savings by reducing uncertainty and can, therefore, be a strategic variable in the accommodation market. I investigate its effect in my second essay. In the first essay, I examined variations in the relative value of monetary and hassle savings with consumption context. In this essay, I investigate whether the value of hassle savings itself varies with consumption context. If it does, the strategic role of features that provide hassle savings to sharing economy customers will also vary for providers. Providers should then invest more in features that provide hassle savings in contexts where they are valued more but can reduce such investments in other contexts. Specifically, my goal is to understand if hosts obtain price premiums for receiving higher ratings from guests and how those premiums vary across consumption contexts, which I operationalize as different types of accommodations and regions within the city. Airbnb guests realize hassle savings by relying on ratings provided by other guests to reduce uncertainty about the features and services of listings. The value of the savings should, therefore, be higher in consumption contexts with greater uncertainty. I hypothesize that uncertainty is likely to be higher under two consumptions contexts. One, where the number of listings in a location is very large. Two, where the number of listings and hence the number of ratings is small. I investigate if these are indeed the patterns by estimating a hedonic model of rental prices for Airbnb listings between April 2016 and October 2017 in the five boroughs of New York City for three types of accommodations: (1) entire – a house or apartment rented in its entirety (2) private – one room in an apartment and (c) shared – an accommodation shared by multiple guests. In each of the borough-type combinations, I assume that listings that receive an average rating of 5.0 are the treatment group and those with ratings of 4.0 – 4.99 are part of the control group. I then use propensity score matching to identify the treatment and control samples for each of the combinations. Estimates of the effect of a higher rating on the price premium are consistent with my hypotheses. Premiums are higher in combinations that have fewer listings or have a large number of listings. Essay 3: Social Relationships as Strategic Variable in the Accommodation-Sharing Market In addition to reviews and ratings (as in Essay 2), an additional source that sharing economy providers have been offering is information on whether the host or any previous buyers of a shared accommodation are acquaintances of a prospective renter. Airbnb, for instance, offers this through a feature called social connections that allows visitors to see only those accommodations reviewed by their friends or friends of friends on Facebook. The feature thus provides hassle savings by reducing uncertainty (perceived risk) and can, therefore, be a strategic variable in the accommodation market. I investigate its effect in my third essay. My empirical analysis involves data on the search and time to the first purchase of a sharing accommodation by those who register on the Airbnb site. I examine two outcomes: (1) whether or not a purchase occurs (2) time to purchase if one occurs. The data includes Airbnb consumer prospects who registered between January 2014 and June 2014. I select consumer prospects who have used social connection feature at least once and use a proportional hazards model to relate time to first purchase to my primary variable of interest – social connections. I operationalize social connections as the number of times that a registered user uses the social connections feature before making the first purchase or terminating the search without a purchase. I also control for the effects of demographics (gender and age), how a registered user first arrived at the Airbnb site (e.g., via a link on Facebook or a search engine), and the number devices she uses for accessing the Airbnb site. I model the occurrence of the purchase/non-purchase of an accommodation as a binary logit related to the same variables and model the two outcomes jointly. My findings indicate a significant effect of social connections in reducing the time to, and increasing the likelihood of, the first purchase. The social connections variable could, however, be endogenous with search time. Those who have friends on Facebook may be more experienced online users and hence, faster in searching and more willing to purchase, online. Additionally, they may be using the social connections feature only because it allows them to see which of their friends may be hosts or had used accommodations they are also considering. I take two approaches to investigate whether these are alternative explanations for my findings. First, I use propensity score matching with visitors who use the social connections feature on Airbnb as the treatment group matched with those who do not use this feature and re-estimate my models on the pooled sample. I use signup method which indicates whether people used Facebook/Google to set up an account on Airbnb before searching for accommodations. I also use age as a matching variable as a proxy for experience with- and interest in- using social media and learning about friends’ activities. Results from this re-estimation are consistent with my findings and indicate that social connections are indeed reducing search time and increasing the likelihood of a purchase. Second, I exploit possible geographic differences in the hassle savings’ value of social connections to validate my findings. Specifically, I hypothesize that the value of hassle savings should be larger when someone is searching internationally rather than domestically in the US since uncertainty should be higher with the former. I therefore re-estimate my model with geographic-specific estimates of the effects of social connections. I do find that the effects are larger both on the time to make the first purchase and on the likelihood of the first purchase for international listings than domestic ones

Dealing with Derivatives. Studies on the role, informational content and pricing of financial derivatives

Cyriel de Jong was born on 19 July 1976 in Valkenburg aan de Geul, the Netherlands. From 1994 till 1999 he studied econometrics at Maastricht University. During this time he spent half a year as an exchange student at the Universität Wien in Vienna. He furthermore completed an internship on mortgage prepayment modelling at De Nationale Investeringsbank in The Hague and a research project on European Corporate Bonds at Maastricht University. He obtained his MSc in econometrics in 1999 with honour. From February 1999 onwards Cyriel de Jong has been a PhD student at the Financial Management department of the Rotterdam School of Management at Erasmus University. During this period he has taught several executive and nonexecutive courses. From 2001 till 2003 he furthermore worked for the consultancy firm FinEdge, where he was responsible for the subsidiary Energy Global. His research was published in Energy Power Risk Management, Bedrijfskunde and various Dutch journals. Since 1 May 2003 he has been assistant professor at the Financial Management department at Erasmus University, where his research interests focus on commodity markets in general and derivative valuation in particular. Besides his academic career he continues working part-time as a consultant in financial and commodity markets.The aim of this thesis is to improve the understanding of derivatives markets, which should ultimately lead to a better diversification of risks among market participants. The author first analyzes the impact of derivatives on the market quality of the underlying asset. With experiments and a theoretical model it is shown that derivatives generally make markets more efficient, although volatility may increase, depending on the exact market structure. Next, the author presents two methods that derive information about the underlying price process from traded options. The models approximate the option prices well and the extracted information explains future volatility better than historical data. Finally, a model for the valuation of options in electricity markets is presented that deals with the special characteristics of electricity spot prices and may serve to value electricity generation plants