50th anniversary article option pricing valuation models and applications this paper surveys the literature on option pricing from its origins to the present an extensive review of valuation methods for european and american style claims is provided applications to complex securities and numerical methods are surveyed emphasis is placed on recent trends and developments in methodology and modeling

generating conditional expectations from models with selectivity bias abstract this paper discusses how conditional expectations should be generated from models with sample selectivity we argue that the conventional method ignores relevant and available information and produces unreliable results an alternative approach is suggested and the empirical example of black white wage differentials is presented

tracking the market dynamic pricing and learning in a changing environment dynamic pricing of commodities without knowing the exact relation between price and demand is a much studied problem most existing studies assume that the parameters describing the market are constant during the selling period this severely reduces their practical applicability since in reality market characteristics may change all the time without the firm always being aware of it in the present paper we study dynamic pricing and learning in a changing market environment we introduce a methodology that enables the price manager to hedge against changes in the market and provide explicit upper bounds on the regret a measure of the performance of the firm s pricing decisions in addition this methodology guides the selection of the optimal way to estimate the market process we provide numerical examples from practically relevant situations to illustrate the methodology

male labour force participation following illness or injury this paper develops a model of the disabled individual s labour force participation decision following illness or injury and confronts it with data on the financial consequences of ill health a utility function is specified which allows for the effect of changes in health on work leisure preferences and is evaluated in relation to a household budget constraint estimation is through maximization of the appropriate likelihood function correcting for self selection bias within a switching regression model results are presented showing significant effects of financial variables on participation and these are seen to vary with age disability and income

the value of youth equalizing age differentials in marriages the objective of this paper is to present a model of constrained utility maximizing behaviour which is able to explain serveral features of marriage the model predicts that individuals meet in the

joint stochastic dynamic pricing and advertising with time dependent demand abstract this paper examines the sale of a finite number of items in a class of stochastic dynamic pricing and advertising models with time dependent demand elasticities we prove structural properties of the optimal expected profits with respect to time inventory level price impact advertising impact and different model parameters such as discount rate marginal unit costs and holding costs we find that the value of an additional item opportunity costs is decreasing in the unit costs the discount rate the holding cost rate and the number of items left to sell we also derive structural properties of optimal joint pricing and advertising strategies this way we obtain general qualitative insights in the complex interplay and the mutual dependence of optimal pricing and advertising decisions among other properties we show that a higher advertising impact leads to higher optimal prices and lower advertising rates which in turn implies a lower speed of sale the results obtained help practitioners to respond to changes in market conditions by adjusting price and advertising accordingly our results allow speeding up numerical computations of decisions as the set of possible actions can be reduced significantly our analysis implies general results for pure pricing as well as pure advertising models with time dependent demand elasticities

diagnosing affine models of options pricing evidence from vix abstract affine jump diffusion models have been the mainstream in options pricing because of their analytical tractability popular affine jump diffusion models however are still unsatisfactory in describing the options data and the problem is often attributed to the diffusion term of the unobserved state variables using prices of variance swaps i e squared vix implied from options prices we provide fresh evidence regarding the misspecification of affine jump diffusion models as variance swap prices are affine functions of the state variables in a broader class of models that do not restrict the diffusion term of the state variables we apply the nonparametric methodology used by ait sahalia 1996b supplemented with bootstrap tests and other parametric tests to the s p 500 index options data from january 1996 to september 2008 we find that while the affine diffusion term of the state variables may contribute to the misspecification as the literature has suggested the affine drift of the state variables jump intensities and risk premiums are also sources of misspecification

jump and volatility risk premiums implied by vix abstract an estimation method is developed for extracting the latent stochastic volatility from vix a volatility index for the sp 2 the jump and volatility risks are priced 3 the popular square root stochastic volatility process is a poor model specification irrespective of allowing for price jumps or not our simulation study shows that statistical inference is reliable and not materially affected by the approximation used in the vix index construction

stochastic dynamic pricing and advertising in isoelastic oligopoly models abstract in this paper we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticity we consider the sale of perishable as well as durable goods and include adoption effects in the demand based on a unique stochastic feedback nash equilibrium we derive closed form solution formulas of the value functions and the optimal feedback policies of all competing firms efficient simulation techniques are used to evaluate optimally controlled sales processes over time this way the evolution of optimal controls as well as the firms profit distributions are analyzed moreover we are able to compare feedback solutions of the stochastic model with its deterministic counterpart we show that the market power of the competing firms is exactly the same as in the deterministic version of the model further we discover two fundamental effects that determine the relation between both models first the volatility in demand results in a decline of expected profits compared to the deterministic model second we find that saturation effects in demand have an opposite character we show that the second effect can be strong enough to either exactly balance or even overcompensate the first one as a result we are able to identify cases in which feedback solutions of the deterministic model provide useful approximations of solutions of the stochastic model

nonparametric estimation of american options exercise boundaries and call prices abstract unlike european type derivative securities there are no simple analytic valuation formulas for finite lived american options even when the underlying asset price has constant volatility the early exercise feature considerably complicates the valuation of american contracts the strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries a comparison is made with parametric constant volatility model based prices and exercise boundaries the paper focuses on assessing the adequacy of conventional formulas by comparing them to nonparametric estimates we use daily market option prices and exercise data on the s p100 contract the most actively traded american option contract we find large discrepancies between the parametric and nonparametric call prices and exercise boundaries we also find remarkable similarities of the nonparametric estimates before and after the crash of october 1987

analyzing structure of two echelon closed loop supply chain for pricing quality and recycling management abstract this paper analyzes the effects of recycling and product quality level on pricing decision in a two echelon closed loop supply chain clsc where demand is sensitive with price and quality level of the product under stackelberg game setting this paper considers three possible collection activities of used product for recycling viz retailer led collection manufacturer led collection and third party led collection it is found that third party s involvement in used product collection activity is always disadvantageous in this proposed model cost parameters of the reverse channel play an important role in determining best channel structure quality level and price of the product directly vary with recycling a threshold of collection effort determines which party between manufacturer and retailer can provide the best quality product at least price to resolve channel conflict and to distribute surplus profit the concepts of sub game perfect equilibrium and alternative offer bargaining strategy are used the analysis reveals that the subgame perfect equilibrium retail price cuts out channel conflict and depicts particular profit split irrespective of the offering party the proposed model is also justified by illustrating numerical examples

an analytical framework for retailer price and advertising decisions for products with temperature sensitive demand abstractthe demand for weather sensitive products such as beverages ice creams or chocolate varies with changes in temperature yet retailers lack a framework to adapt the marketing mix element

nonparametric estimation of state price densities implicit in interest rate cap prices based on a multivariate extension of the constrained locally polynomial estimator of ait sahalia and duarte 2003 we provide one of the first nonparametric estimates of probability densities of libor rates under forward martingale measures and state price densities spds implicit in interest rate cap prices the forward densities and spds depend significantly on the slope and volatility of libor rates and mortgage markets activities have strong impacts on the shape of the forward densities the spds exhibit a pronounced u shape as a function of future libor rates suggesting that the state prices are high at both extremely low and high interest rates which tend to be associated with recessions and periods of high inflation respectively our results provide nonparametric evidence of unspanned stochastic volatility and suggest that the unspanned factors could be partly driven by activities in the mortgage markets the author 2009 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please e mail journals permissions oxfordjournals org oxford university press

a closed form garch option valuation model this paper develops a closed form option valuation formula for a spot asset whose variance follows a garch p q process that can be correlated with the returns of the spot asset it provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables the single lag version of this model contains heston s 1993 stochastic volatility model as a continuous time limit empirical analysis on s p500 index options shows that the out of sample valuation errors from the single lag version of the garch model are substantially lower than the ad hoc black scholes model of dumas fleming and whaley 1998 that uses a separate implied volatility for each option to fit to the smirk smile in implied volatilities the garch model remains superior even though the parameters of the garch model are held constant and volatility is filtered from the history of asset prices while the ad hoc black scholes model is updated every period the improvement is largely due to the ability of the garch model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

on the number of state variables in options pricing in this paper we investigate the methodological issue of determining the number of state variables required for options pricing after showing the inadequacy of the principal component analysis approach which is commonly used in the literature we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and maturities as proxies for the transformed state variables the methodology is applied to the prices of s p 500 index options from the period 1996 2005 we find that in addition to the index value itself two state variables approximated by the first two nonlinear principal components are adequate for pricing the index options and fitting the data in both time series and cross sections

optimal pricing and advertising policies for an entertainment event abstract the paper suggests an optimal control model to determine optimal pricing and advertising policies for a one time entertainment event there are two periods an initial period of regular price sales and a terminal period of last minute sales at a possibly reduced price the price in a period is constant over time in the initial period the organizers of the event advertise the event to potential attendees if tickets are sold out by the end of the first period there will be no last minute sales we find that advertising should be decreased over time during the first period there are three different advertising scenarios it may be optimal not to advertise at all to advertise at a positive rate until the end of the first period or to stop advertising at an earlier instant of time in the last minute sales the organizers implement a feedback pricing policy such that the selected price depends on the number of tickets that have been sold in the regular sales period finally we establish optimality conditions for the time instant where to switch to last minute sales

promocast a new forecasting method for promotion planning this article describes the implementation of a promotion event forecasting system promocasttm and its performance in several pilot applications and validity studies pilot studies involved retail grocery chains with 95 to 185 stores per trading area the goal was to provide short term tactical forecasts useful for planning promotions from a retailer s perspective thus the forecast system must be able to handle any of the over 150 000 upcs in each store s item master file and must be scalable to produce approximately 800 000 000 forecasts per year across all the retailers served by efficient marketing services inc ems inc this is a much different task than one that confronts a manufacturer even one with abroad product line manufacturers can benefit from custom modeling in a product line or category retailers need a production system that generates forecasts that help promotion planning marketing scientists have typically approache promotion analysis from the manufacturer s perspective one objective of this article is to encourage marketing scientists to rethink promotion analysis from a different perspective from the retailer s point of view the planning unit is the promotion event neither weekly store tracking data norshopping trip data from consumer panels are easily aggregated to reflect total sales during a promotion event we describe the promotion event databases and the statistical model developed using these databases the data are the strategic asset our goal is to help retailers use their data to increase the profitability of promotions we have data on the performance of each upc in each store under a variety of promotion conditions on each store s adeptness at executing various styles of promotions as well as on chain wide historical performance for each upc we use many historical averages from these databases to build a 67 variable regression style model the forecast incorporates a simple bias correction needed when using a log transformed dependent variable the natural log of total unit sales we argue that the historical averages matching the planned ad and display conditions provide a benchmark superior to the widely used base times lift method when aggregated into case units the natural unit for product ordering 69 of the forecasts in our first validation study were within one case compared to 39 within one case using the appropriate historical averages we report the results of two over time validity studies that reflect the value of our model for retailers the limitations and implications of this planning tool for managerial decision making concerning stocking levels are discussed whenever historical data are the strategic asset we face inherent limitations our model does not forecast new products the forecast error increases when an existing product is promoted in a new way over 99 5 of the time we have full data from which to create a forecast however with a database for a typical chain market containing over 20 million promotion events in the 30 month time frame we use 100 000 events have less than ideal data the breadth of the database typically 150 000 ups makes it impractical to incorporate data on competitive offerings we find that regression style modeling is not adept at incorporating information on the 1 200 subcommodities managed in our pilot stores or the 1 000 manufacturers who supply those stores despite these limitations we show the value of using promotion event data how tactical forecasts based on these data can directly impact the bottom line of grocery retailers and how store by store forecasts can help retailers with problems of running out of stock or overstocking

differntial fecundity markets and gender roles women are fecund for a shorter period of their lives than men this paper investigates how differential fecundity interacts with marriage labor and financial markets to affect gender roles the main findings of the paper are as follows i fecund women are relatively scarce men will behave differently than women in response to this scarcity in the most fundamental way demand and supply conditions in the marriage market affect gender roles ii differential fecundity does not have any market invariant gender effect gender roles depend on the way in which marriage labor and financial markets interact iii gender differences in the labor market can occur without corresponding differences in labor market opportunities productivities in child rearing or social norms iv with uncertainty in human capital accumulation and no insurance against this uncertainty the model s predictions are consistent with observed gender roles

dynamic pricing product and process innovation abstract the question of simultaneous dynamic pricing product and process investment policies is crucial for manufacturing and high tech industries this paper models these policies in an optimal control setting on the supply side the firm sets prices product and process investment levels over time on the demand side current demand depends on price and quality under an additive separable demand function dynamic pricing increases with quality and cost therefore both product innovation and process innovation impact the pricing policy under a multiplicative separable demand function dynamic pricing policy follows the dynamic of production cost and is independent of the evolution of product quality thus process innovation is the main determinant of a firm s pricing policy over time and product innovation has no impact

monopolist pricing with dynamic demand and production cost this paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream the interdependency of cost and demand on cumulative production makes the problem inherently dynamic cost is assumed to be declining with cumulative production learning curve effect while demand is a function of price and cumulative sales representing word of mouth and saturation effects the paper addresses this problem in a general framework that includes several previous results as special cases and provides new insights in other situations while the learning curve and word of mouth effect cause prices to be lower than the price that maximizes immediate revenues the saturation factor has the opposite effect the price path over time is affected by these factors and the interest rate we characterize the price path under several different situations and interpret the results for policy guidelines