optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

effects of speculation and interest rates in a carry trade model of commodity prices abstract the paper presents and estimates a model of the prices of oil and other storable commodities a model that can be characterized as reflecting the carry trade it focuses on speculative factors here defined as the trade off between interest rates on the one hand and market participants expectations of future price changes on the other hand it goes beyond past research by bringing to bear new data sources survey data to measure expectations of future changes in commodity prices and options data to measure perceptions of risk some evidence is found of a negative effect of interest rates on the demand for inventories and thereby on commodity prices and positive effects of expected future price gains on inventory demand and thereby on today s commodity prices

stock returns implied volatility innovations and the asymmetric volatility phenomenon we study the dynamic relation between daily stock retums and daily innovations in optionderived implied volatilities by simultaneously analyzing innovations in index and firmlevel implied volatilities we distinguish between innovations in systematic and idiosyncratic volatility in an effort to better understand the asymmetric volatility phenomenon our results indicate that the relation between stock retums and innovations in systematic volatility idiosyncratic volatility is substantially negative near zero these results suggest that asymmetric volatility is primarily attributed to systematic market wide factors rather than aggregated firm level effects we also present evidence that supports our assumption that innovations in implied volatility are good proxies for innovations in expected stocic volatility

dynamic pricing of perishable assets under competition we study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon customers sequentially arrive at the market make a purchase choice and then leave immediately with some likelihood of no purchase the purchase likelihood depends on the time of purchase product attributes and current prices the demand structure includes time variant linear and multinomial logit demand models as special cases assuming deterministic customer arrival rates we show that any equilibrium strategy has a simple structure involving a finite set of shadow prices measuring capacity externalities that firms exert on each other equilibrium prices can be solved from a one shot price competition game under the current time demand structure taking into account capacity externalities through the time invariant shadow prices the former reflects the transient demand side at every moment and the latter captures the aggregate supply constraints over the sales horizon this simple structure sheds light on dynamic revenue management problems under competition which helps capture the essence of the problems under demand uncertainty we show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart when demand and supply are sufficiently large this paper was accepted by yossi aviv operations management

economic determinants of oil futures volatility a term structure perspective to assess the economic determinants of oil futures volatility we firstly develop and estimate a multi factor oil futures pricing model with stochastic volatility that is able to disentangle long term medium term and short term variations in commodity markets volatility the volatility estimates reveal that in line with theory the volatility factors are unspanned persistent and carry negative market price of risk while crude oil markets are becoming more integrated with financial markets after 2004 short term volatility is driven by industrial production term and credit spreads the s p 500 and the us dollar index along with the traditional drivers including hedging pressure and vix medium term volatility is consistently related to open interest and credit spreads while after 2004 oil sector variables such as inventory and consumption also impact this part of the term structure interest rates mostly matter for long term futures price volatility

dynamic pricing with real time demand learning in many service industries the firm adjusts the product price dynamically by taking into account the current product inventory and the future demand distribution because the firm can easily monitor the product inventory the success of dynamic pricing relies on an accurate demand forecast in this paper we consider a situation where the firm does not have an accurate demand forecast but can only roughly estimate the customer arrival rate before the sale begins as the sale moves forward the firm uses real time sales data to fine tune this arrival rate estimation we show how the firm can first use this modified arrival rate estimation to forecast the future demand distribution with better precision and then use the new information to dynamically adjust the product price in order to maximize the expected total revenue numerical study shows that this strategy not only is nearly optimal but also is robust when the true customer arrival rate is much different from the original forecast finally we extend the results to four situations commonly encountered in practice unobservable lost customers time dependent arrival rate batch demand and discrete set of allowable prices

option valuation with systematic stochastic volatility we use an extension of the equilibrium framework of rubinstein 1976 and brennan 1979 to derive an option valuation formula when the stock return volatility is both stochastic and systematic our formula incorporates a stochastic volatility process as well as a stochastic interest rate process in the valuation of options if the mean volatility and covariance processes for the stock return and the consumption growth are predictable our option valuation formula can be written in preference free form further many popular option valuation formulae in the literature can be written as special cases of our general formula in this paper we investigate the valuation of individual stock options when the volatility of the underlying stock return is stochastic and has a systematic component which is related to the stochastic volatility of the consumption growth or the market return such an investigation is timely and of significant interest because there is now a considerable amount of evidence that the volatility of stock prices is not only stochastic but that it is also highly correlated with the volatility of the market as a whole for example see black 1975 conrad kaul and gultekin 1991 jarrow and rosenfeld 1984 jorion 1988 and ng engle and rothschild 1992 furthermore empirical work by black and scholes 1972 gultekin rogalski and tinic 1982 and whaley 1982 has shown that the empirical biases inherent in the black scholes option prices are different for options on high and low risk stocks because low risk stocks are mainly large firm stocks with stochastic return volatilities that are highly correlated with the return volatility of the market and high risk stocks are mainly small firm stocks with a lessimportant systematic volatility component incorporating systematic volatility effects in option valuation models has the potential to reduce the empirical biases exhibited by prices computed from the black scholes formula we use equilibrium arguments that extend the consumption based representative agent framework of rubinstein 1976 brennan 1979 and stapleton and subrahmanyam 1984 to allow individual asset returns and the consumption growth to exhibit stochastic volatility in particular we permit the volatility of individual asset returns to consist of a systematic component that is related to the consumption or market volatility in addi

stochastic convenience yield and the pricing of oil contingent claims this paper develops and empirically tests a two factor model for pricing financial and real assets contingent on the price of oil the factors are the spot price of oil and the instantaneous convenience yield the parameters of the model are estimated using weekly oil futures contract prices from january 1984 to november 1988 and the model s performance is assessed out of sample by valuing futures contracts over the period november 1988 to may 1989 finally the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time

economic linkages relative scarcity and commodity futures returns this paper shows that economic linkages among commodities create a source of long term correlation between futures returns we extend the theory of storage to a multi commodity level and find that the convenience yield of a commodity depends on its relative scarcity with respect to other related commodities this implies a feedback effect between commodities that is necessary to replicate the upward sloping correlation term structure of futures returns observed for related commodities we present a multi commodity affine model that validates our theoretical predictions and considerably reduces the pricing errors in out of sample crack spread options the author 2012 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please e mail journals permissions oup com oxford university press

non cooperative competition among revenue maximizing service providers with demand learning this paper recognizes that in many decision environments in which revenue optimization is attempted an actual demand curve and its parameters are generally unobservable herein we describe the dynamics of demand as a continuous time differential equation based on an evolutionary game theory perspective we then observe realized sales data to obtain estimates of parameters that govern the evolution of demand these are refined on a discrete time scale the resulting model takes the form of a differential variational inequality we present an algorithm based on a gap function for the differential variational inequality and report its numerical performance for an example revenue optimization problem

adaptive ordering and pricing for perishable products we consider the combined problem of pricing and ordering for a perishable product with unknown demand distribution and censored demand observations resulting from lost sales faced by a monopolistic retailer we develop an adaptive pricing and ordering policy with the asymptotic property that the average realized profit per period converges with probability one to the optimal value under complete information on the distribution the pricing mechanism is modeled as a multiarmed bandit problem while the order quantity decision made after the price level is established is based on a stochastic approximation procedure with multiplicative updates

long term spread option valuation and hedging this paper investigates the valuation and hedging of spread options on two commodity prices which in the long run are in dynamic equilibrium i e cointegrated the spread exhibits properties different from its two underlying commodity prices and should therefore be modelled directly this approach offers significant advantages relative to the traditional two price methods since the correlation between two asset returns is notoriously hard to model in this paper we propose a two factor model for the spot spread and develop pricing and hedging formulae for options on spot and futures spreads two examples of spreads in energy markets the crack spread between heating oil and wti crude oil and the location spread between brent blend and wti crude oil are analyzed to illustrate the results

bond pricing and the term structure of interest rates a new methodology for contingent claims valuation this paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates the methodology based on the equivalent martingale measure technique takes as given an initial forward rate curve and a family of potential stochastic processee for its subsequent movements a no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk examples are provided to illustrate the key results in relation to the term structure of interest rates arbitrage pricing theory has two purposes the first is to price all zero coupon default free bonds of varying maturities from a finite number of economic fundamentals called state variables the second is to price all interest rate sensitive contingent claims taking as given the prices of the zero coupon bonds this paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context of which all existing arbitrage pricing models are special cases in particular vasicek 1977 brennan and schwartz 1979 langetieg 1980 ball and torous 1983 ho and lee 1986 schaefer and schwartz 1987 and artzner and delbaen 1988 the primary contribution of this paper however is a new methodology for solving the second problem i e the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds the methodology is new because i it imposes its stochastic structure directly on the evolution of the forward rate curve ii it does not require an inversion of the term structure to eliminate the market prices of risk from contingent claim values and iii it has a stochastic spot rate process with multiple stochastic factors influencing the term structure the model can be used to consistently price and hedge all contingent claims american or european on the term structure and it is derived from necessary and more importantly sufficient conditions for the absence of arbitrage the arbitrage pricing models of vasicek 1977 brennan and schwartz 1979 langetieg 1980 and artzner and delbaen 1988 all require an iformerly titled bond pricing and the term structure of interest rates a new methodology

soybean inventory and forward curve dynamics we present two results concerning soybean prices first we exhibit a simple relationship between stocks and price volatility the observation of an increasing price volatility with decreasing inventory is often mentioned in the literature but has so far been documented using a proxy for inventory see fama and french 1987 1988 litzenberger and rabinowitz 1995 instead we reconstruct a yearly quarterly and monthly database of worldwide soybean inventories using aggregate data from the united states brazil and argentina we show that under all time scales price volatility is an increasing linear function of inverse inventory which we term scarcity second we show how the addition of the factor scarcity in a state variable approach to the dynamics of the term structure of soybean forward prices improves the quality of the fit we document this property on a 25 year database of cbot futures contracts and show that the superior accuracy also affects long maturity futures contracts an important property for the valuation of long term origination contracts between producing countries and the agrifood industry

actively learning about demand and the dynamics of price adjustment by observing the quantity demanded at particular prices a firm may learn about the parameters of its demand curve in such an environment price changes obstruct the learning process by inducing additional noise the authors paper constructs a dynamic model where a price setting firm endogenously controls the speed of learning the model provides a possible explanation for price inertia as a stable pricing policy allows the firm to learn more rapidly which improves future expected profits furthermore even in the long run learning continues to affect the firm s optimal price copyright 1990 by royal economic society

kerala s industrial backwardness a case of path dependence in industrialization summary the indian state of kerala presents a paradox of development with its remarkable social achievements and relative industrial backwardness this paper describes kerala s industrial backwardness as due to a path dependent process of industrialization a policy decision in the 1930s marked by a priority for investments in chemical based industries and the identification of hydroelectricity as a potential basis for industrialization continue to have implications for industrial growth in kerala today with the policy decision in the 1930s industrial structure in kerala came to be locked into a pattern that offered very little potential for interindustry interlinkages and industrial growth

implementing a stochastic model for oil futures prices this paper develops a parsimonious three factor model of the term structure of oil futures prices that can be easily estimated from available futures price data in addition it proposes a new simple spreadsheet implementation procedure the procedure is flexible may be used with market prices of any oil contingent claim with closed form pricing solution and easily deals with missing data problems the approach is implemented using daily prices of all futures contracts traded at the new york mercantile exchange between 1991 and 2001 in sample and out of sample tests indicate that the model fits the data extremely well though the paper concentrates on oil the approach can be used for any other commodity with well developed futures markets

oligopolies in pollution permit markets a dynamic game approach abstract we reconsider the pollution permit concept in a setting extended to include dynamics spatially diversified firms and an oligopoly in product markets the firms can manage their pollution emissions or stocks by 1 buying pollution permits and emitting pollution 2 shipping pollutants to other nodes and paying such shipping costs or 3 paying environmental costs to mitigate or recycle pollution firms manage these controls strategically to maximize net profits while facing non cooperative rivals within this setting we show that the non cooperative competition among firms may be represented as a differential variational inequality dvi framework furthermore we propose decision rules on permit purchase establish necessary conditions and prove the existence of solution in the formalism of the dvi we also show that the dvi can be equivalently converted to a nonlinear complementarity problem ncp and show this problem despite high dimensions is efficiently solvable using off the shelf software gams with the path solver we illustrate this method s feasibility with a computationally intensive numerical example

stock price distributions with stochastic volatility an analytic approach we study the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter we use analytic techniques to derive an explicit closed form solution for the case where volatility is driven by an arithmetic ornstein ublenbeck or ar1 process we then apply our results to two related problems in the finance literature 1 options pricing in a world of stochastic volatility and 2 the relationship between stochastic volatility and the nature of fat tailes in stock price distributions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

computing the market price of volatility risk in the energy commodity markets abstract in this paper we demonstrate the need for a negative market price of volatility risk to recover the difference between black scholes black f scholes m 1973 the pricing of options and corporate liabilities journal of political economy 81 637 654 black black f 1976 studies of stock price volatility changes in proceedings of the 1976 meetings of the business and economics statistics section american statistical association pp 177 181 implied volatility and realized term volatility initially using quasi monte carlo simulation we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk neutral and statistical volatility in both equity and commodity energy markets this is robust to multiple specifications that also incorporate jumps next using futures and options data from natural gas heating oil and crude oil contracts over a 10 year period we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities additionally there appear distinct seasonality patterns for natural gas and heating oil where winter withdrawal months have higher volatility risk premiums computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets

bayes solution to dynamic inventory models under unknown demand distribution this paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate

short term variations and long term dynamics in commodity prices in this article we develop a two factor model of commodity prices that allows meanreversion in short term prices and uncertainty in the equilibrium level to which prices revert although these two factors are not directly observable they may be estimated from spot and futures prices intuitively movements in prices for long maturity futures contracts provide information about the equilibrium price level and differences between the prices for the short and long term contracts provide information about short term variations in prices we show that although this model does not explicitly consider changes in convenience yields over time this short term long term model is equivalent to the stochastic convenience yield model developed in gibson and schwartz 1990 we estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil linked assets to demonstrate its use and some of its advantages over the gibson schwartz model

back to basics in malaysia and thailand the role of resource based exports in their export led growth abstract malaysia and thailand s remarkable economic growth in recent decades has been widely attributed to rapid growth of their labor intensive manufactured exports this paper demonstrates the important role that resource based products especially simply processed goods have played in their export growth while exports have thus followed their dual static comparative advantage in abundant resources and unskilled labor there has been limited movement into higher end exports a dual strategy of supporting forward linkages into higher value added resource based industries while continuing to encourage the development of backward linkages from the non resource based manufactures is suggested

path dependence in regional development persistence and change in three industrial clusters in santa catarina brazil abstract the concept of path dependence is useful to understand why economic actors who face a fundamental change in the overall incentive structure behave in a way that would appear irrational to the external observer industrial clusters in the southern brazilian state of santa catarina gave an impressive performance in the closed market of the past it was perfectly rational for individual firms to try to internalize as many activities as possible for various reasons thus emerged an extremely noncooperative business culture which does not change easily even under the new conditions of an opening market and increasing competitive pressure firms try to adjust to the new conditions based on their established practices yet the comparison between different clusters reveals that under certain conditions the behavior of firms can change profoundly toward cooperation and collective efficiency these conditions include an existential crisis the presence of change agents and the existence of organizations they can use and the existence of a role model that shows a possible alternative path for the adjustment process the most important changes are attempts to stimulate cooperation between firms and attempts to shape the supporting environment most changes occur inside the business community the political administrative system at the municipal and state levels is much more resistant to change

valuation of commodity futures and options under stochastic convenience yields interest rates and jump diffusions in the spot this paper investigates the effects of stochastic convenience yields stochastic interest rates and jumps in the spot price on the pricing of commodity futures forwards and futures options numerical examples show that one factor prices differ materially from the stochastic convenience yield two factor prices when convenience yield is considerably above its long term average the extension to a three factor model with stochastic interest rates leads to a different futures price but the forward price is unchanged the extension ofthe three factor model to include jumps in the spot price process does not affect forward or futures prices but it can have an impact on options prices the model is applied to price the present value of future cash flows from a real asset

optimal starting times for end of season sales and optimal stopping times for promotional fares many industries face the problem of selling a fixed stock of items over a finite horizon these industries include airlines selling seats before planes depart hotels renting rooms before midnight theaters selling seats before curtain time and retailers selling seasonal goods such as air conditioners or winter coats before the end of the season given a fixed number of seats rooms or coats the objective for these industries is to maximize revenues in excess of salvage value when demand is price sensitive and stochastic pricing is an effective tool to maximize revenues in this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price under mild conditions we show that it is optimal to decrease resp to increase the initial price as soon as the time to go falls below resp above a time threshold that depends on the number of yet unsold items

humps in the volatility structure of the crude oil futures market new evidence abstract this paper analyses the volatility structure of commodity derivatives markets the model encompasses hump shaped unspanned stochastic volatility which entails a finite dimensional affine model for the commodity futures curve and quasi analytical prices for options on commodity futures using an extensive database of crude oil futures and futures options spanning 21 years we find the presence of hump shaped partially spanned stochastic volatility in the crude oil market the hump shaped feature is more pronounced when the market is more volatile and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes

a continuous time yield management model with multiple prices and reversible price changes this article studies a continuous time yield management model in which reversible price changes are allowed we assume that perishable assets are offered at a set of discrete price levels demand at each level is a poisson process to maximize the expected revenue management controls the price dynamically as sales evolve we show that a subset of these prices that form a concave envelope is potentially optimal we formulate the problem into an intensity control model and derive the optimal solution in closed form properties of the optimal solution and their policy implementations are discussed numerical examples are provided

do oil prices respond to real interest rates abstract we show that the robustness of an inverse relationship between the real interest rate and real oil price depends crucially on how the real interest rate is calculated and the time frame of the sample consistent with earlier studies we find that the oil price falls with an unexpected rise in either u s or international ex ante real interest rates when the ex post real interest rate is used the oil price only falls with rises to short term rates 3 months or less additionally the response of the oil price to long term ex ante real interest rates must include the period through the mid 2000s for the inverse relationship to appear in contrast the oil price consistently falls with unexpected rises in short term real interest rates throughout the entire sample we draw two conclusions from the results the first is that the oil price is consistently responsive to short term u s and international real interest rates underlying the importance of storage second oil prices have become more responsive to long term real interest rates over time

commodity prices interest rates and the dollar this paper sheds light on recent fluctuations in commodity prices we investigate whether a decline in real interest rates and the us dollar contributes to higher commodity prices and whether commodity prices display overshooting behavior in response to changes in real interest rates we analyze the behavior of real prices of crude oil food metals and industrial raw materials the analysis is based on structural var models estimated on quarterly data over the period 1990q1 2007q4 our results suggest that commodity prices increase significantly in response to reductions in real interest rates moreover oil prices and prices of industrial raw materials tend to display overshooting behavior in response to such interest rate changes the evidence also suggests that a weaker dollar leads to higher commodity prices shocks to interest rates and the dollar are found to account for substantial shares of fluctuations in commodity prices

unspanned stochastic volatility and the pricing of commodity derivatives commodity derivatives are becoming an increasingly important part of the global derivatives market here we develop a tractable stochastic volatility model for pricing commodity derivatives the model features unspanned stochastic volatility quasi analytical prices of options on futures contracts and dynamics of the futures curve in terms of a low dimensional affine state vector we estimate the model on nymex crude oil derivatives using an extensive panel data set of 45 517 futures prices and 233 104 option prices spanning 4082 business days we find strong evidence for two predominantly unspanned volatility factors jel g13

stalking information bayesian inventory management with unobserved lost sales retailers are frequently uncertain about the underlying demand distribution of a new product when taking the empirical bayesian approach of scarf 1959 they simultaneously stock the product over time and learn about the distribution assuming that unmet demand is lost and unobserved this learning must be based on observing sales rather than demand which differs from sales in the event of a stockout using the framework and results of braden and freimer 1991 the cumulative learning about the underlying demand distribution is captured by two parameters a scale parameter that reflects the predicted size of the underlying market and a shape parameter that indicates both the size of the market and the precision with which the underlying distribution is known an important simplification result of scarf 1960 and azoury 1985 which allows the scale parameter to be removed from the optimization is shown to extend to this setting we present examples that reveal two interesting phenomena 1 a retailer may hope that compared to stocking out realized demand will be strictly less than the stock level even though stocking out would signal a stochastically larger demand distribution and 2 it can be optimal to drop a product after a period of successful sales we also present specific conditions under which the following results hold 1 investment in excess stocks to enhance learning will occur in every dynamic problem and 2 a product is never dropped after a period of poor sales the model is extended to multiple independent markets whose distributions depend proportionately on a single unknown parameter we argue that smaller markets should be given better service as an effective means of acquiring information

pricing of long dated commodity derivatives do stochastic interest rates matter abstract does modelling stochastic interest rates beyond stochastic volatility improve pricing performance on long dated commodity derivatives to answer this question we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables we examine the empirical pricing performance of these models on pricing long dated crude oil derivatives estimating the model parameters from historical crude oil futures prices and option prices we find that stochastic interest rate models improve pricing performance on long dated crude oil derivatives when the interest rate volatility is relatively high furthermore increasing the model dimensionality does not tend to improve the pricing performance on long dated crude oil option prices but it matters for long dated futures prices we also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long dated crude oil option prices

the relation between forward prices and futures prices abstract this paper consolidates the results of some recent work on the relation between forward prices and futures prices it develops a number of propositions characterizing the two prices these propositions contain several testable implications about the difference between forward and futures prices many of the propositions show that equilibrium forward and futures prices are equal to the values of particular assets even though they are not in themselves asset prices the paper then illustrates these results in the context of two valuation models and discusses the effects of taxes and other institutional factors

myopic policies for some inventory models with uncertain demand distributions the majority of papers on stochastic inventory theory make the assumption that the distribution of consumer demand in each time period is known with certainty while this assumption is unsupported in many applied contexts it is conventionally held that more realistic models are more difficult to solve and will not yield simple operational policies this paper shows that a simple inventory policy based upon a critical fractile can be optimal or near optimal in some inventory models with parameter adaptive demand processes in these some parameter of the demand distribution is not known with certainty and estimates of the parameter are updated in a statistical fashion as demand is observed through time examples include exponentially smoothed forecasts and bayesian updating of parameter estimates bounds on the value loss relative to optimal cost when using the critical fractile policy can be calculated directly from the problem data some numerical examples illustrate the technique

analytical pricing of discretely monitored asian style options theory and application to commodity markets we compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square root price dynamics this result combined with the fourier transform pricing method proposed by carr and madan carr p madan d 1999 option valuation using the fast fourier transform journal of computational finance 2 4 summer 61 73 allows us to derive a closed form formula for the fair value of discretely monitored asian style options our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae empirical results based on natural gas data from nymex and corn data from cbot show a remarkable improvement over the main alternative techniques developed for pricing asian style options within the market standard framework of geometric brownian motion

technology entrepreneurship and path dependence industrial clustering in silicon valley and route 128 silicon valley and route 128 have been the centers of innovation and commercialization for the electronics computer and data communications industries in the postwar period however since the 1960s silicon valley has grown more rapidly and from approximately 1985 through 1995 route 128 experienced retarded growth their success had diverged dramatically in the last decade the most common explanations for this divergence are differing cultures interfirm relations or and internal organizational style organization this paper builds upon path dependent and dominant design explanations of technical and industrial change arguing that the technological trajectories of the industries underlying the two regions were different and this led to their differential destinies to explain the dynamics of the two regions and analytical separation is made between the economy of the existing firms and a separate economy of institutions that evolved to nurture new firm formation copyright 1999 by oxford university press

pricing of index options when interest rates are stochastic an empirical test abstract this paper tests amin and jarrow s amin and jarrow 1992 version of merton s merton 1973 stochastic interest rate option pricing formula for stock options in their model the interest rate dynamics are given by the heath et al 1992 term structure model the empirical results using data on european stock index options from the swedish option market show that the amin and jarrow model clearly outperforms the black and scholes 1973 model furthermore the time to maturity bias found in tests of the black and scholes model disappears when the options are priced with the amin and jarrow model

pricing interest rate derivative securities this article shows that the one state variableinterest rate models of vasicek 1977 and cox ingersoll and ross 1985b can be extended sothat they are consistent with both the current termstructure of interest rates and either the currentvolatilities of all spot interest rates or the currentvolatilities of all forward interest rates theextended vasicek model is shown to be very tracta ble analytically the article compares option pricesobtained using the extended vasicek model withthose obtained using a number of other models