jump diffusion processes and the term structure of interest rates the authors investigate the term structure of interest rates when the underlying state variables and production technologies follow the jump diffusion processes even in some cases where the traditional expectations theory about the term structure is consistent with general equilibrium under diffusion processes the traditional theory is not consistent under jump diffusion processes it is shown that bond prices are strictly higher under jump risks than otherwise and that consumers with logarithmic utility functions will develop hedge portfolios in the presence of jump diffusion a number of continuous time asset pricing models have been derived under stochastic diffusion processes with continuous sample paths see e g black and scholes 2 merton 21 breeden 3 and cox ingersoll and ross 8 however recent empirical studies see e g brown and dybvig 4 feinstone 10 and jarrow and rosenfeld 17 suggest that the underlying processes may follow

option pricing for a jump diffusion model with general discrete jump size distributions we obtain a closed form solution for pricing european options under a general jump diffusion model that can incorporate arbitrary discrete jump size distributions including nonparametric distributions such as an empirical distribution the flexibility in the jump size distribution allows the model to better capture leptokurtic features found in real world data the model uses a discrete time framework and leads to a pricing formula that is provably convergent to the continuous time price as the discretization is increased the solution is easy to implement with fast convergence properties numerical results illustrate the efficiency and accuracy of the proposed model and highlight its robustness and flexibility this paper was accepted by noah gans stochastic models and simulation

jump risks and the intertemporal capital asset pricing model the specification of the stochastic process for stock prices is an important assumption underlying most equilibrium and option pricing models in modern finance this is particularly true of the continuous time capital asset pricing models where it is assumed that asset prices follow diffusion processes with continuous sample paths see merton 1973a breeden 1979 grossman and shiller 1982 the extent to which the implications of these models generalize to discontinuous sample paths is an unanswered question in theoretical finance however the answer to this question is of more than just theoretical interest since accumulated empirical evidence appears to be inconsistent with the continuous sample path assumption see rosenberg 1972 oldfield rogalski and jarrow 1977 rosenfeld 1982 one purpose of this paper is to provide some answers to this question we do this by extending merton s 1973a intertemporal asset pricing model in the special case of a constant investment opportunity set to include discontinuous sample paths for asset prices the constant investment opportunity set assumption is imposed because we are interested in obtaining sufficient conditions under which an instantaneous capital asset pricing model capm results the extension of our model to a stochastic opportunity set is discussed briefly in the text this paper investigates an economy where stock prices follow a jump diffusion process the first part of the analysis derives a sufficient condition under which an instantaneous capm will characterize equilibrium expected returns the sufficient condition is that the jump component of a stock s return must be unsystematic and diversifiable in the market portfolio the second part of the paper is an empirical investigation of the satisfaction of this condition the evidence is seen to be inconsistent with the satisfaction of this hypothesis that is the market portfolio appears to contain a jump component

option listing and stock returns abstract this article examines the effect of option introductions on the underlying stocks in addition to the price increase and volatility decrease that take place when new options are listed we obtain and explain the following new empirical results i an increase in the value of the market around the listing dates of new options ii an increase in the value of an industry index which excludes the optioned stocks iii the dissipation of the price and volatility effects in recent periods and iv the existence of an announcement effect in one subperiod of our sample and its dissipation in recent periods

price barriers and the dynamics of asset prices in equilibrium a price barrier is a price level at which a large number of investors either buy or sell securities we analyze the dynamics of asset prices in an economy in which price barriers exist our analysis suggests that asset prices and volatility can exhibit jumps when the price barrier is reached interestingly the market s anticipation of future trades can influence prices in the opposite direction from what one might expect for example when multiple barriers exist stock prices can be inflated rather than depressed in the proximity of an anticipated stock sale

on jumps in common stock prices and their impact on call option pricing the black scholes call option pricing model exhibits systematic empirical biases the merton call option pricing model which explicitly admits jumps in the underlying security return process may potentially eliminate these biases we provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of nyse listed common stocks however we find no operationally significant differences between the black scholes and merton model prices of the call options written on the sampled common stocks

roughing it up including jump components in the measurement modeling and forecasting of return volatility a rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from high frequency returns coupled with simple modeling procedures building on recent theoretical results in barndorff nielsen and shephard 2004a 2005 for related bi power variation measures the present paper provides a practical and robust framework for non parametrically measuring the jump component in asset return volatility in an application to the dm exchange rate the s p500 market index and the 30 year u s treasury bond yield we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process moreover many jumps appear directly associated with specific macroeconomic news announcements separating jump from non jump movements in a simple but sophisticated volatility forecasting model we find that almost all of the predictability in daily weekly and monthly return volatilities comes from the non jump component our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling forecasting and pricing the continuous and jump components of the total return variation process

understanding the role of trade ins in durable goods markets theory and evidence the act of trading in a used car as partial payment for a new car resonates with practically all consumers such transactions are prevalent in many other durable goods markets ranging from golf clubs to ct scanners what roles do trade ins play in these markets what motivates the seller to set up a channel to facilitate trade ins intuitively accepting a trade in would appear to stimulate demand for the producer s product but facilitating the resale of these used goods that substitute for new goods might also increase cannibalization although such transactions involve billions of dollars we know relatively little about this practice from the extant research literature this paper develops an analytical model that incorporates key features of real world durable goods markets i coexistence of new and used goods markets ii consumer heterogeneity with respect to quality sensitivity iii firms that anticipate the cannibalization problem arising from the coexistence of new and used goods and iv lemon problems in resale markets whereby sellers of used goods are better informed than buyers about the quality of their particular item in our analysis a trade in policy amounts to an intervention by the firm in the used goods market which reduces inefficiencies arising from the lemon problem it motivates owners to purchase new goods and reduces their proclivity to hold on to purchased goods because of the low price the latter would fetch in a lemon market we also show that trade in programs are more valuable for less reliable products as well as for products that deteriorate more slowly our analysis shows that producers in durable goods markets should consider trade in programs as a matter of routine despite cannibalization concerns arising from a more active resale market a producer s profits will inevitably rise from introducing trade ins given pervasive lemon problems we test the key predictions of the model about price and volume of trade by assembling a data set of transactions of u s automobile consumers and find broad support for our model

a continuous time arbitrage pricing model with stochastic volatility and jumps we formulate and test a continuous time asset pricing model using u s equity market data we assume that stock returns are driven by common factors including random jump size poisson processes and brownian motions with stochastic volatility the model places overidentifying restrictions on the mean returns allowing one to identify risk neutral probability distributions useful in pricing derivative securities we test for the restrictions and decompose moments of the asset returns into the contributions made by different factors our econometric methods take full account of time aggregation

estimating the effects of information surprises and trading on stock returns using a mixed jump diffusion model i present a methodology that uses the mixed jump diffusion model for stock returns to estimate the separate effects of information surprises and strategic trading around corporate events using simulation techniques i show that for events with multiple announcements spread over a long time the estimators derived from the mixed jump diffusion model are more powerful compared to the traditional cumulative abnormal return estimators the new methodology is used to study the separate effects of information surprises and strategic trading associated with blockholdings and subsequent targeted repurchases i find that for more than 93 percent of the firms in our sample the mixed jump diffusion model is statistically superior to the pure diffusion model in describing stock returns more important i find a statistically significant negative effect due to trading while the average effect around announcements is statistically insignificant in contrast the standard cumulative abnormal return is not statistically different from zero article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

hedging for multi period downside risk in the presence of jump dynamics and conditional heteroskedasticity this study extends the one period zero var value at risk hedge ratio proposed by hung et al 2005 to the multi period case and incorporates the hedging horizon into the objective function under var framework the multi period zero var hedge ratio has several advantages first compared to existing hedge ratios based on downside risk it has an analytical solution and is simple to calculate second compared to the traditional minimum variance mv hedge ratio it considers expected return and remains optimal while the martingale process is invalid thirdly hedgers may elect an adequate hedging horizon and confidence level to reflect their level of risk aversion using the concept of var pondering the occurrence of volatility clustering and price jumps this study utilizes the arji model to compute time varying hedge ratios finally both in sample and out of sample hedging effectiveness between one period hedge ratio and multi period hedge ratio are evaluated for four hedging horizons and various le

optimal filtering of jump diffusions extracting latent states from asset prices this paper provides an optimal filtering methodology in discretely observed continuoustime jump diffusion models although the filtering problem has received little attention it is useful for estimating latent states forecasting volatility and returns computing model diagnostics such as likelihood ratios and parameter estimation our approach combines time discretization schemes with monte carlo methods it is quite general applying in nonlinear and multivariate jump diffusion models and models with nonanalytic observation equations we provide a detailed analysis of the filter s performance and analyze four applications disentangling jumps from stochastic volatility forecasting volatility comparing models via likelihood ratios and filtering using option prices and returns jel c11 c13 c15 c51 c52 g11 g12 g17 this paper develops a filtering approach for learning about unobserved shocks and states from discretely observed prices generated by continuous time jumpdiffusion models the optimal filtering problem which has received little attention is the natural companion to the parameter estimation problem as filters allow researchers to analyze and use their models for practical applications 1 despite its usefulness there is currently no general method for solving the filtering problem in continuous time models

small dimension pde for discrete asian options abstract this paper presents an efficient method for pricing discrete asian options in presence of smile and non proportional dividends using an homogeneity property we show how to reduce an n 0 dimensional problem to a one or two dimensional one we examine different numerical specifications of our dimension reduced pde using a crank nicholson method interpolation method grid boundaries time and space steps as well as the extension to the case of non proportional discrete dividends using a jump condition we benchmark our results with quasi monte carlo simulation and a multi dimensional pde

pricing weather derivatives this article presents a general method for pricing weather derivatives specification tests find that a temperature series for fresno ca follows a mean reverting brownian motion process with discrete jumps and autoregressive conditional heteroscedastic errors based on this process we define an equilibrium pricing model for cooling degree day weather options comparing option prices estimated with three methods a traditional burn rate approach a black scholes merton approximation and an equilibrium monte carlo simulation reveals significant differences equilibrium prices are preferred on theoretical grounds so are used to demonstrate the usefulness of weather derivatives as risk management tools for california specialty crop growers

are jumps in stock returns diversifiable evidence and implications for option pricing this paper studies the diversiflability of jumps in stock returns it presents a multivariate time series model of the stochastic process for an index and its component stocks that explicitly admits discrete common jumps maximum likelihood estimation for such a model is developed and applied to the daily major market index and its component stocks for the period 1985 through 1990 the paper finds that poisson distributed jumps observed from both the index and its component stocks constitute nondiversiflable risk implying that the standard assumption in option pricing that these jumps are not priced may be invalid

consuming durable goods when stock markets jump a strategic asset allocation approach in this paper we show the impact of considering jumps in the return process of risky assets when deciding how to invest and consume throughout time agents derive their utilities from consumption over time we consider an agent that invests in the financial market and in durable and perishable consumption goods assuming that there are costs for transacting the durable good we show that an agent who does not consider the possibility of jumps will make suboptimal decisions not only regarding the fraction of wealth invested in the stock market but also with respect to the timing for trading on the durable good furthermore we also show that jumps cause a non obvious asymmetric impact on the thresholds that lead the consumer to trade the durable good even when the jump distribution is symmetric

monetary policy preferences of individual fomc members a content analysis of the memoranda of discussion the memoranda of discussion provide detailed records of federal open market committee fomc meeting deliberations procedures are developed for coding the textual data in the memoranda and assessing the reliability of those codings the codings are then used in the estimation of parameters of individual fomc members reaction functions data from the 1970 to 1976 period are employed in the estimation in the future similar methods could be used to analyze newly released transcripts of fomc meetings held after 1976

on jump processes in the foreign exchange and stock markets exchange rates exhibit systematic discontinuities even after allowingfor conditional heteroskedasticity in the diffusion process the results are much more significant in theforeign exchange market than in the stock market which suggests differences in the structure of these markets finally this jump component is shown to explain some of the empirically observed mispricings in the currency options market the objective of this article is to analyze and compare the empirical distribution of returns in the stock market and in the foreign exchange market there are a number of reasons why a better understanding of the stochastic processes driving prices in these markets would be useful many financial models rely heavily on the assumption of a particular stochastic process while relatively little attention is paid to the empirical fit of the postulated distribution as a result models like option pricing models are applied indiscriminately to various markets such as the stock market and the foreign exchange market when the underlying processes may be fundamentally different the foreign exchange market for instance is characterized by active exchange rate man

the intersection of market and credit risk abstract economic theory tells us that market and credit risks are intrinsically related to each other and not separable we describe the two main approaches to pricing credit risky instruments the structural approach and the reduced form approach it is argued that the standard approaches to credit risk management creditmetrics creditrisk and kmv are of limited value when applied to portfolios of interest rate sensitive instruments and in measuring market and credit risk empirically returns on high yield bonds have a higher correlation with equity index returns and a lower correlation with treasury bond index returns than do low yield bonds also macro economic variables appear to influence the aggregate rate of business failures the creditmetrics creditrisk and kmv methodologies cannot reproduce these empirical observations given their constant interest rate assumption however we can incorporate these empirical observations into the reduced form of jarrow and turnbull 1995b drawing the analogy risk 5 63 70 model here default probabilities are correlated due to their dependence on common economic factors default risk and recovery rate uncertainty may not be the sole determinants of the credit spread we show how to incorporate a convenience yield as one of the determinants of the credit spread for credit risk management the time horizon is typically one year or longer this has two important implications since the standard approximations do not apply over a one year horizon first we must use pricing models for risk management some practitioners have taken a different approach than academics in the pricing of credit risky bonds in the event of default a bond holder is legally entitled to accrued interest plus principal we discuss the implications of this fact for pricing second it is necessary to keep track of two probability measures the martingale probability for pricing and the natural probability for value at risk we discuss the benefits of keeping track of these two measures

optimal hedged portfolios the case of jump diffusion risks abstract the paper derives rules for optimal hedged portfolios when the foreign spot exchange rate changes follow a mixed jump diffusion process the paper shows that the sign of the third order derivative of the utility function plays a crucial role in differentiating the jump risk from the diffusion risk the result of the paper is compared to earlier ones under a diffusion process for the foreign exchange rate changes the paper also draws some important implications along the line of the issue of the time varying risk premiums in the foreign exchange market jel 431

making cents of tick sizes the effect of the 2016 u s sec tick size pilot on limit order book liquidity abstract we use the 2016 u s sec tick size pilot to examine the effects of an increase in the minimum price variation on limit order book liquidity in nasdaq listed stocks on the nasdaq exchange for treatment stocks with an average pre pilot quoted spread less than 0 05 the tick size increase is binding and leads to a significant decrease in liquidity in the limit order book specifically the implied cost to trade at and away from the best bid and offer prices increases and the limit order book becomes less resilient the amount of time required for a deviation in liquidity to return to its long run mean for treatment stocks with an average pre pilot quoted spread of at least 0 05 the tick size increase is non binding and leads to either a slight decrease or no change in limit order book liquidity

the compound option approach to american options on jump diffusions abstract we derive analytical valuation formulas for compound options when the underlying asset follows a jump diffusion process we then apply these results to value extendible options american call options on stocks that pay discrete dividends and american options on assets that pay continuous proportional dividends numerical results are provided

general equilibrium pricing of options on the market portfolio with discontinuous returns when the price process for a long lived asset is of a mixed jump diffusion type pricing of options on that asset by arbitrage is not possible if trading is allowed only in the underlaying asset and a risk less bond using a general equilibrium framework we derive and analyze option prices when the underlying asset is the market portfolio with discontinuous returns the premium for the risk of jumps and the diffusion risks forms a significant part of the prices of the options in this economy an attempted replication of call and put options by the black scholes type of trading strategies may require substantial infusion of funds when jumps occur we study the cost and risk implications of such dynamic hedging plans article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

option pricing and implicit volatilities abstract this paper demonstrates that black scholes implied volatilities can be used to value options in many situations where the assumptions of the black scholes model are violated including i alternative stock processes ii stochastic interest rates and iii market frictions given its computational simplicity this procedure provides an attractive alternative to the more complex models with a direct estimation procedure