black scholes approximations of call option prices with stochastic volatilities a note a piecewise linear weighting function for black scholes implied volatilities is used in conjunction with the black scholes call pricing model to approximate stochastic volatility european call prices a sensitivity analysis is conducted to compare simulated stochastic volatility call prices to the black scholes prices calculated with the weighted implied vo latilities the analysis indicates that a simple model can provide close approximations to the simulated prices with far less computational effort i introduction the volatility of the underlying asset is one of the more difficult parameters to estimate in any option pricing model the stochastic nature of the volatility of most financial assets is responsible for much of the difficulty while the early tests of the black scholes 1973 option pricing model rely upon historical prices for volatility estimates latane and rendleman s 1976 implied volatility technique has become the standard method of estimation unfortunately as beckers 1981 stresses although implied volatilities calculated from a stationary vari ance model may be of practical use it is inconsistent to use the black scholes model with a constant variance to obtain estimates of nonstationary variances l recent work conducted by hull and white 1987 and johnson and shanno 1987 has been directed at solving the problem of pricing european calls on assets with stochastic volatilities while hull and white provide a series solution for the case in which the variance and stock price are uncorrelated convergence is slow unless the variance of the assets volatility is relatively small for more general cases both hull and white and johnson and shanno rely upon monte carlo simulations to estimate option prices although the application of simulation techniques to option pricing first explored by boyle 1977 is often a useful method of estimating option prices the monte carlo method tends to be expensive and is often too time consuming for real time applications this study examines a simple method of approximat

hedging with options under variance uncertainty an illustration of pricing new crop soybeans the behavior of a commodity s price return variance over time is critical to both the theory and practice of commodity option valuation in this paper three models are used to forecast soybean price variance for the period during which a seasonal increase in variance has been found in previous studies a time series model outperforms the ordinary least squares and naive models the significance of the forecast error levels is then examined in terms of expected deviations above and below a price target for a put hedge the resulting trade off between risk and return is shown by strike price and variance expectation

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

on the frequency of large stock returns putting booms and busts into perspective textabstractnumerous articles have investigated the distribution of share prices and find that the returns are fat tailed nevertheless there is still controversy about the amount of probability mass in the tails and hence about the most appropriate distribution to use in modeling returns this controversy has proven hard to resolve as the alternatives are non nested we employ extreme value theory focusing exclusively on the larger observations in order to assess the tail shape within a unified framework we find that at least the first two moments exist this enables one to generate robust probabilities on large returns which put the recent stock market swings into historical perspective

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

an empirical test of a valuation model for american options on futures contracts pricing models for american call and put options on futures contracts are derived herein these models are used to investigate the efficiency of the market for options on standard poor 500 and german mark futures the evidence presented here indicates that market prices for these options deviate substantially from their corresponding model prices in addition it is shown that a hedging strategy originated at prices that indicate a deviation of market from model is successful in translating the observed mispricing into excess profits after transactions costs however these net profits are eliminated if the origination of the strategy is delayed by one trade or if bid ask spreads are accounted for

differences between continuous and discrete contingent value estimates in a split sample contingent valuation study of willingness to pay wtp for food safety improvements the dichotomous choice dc elicitation method consistently generated much larger estimates of wtp than did a continuous method little or none of these differences was due to bias introduced by the statistical techniques used with the dc data most or all of the difference was due to differences in respondent behavior in addition the continuous wtp responses showed a significant scope effect while the dc responses did not the observed difference in behavior may be attributable in part to yea saying by dc respondents

unexpected tails in risk measurement some international evidence risk management critically depends on the assumptions made about the distribution of stock returns this paper applies extreme value methods to investigate the limiting distribution of the extreme returns of the nikkei225 ftse100 and s p500 indices as well as the indices of some of largest sectors in japan uk and us the results indicate that the much celebrated generalised extreme value distribution does not provide the most accurate description of the minima since the generalised logistic distribution performs better due to its ability to better capture the fat tails of returns the time varying nature of extremes is also confirmed while a simulation exercise adds to the robustness of our results it is also shown that the findings may have important implications for risk models such as var and expected shortfall since risk measures which cannot capture the fatness of tails of the empirical distribution function of returns may lead to serious underestimation of downside risk

evaluating interval forecasts a complete theory for evaluating interval forecasts has not been worked out to date most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage consequently i set out to build a consistent framework for conditional interval forecast evaluation which is crucial when higher order moment dynamics are present the new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management

the asymptotic distribution of extreme stock market returns this article presents a study of extreme stock market price movements according to extreme value theory the form of the distribution of extreme returns is precisely known and independent of the process generating returns using data for an index of the most traded stocks on the new york stock exchange for the period 1885 1990 the author shows empirically that the extreme returns obey a frechet distribution copyright 1996 by university of chicago press

pricing and trading european options by combining artificial neural networks and parametric models with implied parameters we compare the ability of the parametric black and scholes corrado and su models and artificial neural networks to price european call options on the s p 500 using daily data for the period january 1998 to august 2001 we use several historical and implied parameter measures beyond the standard neural networks in our analysis we include hybrid networks that incorporate information from the parametric models our results are significant and differ from previous literature we show that the black and scholes based hybrid artificial neural network models outperform the standard neural networks and the parametric ones we also investigate the economic significance of the best models using trading strategies extended with the chen and johnson modified hedging approach we find that there exist profitable opportunities even in the presence of transaction costs

capturing downside risk in financial markets the case of the asian crisis abstract using data on asian equity markets we observe that during periods of financial turmoil deviations from the mean variance framework become more severe resulting in periods with additional downside risk to investors current risk management techniques failing to take this additional downside risk into account will underestimate the true value at risk with greater severity during periods of financial turnoil we provide a conditional approach to the value at risk methodology known as conditional var x which to capture the time variation of non normalities allows for additional tail fatness in the distribution of expected returns these conditional var x estimates are then compared to those based on the riskmetrics methodology from j p morgan where we find that the model provides improved forecasts of the value at risk we are therefore able to show that our conditional var x estimates are better able to capture the nature of downside risk particularly crucial in times of financial crises

arbitrage continuous trading and margin requirements this paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options in the context of the blackscholes economy margin restrictions are shown to exclude continuous trading arbitrage opportunities and with two additional hypotheses still to allow the black scholes call model to apply the black scholes economy consists of a continuously traded stock with a price process that follows a geometric brownian motion and a continuously traded bond with a price process that is deterministic continuous trading security market models constitute a significant area of continuing reesearch in financial economics these models form the basis of the option pricing methodology see merton 16 for a review and current intertemporal asset pricing models see merton 15 breeden 3 and cox ingersoll and ross 5 given the importance of these models it is of no surprise that there has been significant academic concern see dybvig 9 cox ingersoll and ross 4 p 341 and ingersoll 13 pp 13 25 over the discovery of a continuous trading strategy by harrison and kreps 10 called the doubling strategy that generates a sure dollar from a zero investment the existence of this doubling strategy violates a basic premise of the option pricing methodology the premise of no arbitrage opportunities given this violation the question naturally arises as to whether the option pricing methodology is internally consistent fortunately harrison and pliska 11 showed that the exclusion of arbitrage opportunities and the doubling strategy does not invalidate the familiar derivation of the black scholes call option formula the exogenous exclusion of these doubling strategies is somewhat arbitrary however types of constraints that exclude continuous trading arbitrage opportunities were studied by kreps 14 harrison and kreps 10 and dybvig 9 these papers provide constraints that are unsatisfactory from an institutional point of view since they have no market analogue margin requirements on the other hand have a market analogue one purpose of this paper is to show that margin requirements also exclude continuous trading arbitrage opportunities to make this argument self contained we first provide a unified framework that synthesizes the previously stated results our assertion concerning margin re

sensitivity of willingness to pay estimates to bid design in dichotomous choice contingent valuation models this paper addresses the sensitivity of dichotomous choice contingent valuation method dc cvm based mean willingness to pay wtp estimates to the dc cvm sample design and to alternative measures of wtp this issue is examined both analytically and empirically the analysis of ten different dc cvm data sets revealed a sensitivity in estimated mean wtp to the sample design and to the measure chosen to calculate mean wtp

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

pricing hang seng index options around the asian financial crisis a garch approach abstract this paper investigates how well the hang seng index options the most important class of option contracts traded in hong kong are priced using the garch approach we calibrated the garch parameters using the call and put option data and used them to price options in the subsequent weeks we found the garch model performs very well in comparison with the black scholes model even after allowing for a smile smirk adjustment its superior performance was also evident both before and during the recent asian financial turmoil

trader rationality in the exercise of futures options abstract we examine the rationality of investor exercise behavior by analyzing two years tendered exercise notices for treasury bond futures options we conclude that exercise behavior is generally rational but document numerous failures to exercise as well as some exercises that should not have occured both at and prior to expiration the most frequent type of error is failing to exercise suggesting that traders do not monitor their positions with sufficient care finally we show that investors use information arriving after trading closes but before exchange imposed exercise deadlines in forming their exercise decisions

the effects of transaction costs and different borrowing and lending rates on the option pricing model a note this paper modifies the black scholes option pricing model to include the effects of transaction costs and different borrowing and lending rates the paper demonstrates that these market imperfections tend to offset each other yielding a bounded range of prices for each option the paper also shows that under some conditions the option pricing hedge may be society s lowest cost financial intermediary

the effect of distance on willingness to pay values a case study of wetlands and salmon in california most contingent valuation studies in the literature utilized a pre determined geographic market area for their sample frame in other words they did not include variables that would measure the extent of the geographic areas over which to aggregate willingness to pay these studies implicitly assumed that the effects of geographic distance were moot an assumption that could have led to an understatement of the aggregate benefit values computed in these studies the overall goal of this study was to determine if distance affects willingness to pay for public goods with large non use values the data used came from a contingent valuation study regarding the san joaquin valley ca respondents were asked about their willingness to pay wtp for three proposed programs designed to reduce various environmental problems in the valley a logit model was used to examine the effects of geographic distance on respondents willingness to pay for each of the three programs results indicate that distance affected wtp for two of the three programs wetlands habitat and wildlife and the wildlife contamination control programs we calculate the underestimate in benefits if the geographic extent of the public good market is arbitrarily limited to one political jurisdiction

information bias in contingent valuation effects of personal relevance quality of information and motivational orientation abstract a laboratory experiment examined the potential for information bias in contingent valuation cv consistent with the view that information about a public or private good can function as a persuasive communication willingness to pay wtp was found to increase with the quality of arguments used to describe the good especially under conditions of high personal relevance under low personal relevance wtp for a public but not for a private good was higher when an altruistic as opposed to an individualistic orientation was activated it is concluded that the nature of the information provided in cv surveys can profoundly affect wtp estimates and that subtle contextual cues can seriously bias these estimates under conditions of low personal relevance

the pricing of convexity risk and timedecay in options markets abstract option valuation formulas typically assume all risk can be eliminated in a continuously rebalanced hedge but convexity of the option pricing function and time decay cause risk in real world hedges we find strong evidence in stock options transactions data from periods 10 years apart that the market prices these risks there is a significant price effect associated with convexity that becomes larger immediately following a period of larger stock price movements although time decay is highly correlated with convexity a multiple regression including both factors shows it to have a significant independent effect the results from the two sample periods are highly consistent as are pre and post crash results from the year 1987

the weekend effect on the distribution of stock prices abstract evidence of weekend effects on the distribution of security returns suggests that returns are generated by a process operating closer to trading time rather than calendar time in contrast accumulation of interest over the weekend follows a calendar time process since both the variance of returns and the interest rate are important parameters of the black scholes option pricing model this paper suggests that the model be stated to account for this by utilizing a trading time variance and a calendar time interest rate empirical evidence indicates that this allows the model to better explain market option prices

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

hedging the risks from writing foreign currency options abstract this paper considers the ways in which banks and other financial institutions can hedge their risks when they write non exchange traded foreign currency options key factors affecting the performance of delta hedging are identified and hedging schemes involving the use of exchange traded options are analyzed the schemes are tested using both simulated data and data from trades on the philadelphia exchange between february 1983 and september 1984

the measurement of option mispricing abstract different studies have examined the ability of the black scholes option pricing model to estimate accurately market prices of publicly traded options and reached conflicting results this study examines commonly used ex ante measures of option mispricing finds that they can produce differing conclusions about option prices and develops an alternative measure for gauging option mispricing empirical analysis of returns to options selected using the various mispricing measures indicates that this new measure is more likely to detect mispricing and identify options that yield excess returns before commissions

comparative performance of the black scholes and roll geske whaley option pricing models the original black scholes bs 2 european call option pricing model does not take account of divided payments on the underlying stock and does not allow for the possibility of early exercise that may be optimal when the stock pays dividends black 1 has suggested that the original bs model can be modified to take account of dividends and sharpe 14 predicts that this modified or pseudo american bs approach while not exact is probably sufficient for many listed options

the risk premium of volatility implicit in currency options this article provides an empirical investigation of the risk neutral variance process and the market price of variance risk implied in the foreign currency options market there are three principal contributions first the parameters of heston s mean reverting square root stochastic volatility model are estimated using dollar mark option prices from 1987 to 1992 second it is shown that these implied parameters can be combined with historical moments of the dollar mark exchange rate to deduce an estimate of the market price of variance risk these estimates are found to be nonzero time varying and of sufficient magnitude to imply that the compensation for variance risk is a significant component of the risk premia in the currency market finally the out of sample test suggests that the historical variance and the hull and white implied variance contain no more information than that imbedded in the heston implied variance

a conditional extreme value volatility estimator based on high frequency returns abstract this paper introduces a conditional extreme value volatility estimator evt based on high frequency returns the relative performance of the evt is compared with the discrete time garch and implied volatility models for 1 day and 20 day ahead forecasts of realized volatility this is also a first attempt towards detecting any time series variation in extreme value distributions using high frequency intraday data the information content of evt is examined in the context of forecasting sp 2 vix generally yields a less accurate characterization of realized volatility than evt and garch models these results have implications for financial risk management and are thus relevant to both regulators and practitioners

reconsidering heterogeneity and aggregation issues in environmental valuation a multi attribute approach the economic valuation of complex environmental goods composed of multiple attributes is an expanding field of research in ecological and environmental economics however several issues are still subjects of debate this paper focuses on three of them the linearity of the valuation function in the attributes aggregation criteria for obtaining social values and the heterogeneity of individuals utility functions a methodological approach based on multi attribute utility theory which enables us to contrast the impact of these concerns on the valuation of environmental goods is proposed we employ the methodology to value a protected natural area and from the results obtained we can conclude that the non linearity and the heterogeneity of the individual utility function are relevant aspects of environmental valuation that need to be taken into account when valuing environmental goods

fat tails and truncated bids in contingent valuation an application to an endangered shorebird species a yes response function in a contingent valuation study is said to have fat tails if it has a high and slowly declining yes response rate at high bid levels truncated bids refer to the practice of dropping high bid offers before a yes response rate of near zero is reached this is a common practice in contingent valuation we explore the extent and implications of fat tails and truncated bids in a study of an endangered shorebird species we find among other things that mean willingness to pay is quite sensitive to the highest bid offered so much so that the choice of highest bid nearly dictates outcomes

the relative performance of five alternative warrant pricing models five warrant pricing models are examined in this study a pair based on the black scholes model a pair based on the constant elasticity of variance cev modification and an extendible warrant model a la longstaff based on more than 20 000 warrant price observations the flexible exponent cev model generates the lowest average absolute pricing error in most of the warrants examined the dilution adjusted black scholes model however remains a reasonable economical alternative in many cases

the contingent valuation debate why economists should care t he contingent valuation method involves the use of sample surveys questionnaires to elicit the willingness of respondents to pay for generally hypothetical projects or programs the name of the method refers to the fact that the values revealed by respondents are contingent upon the constructed or simulated market presented in the survey a spirited and occasionally mean spirited battle over such methods is currently being waged involving competing factions within the federal government economists and lawyers representing business and environmental groups and interested academics as well at issue is a seemingly quite specific question should environmental regulations currently under development at both the department of the interior and the department of commerce sanction the use of the contingent valuation method in estimating the damage done by spills of oil chemicals or other substances covered by federal law more generally the debate raises broad questions about what economists have to say about the values that individuals place on public or private goods the two papers that follow this one make cases for and against the use of the contingent valuation method my aim here is to provide an overview of the technique and the debate surrounding it i also want to suggest why this debate should matter to economists both professionally and in their roles as citizens and consumers

the valuation of american call options and the expected ex dividend stock price decline abstract this study focuses on the ex dividend stock price decline implicit within the valuation of american call options on dividend paying stocks the roll 1977 american call option pricing formula and the observed structure of cboe call option transaction prices are used to infer the expected ex dividend stock price decline as a proportion of the amount of the dividend the relative decline is shown to be not meaningfully different from one confirming some recent evidence from studies which examined stock prices in the days surrounding ex dividend

using contingent pricing analysis to value open space and its duration at residential locations to estimate benefits from open space adjacent to residences this paper blends contingent valuation and conjoint analysis within a housing market context the resulting framework contingent pricing analysis represents the stated preference counterpart to hedonic pricing analysis by asking individuals to state prices for hypothetical housing locations which include an environmental amenity then it asks individuals to state their willingness to pay for a better and longer lasting environmental amenity as an advantage over hedonic pricing analysis it directly isolates willingness to pay results indicate that potentially short lasting open space adds no value while preserved open space adds 5 066 or 5 to housing value

extreme us stock market fluctuations in the wake of 9 11 we apply extreme value analysis to us sectoral stock indices in order to assess whether tail risk measures like value at risk and extremal linkages were significantly altered by 9 11 we test whether semi parametric quantile estimates of downside risk and upward potential have increased after 9 11 the same methodology allows one to estimate probabilities of joint booms and busts for pairs of sectoral indices or for a sectoral index and a market portfolio the latter probabilities measure the sectoral response to macro shocks during periods of financial stress so called tail s taking 9 11 as the sample midpoint we find that tail s often increase in a statistically and economically significant way this might be due to perceived risk of new terrorist attacks copyright 2008 john wiley sons ltd

option pricing when the variance is changing the monte carlo method is used to solve for the price of a call when the variance is changing stochastically

time varying volatilities and calculation of the weighted implied standard deviation rogalski tinic have reported a monthly pattern in ex post stock return variances that differs between small and large market capitalization firms maloney rogalski find that option prices reflect these monthly patterns ex ante this study extends maloney rogalski s work by devising an expiration specific weighted implied standard deviation wisd it is found that i the monthly patterns in one month wisds are basically similar to the monthly patterns in ex post variances detected by rogalski tinic for both large and small size firms and ii use of expiration specific wisds as opposed to standard composite wisds results in improved performance of option pricing models

spike models in contingent valuation spike models allow for a nonzero probability of zero willingness to pay in referendum style contingent valuation experiments they include many of the often used models as special cases and allow various analyses that are not possible in standard applications in this paper the economic rationale for the spike models and their estimation techniques are discussed and empirical illustrations are provided one study suggests that mean willingness to pay is zero and both studies strongly suggest that median wtp is zero these results have some bearing on the continuing debate of the incentive properties of hypothetical surveys and the construction of scenarios in contingent valuation experiments

a simple linear weighting scheme for black scholes implied volatilities a note abstract this study presents a piecewise linear weighting function for implied volatilities calculated from black scholes call and put prices a sensitivity analysis is conducted to compare black scholes prices calculated using the weighted implied volatilities to american model prices the analysis indicates that a relatively simple european model can provide close approximations to american prices

an extreme value approach to estimating volatility and value at risk this article determines the type of asymptotic distribution for the extreme changes in u s treasury yields the thin tailed gumbel and exponential distributions are strongly rejected against the fat tailed frechet and pareto distributions the empirical results indicate that the volatility of maximal and minimal changes in interest rates declines as time to maturity rises yielding a downward sloping volatility curve for the extremes the article proposes an extreme value approach to estimating value at risk and shows that the statistical theory of extremes provides a more accurate approach for risk management and value at risk var calculations than the standard models

bid ask spreads and volatility estimates the implications for option pricing abstract this paper re examines the variance related mispricing exhibited by the black scholes model by accounting for the effects of bid ask spreads on the estimation of the variance of returns on a security it is shown that volatility estimates based on observed sequences of transaction prices overestimate the true volatility of returns on a security with the magnitude of the overestimation being an increasing function of the level of the volatility the paper then provides empirical tests of the proposition that the variance related bias exhibited by the black scholes model is due to this misestimation of volatility the results indicate that although the misestimation is systematically related to the variance it is not of sufficient magnitude to explain the volatility bias exhibited by black scholes model

valuation of tropical rainforests philosophical and practical issues in the use of contingent valuation abstract this paper explores the possibility of using a large scale multi country contingent valuation study for making decisions concerning global resources in the specific context of valuing a large set of tropical rainforests before considering the practical issues involved in implementing such a study the paper addresses philosophical issues related to the use of contingent valuation including the role of passive use motives such as altruism and the role of information the implications of empirically based criticisms which argue that contingent valuation results are unreliable are also considered the main portion of the paper sketches the practical difficulties likely to be encountered in actually implementing a large contingent valuation study in multiple countries which seeks to value a common set of tropical rainforests some key study design choices are discussed

a generalized extreme value approach to financial risk measurement this paper develops an unconditional and conditional extreme value approach to calculating value at risk var and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes the new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks both the in sample and out of sample performance results indicate that the box cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets the new approach yields more precise var estimates than the normal and skewed t distributions

stock price volatility mean reverting diffusion and noise abstract using weekly call option prices on twenty five stocks over a ten year period 1975 1985 and calls on the s p 500 stock index futures we find that ex ante market volatility follows a mixed mean reverting diffusion with noise process changes in volatility are correlated across stocks and a marketwide volatility effect is found strong forces pull the volatility back to its long term value the findings suggest the development of new option pricing models

valuation of american options on foreign currency abstract pricing models for american call and put options on foreign currency are derived herein these models are used to investigate the efficiency of the market for foreign currency options the evidence presented here indicates that market prices for these options deviate substantially from their corresponding model prices in addition it is shown that a hedging strategy executed at transaction prices can be used to translate an observed deviation of market from model prices into positive excess profits however these profits are eliminated if the strategy is executed at bid and offer prices

errors in implied volatility estimation estimating implied volatility by inverting the black scholes formula is subject to considerable error when option characteristics are observed with plausible errors especially for options away from the money large changes in volatility produce small changes in option prices conversely small errors in option prices and other option characteristics produce large errors in implied volatilities in the presence of small measurement errors unobserved truncation of option prices that violate lower bounds for absence of arbitrage can also lead to systematic volatility smiles the paper proposes feasible gls estimators that reduce the noise and bias in implied volatility estimates

a nonparametric kernel regression approach for pricing options on stock market index abstractprevious options studies typically assume that the dynamics of the underlying asset price follow a geometric brownian motion gbm when pricing options on stocks stock indices currencies or futures however there is mounting empirical evidence that the volatility of asset price or return is far from constant this article in contrast to studies that use parametric approach for option pricing employs nonparametric kernel regression to deal with changing volatility and accordingly prices options on stock index specifically we first estimate nonparametrically the volatility of asset return in the gbm based on the nadaraya watson n w kernel estimator then based on the n w estimates for the volatility we use monte carlo simulation to compute option prices under different settings finally we compare the index option prices under our nonparametric model with those under the black scholes model and the stein stein model

the efficiency of the finnish market for right issues abstract this paper analyzes the efficiency of the finnish market for right issues the rights traded on the helsinki stock exchange hse are similar instruments to warrants with some special features attached to them the paper first derives appropriate arbitrage conditions for these rights which must be satisfied in informationally efficient markets and then examines these conditions using both ex post and ex ante test procedures the ex post tests which jointly examine market efficiency and synchroneity of the rights and stock market show a staggering amount of violations against the arbitrage bounds however the ex ante tests reveal that high transaction costs prevent normal investors from benefitting from these violations stockbrokers themselves however seem to be able to earn arbitrage profits in the rights market

tests of an american option pricing model on the foreign currency options market this paper tests the ability of the american option pricing model proposed by parkinson 18 or mason 14 to explain the pricing of the foreign currency options traded on the philadelphia stock exchange from february 28 1983 to march 26 1985 we find that the model underprices out of the money options relative to at the money and in the money options this relative underpricing is driven by an underpricing of out of the money call options of short maturity in addition the degree of relative mispricing for most categories of options is shown to be a decreasing function of the time to maturity of the options longer maturity options appear to trade at similar levels of implied volatility whether they are in at or out of the money most of these biases appear consistent with the fact that the underlying spot currency rate follows a mixed jump diffusion process as described in 17

forecasting the var of crude oil market do alternative distributions help abstract accurate modeling of the empirical distribution of crude oil market returns is extremely important in estimating risk measures in addition to several commonly used distributions alternative distributions are explored in this study some of which account for the asymmetry and heavy tails simultaneously found in distributions and contain more tail parameters to separately depict the right and left tails when forecasting the value at risk var of crude oil markets during highly volatile periods seven backtests are also conducted to compare the var forecasting accuracy among different distributions the empirical results indicate that a highly volatile environment challenges the commonly used distributions and the four risk models based on commonly used distributions are rejected about 27 to 38 of the time the alternative distributions i e skewed general error distributions sged generalized hyperbolic skewed student t distributions ghst and generalized asymmetric student t gast distributions generally produce more accurate var measurement and gast gives the best measurement accuracy the empirical results imply that risk managers or policymakers should further consider more flexible distributions such as sged ghst or gast in particular when quantifying or managing the risk in turbulent market times

option values under stochastic volatility theory and empirical estimates abstract this paper numerically solves the call option valuation problem given a fairly general continuous stochastic process for return volatility statistical estimators for volatility process parameters are derived and parameter estimates are calculated for several individual stocks and indices the resulting estimated option values do not differ dramatically from black scholes values in most cases although there is some evidence that for longer maturity index options black scholes overvalues out of the money calls in relation to in the money calls

on the valuation of american call options on stocks with known dividends both the roll and the geske equations for the valuation of the american call option on a stock with known dividends are incorrectly specified this note presents the corrected valuation formula explains the misspecifications and provides a numerical example

unbiased estimation of the black scholes formula abstract the black scholes model gives the price of an option as a function of the true variance rate of the underlying stock and other parameters because the true variance rate is unobservable an estimate of the variance rate is used in empirical tests but because the black scholes formula is non linear in the variance option price estimates using an estimated variance are biased even if the variance estimate itself is unbiased this paper develops an unbiased estimator of the black scholes formula from a taylor series expansion of the formula and the properties of the pdf of the estimated variance

the italian market for premium contracts an application of option pricing theory abstract despite their growing importance on italian stock exchanges premium contracts have not received very much attention in analytical studies this paper starts with a description of the working of the market for premium contracts with the aim of highlighting its institutional peculiarities compared with foreign markets for stock options and then develops a formula for the determination of premia based on arbitrage methods similar to those used in option pricing theory the empirical test of the correspondence between actual market premia and the theoretical values obtained provides some indication of the scope for arbitrage between premium and forward contracts and hence of the efficiency of italian stock exchange markets

willingness to pay for environmental improvements in a large city evidence from the spike model and from a non parametric approach in this paper the contingent valuation method cvm is applied in order toestimate the social benefits of a set of environmental and urbanimprovements planned for the waterfront of the city of valencia spain asa consequence of the expansion and restructuring of its trading port asthe data show a high rate of zero responses we applied the spike model one of the most recent models in cvm literature since traditional models logit and probit are not suitable given the characteristics of our data the non parametric approach is also applied in order to test the validity ofthe spike model the results show certain similarities between the spikemodel and the non parametric approach

anticipation of quarterly earnings announcements a test of option market efficiency abstract this study tests chicago board options exchange efficiency by examining option price behavior in the weeks surrounding a firm s quarterly earnings announcement the evidence presented here suggests that a first order autoregressive seasonal process describes quarterly earnings behavior and demonstrates that the information content of an earnings announcement is fully incorporated in option prices by the end of the announcement week

the emperor has no clothes limits to risk modelling abstract this paper considers the properties of risk measures primarily value at risk var from both internal and external regulatory points of view it is argued that since market data is endogenous to market behavior statistical analysis made in times of stability does not provide much guidance in times of crisis in an extensive survey across data classes and risk models the empirical properties of current risk forecasting models are found to be lacking in robustness while being excessively volatile for regulatory use the var measure may give misleading information about risk and in some cases may actually increase both idiosyncratic and systemic risk

intraday price change and trading volume relations in the stock and stock option markets this study investigates intraday relations between price changes and trading volume of options and stocks for a sample of firms whose options traded on the cboe during the first quarter of 1986 after purging the price change series of the effects of bid ask spreads multivariate time series analysis is used to estimate the lead lag relation between the price changes in the option and stock markets the results indicate that price changes in the stock market lead the option market by as much as fifteen minutes the analysis of trading volume indicates that the stock market lead may be even longer the intense trading activity in and in fact the very existence of organized stock option markets attest to the economic benefits that these financial contracts provide reduced transaction costs and increased financial leverage are two reasons why trading in the stock option market may be more attractive than trading in the market for the underlying stock in addition these cheaper and more flexible trading opportunities attract new and differently informed investors to the marketplace the resulting increase in trading activity together with the inextricable arbitrage linkage between stock and option prices imply an increase in market efficiency this study investigates empirically the intraday price change and trading volume relations between stocks and options for a sample of firms whose options were actively traded on the chicago board options exchange during the first quarter of 1986 in particular intraday call option price changes are translated into implied stock price changes using the american call option pricing model these intraday implied stock price changes are then compared with the actual stock price changes to identify which if either market leads the other in perfectly functioning capital markets there should be complete simultaneity between the series that is new information disseminating into the marketplace should be reflected in the prices and the trading activity of both securities simultaneously institutional factors however may make the stock option market more attractive to information traders this may cause price changes and trading activity due to new information to be observed in the option market first followed by price

long term asset tail risks in developed and emerging markets a power law typically governs the tail decay of financial returns but the constancy of the so called tail index which dictates the tail decay remains relatively unexplored we study the finite sample properties of some recently proposed endogenous tests for structural change in the tail index given that the finite sample critical values strongly depend on the tail parameters of the return distribution we propose a bootstrap based version of the structural change test our empirical application spans developed and emerging financial asset returns somewhat surprisingly emerging stock market tails are not more inclined to structural change than their developed counterparts emerging currency tails on the contrary do exhibit structural shifts in contrast to developed currencies our results suggest that extreme value theory evt applications in hedging tail risks can assume stationary tail behavior over long time spans provided one considers portfolios that solely consist of stocks or bonds

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

the value of online banking to small and medium sized enterprises evidence from firms operating in the uae free trade zones abstractthis study estimates the willingness to pay of small and medium sized enterprises smes for a business online banking services the estimation utilizes a contingent valuation method employing data from 400 smes in the united arab emirates free zones an interval regression model is used to identify company characteristics affecting wtp the results indicate an average wtp for online banking of 518 50 per month firms engaging in international trade value these services at least 10 more than those with only domestic operations other variables that significantly affect wtp include number of employees and the transportation cost of using traditional branch banking

addressing heterogeneous preferences using parametric extended spike models some public programs simultaneously provide a mix of non rejectable public goods and public bads consequently some individuals would pay for the program while others might instead need to becompensated in this paper we estimate twoparametric extended spike models that accountfor positive and negative preferences as wellas indifference for the public good weillustrate the models using data on valuationof prescribed burning of underbrush in forests which reduces the risk of catastrophicwildfires but also produces smoke emissions the public bad we compare the two empiricalapproaches to estimate willingness to pay wtp for the program and contrast these results withthose obtained from modeling specificationsthat only account for non negative preferences substantial differences in public net benefitswere found between the most flexible parametricextended spike model and the simple spike modelwhere negative responses were coded as zero anda standard binary logit of only positivebidders the results from the extended spikemodels demonstrated that accounting forindifference and negative values towards thepublic good resulted in substantially lowerwillingness to pay estimates

a bayesian approach to modeling stock return volatility for option valuation new measures of stock return volatility are developed to increase the precision of stock option price estimates with bayesian statistical methods volatility estimates for a given stock are developed using prior information on the cross sectional patterns in return volatil ities for groups of stocks sorted on size financial leverage and trading volume call option values computed with the bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility standard historical volatility or even the actual ex post volatility that occurred during each option s life although the bayesian methods produce biased call price estimators they do reduce the systematic tendency of standard pricing approaches to overprice underprice options on high low volatility stocks little bias improvement is observed with respect to the time to maturity and moneyness of the call options

caviar conditional autoregressive value at risk by regression quantiles value at risk var has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes var is defined as the value that a portfolio will lose with a given probability over a certain time horizon usually one or ten days despite its conceptual simplicity its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions interpreting the var as the quantile of future portfolio values conditional on current information we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies such as normality or i i d returns the conditional autoregressive value at risk or caviar model moves the focus of attention from the distribution of returns directly to the behavior of the quantile we specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by koenker and bassett to determine the unknown parameters since the objective function is not differentiable we use a differential evolutionary genetic algorithm for the numerical optimization utilizing the criterion that each period the probability of exceeding the var must be independent of all the past information we introduce a new test of model adequacy the dynamic quantile test applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments

valuation of american call options on dividend paying stocks empirical tests abstract this paper examines the pricing performance of the valuation equation for american call options on stocks with known dividends and compares it with two suggested approximation methods the approximation obtained by substituting the stock price net of the present value of the escrowed dividends into the black scholes model is shown to induce spurious correlation between prediction error and 1 the standard deviation of stock return 2 the degree to which the option is in the money or out of the money 3 the probability of early exercise 4 the time to expiration of the option and 5 the dividend yield of the stock a new method of examining option market efficiency is developed and tested

the systematic risk of discretely rebalanced option hedges this paper demonstrates that black scholes option pricing model hedge positions that are risk free when rebalanced continuously will frequently exhibit substantial systematic risk when rebalanced at finite intervals this systematic risk may have biased important empir ical tests of the option pricing model moreover this systematic risk means that the blackscholes option pricing model is inherently inconsistent with the discrete time version of the capital asset pricing model capm