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

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

skill complexity and strategic interaction abstract we present a win loss game between players with explicitly modeled cognitive limitations differences in the players abilities to analyze the available moves induce preferences over the complexity of the environment and hence incentives to manipulate that complexity other things equal higher skill players are more likely to win in a class of long horizon games with constant complexity greater complexity reduces the advantage of the higher skill player when the higher skill player is the last mover when the lower skill player moves last increasing complexity induces countervailing effects either of which may dominate finally when complexity can be manipulated over the course of the game the benefits of strategic manipulation of complexity can override objective considerations about best move choice resulting in purposeful departures from subgame perfect nash equilibrium behavior

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 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

are renewable energy subsidies effective evidence from europe abstract we test if policy support for renewable electricity have been effective in promoting renewables in the five largest european countries in the period 2000 2010 we collect data on the exact amount of monetary incentives and the average tariffs granted the econometric analysis reveals a positive correlation between subsidies and the production of incentivized energy as well as the installed capacity we find that a 1 1c increase in the incentive tariff leads to an increase in renewable generation of 0 4 1 18 26 feed in tariffs appear to outperform tradable green certificates overall the analysis shows that these policies have been effective in promoting renewable energy both in the short and in the long run

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

information processing and bounded rationality a survey this paper surveys recent attempts to formulate a plausible and tractable model of bounded rationality the author focuses in particular on models that view bounded rationality as stemming from limited information processing he discusses partitional models such as computability automata perceptions and optimal networks nonpartitional models and axiomatic approaches

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

skill complexity and strategic behavior abstract boundedly rational players with differing skill are affected differently by complexity thus players have preferences for complexity that depend on their own skill and the skill of their opponents such preferences are likely to be important determinants of players choices to illustrate this paper analyzes a model where differently skilled players sort themselves across two person win draw loss games of differing complexity are randomly paired against opponents who have made similar choices and then play the games they have chosen

does economic growth eat up environmental improvements electricity production and fossil fuel emission in oecd countries 1980 2014 abstract we analyze to what extent electricity production by non fossil fuel replaces fossil fueled electricity production in 27 oecd countries 1980 2014 depending on model specification the long run replacement coefficient is in the range of minus 0 4 1 0 which is considerably larger than found in other studies this means that an increase in non fossil fuel based electricity production by 10 kwh capita replaces fossil fuel based production in the range 4 10 kwh capita over all the estimated replacement is not sufficient to prevent economic growth from increasing fossil based electricity production thus eating up environmental improvements however we identify two important exceptions to this first countries with a low level of fossil based production have an environmental kuznets curve ekc relationship when we allow for separate effects of the economic downturn after the great recession 2008 2009 second results for the eu countries indicate that the eu emission trading system and possibly eu country specific policy instruments have influenced the mix of electricity production in the intended direction

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

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

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

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

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

impact of income inequality and environmental regulation on environmental quality evidence from china abstract china s environmental pollution is of widespread concern and environmental governance has become the country s main method of achieving high quality development environmental quality is a comprehensive indicator which includes many factors such as air water and solid waste pollution this study did not use a single pollutant as a substitute variable for environmental quality firstly we used principal component analysis to construct a comprehensive environmental quality index secondly the stochastic impacts by regression on population affluence and technology and panel quantile regression models were used with data from 30 chinese provinces in china from 1998 to 2017 to analyze the effect of income inequality and environmental regulation on environmental quality the constructed comprehensive index revealed that china s environmental quality had an m type trend over time the mean regression results showed that income inequality and environmental regulation improved environmental quality but higher income inequality reduced environmental quality the panel quantile regression model results revealed that the coefficient of income inequality was positively significant at the 10 30 quantiles and negatively significant at the 70 90 quantiles the coefficients of the absolute value of income inequality at the 10 30 quantiles were less than those at the 70 90 quantiles this implied that higher income inequality reduced environmental quality whereas higher environmental regulations improved environmental quality considering the possible impact of environmental quality on income inequality and environmental regulations we designed a simultaneous equation model to overcome the deviation caused by bilateral causality the conclusions of this study provide policymakers with a new perspective on environmental governance and new paths for achieving high quality development

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

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

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