a spatial mean variance mip model for energy market risk analysis the paper presents a short term market risk model based on the markowitz mean variance method for spatial electricity markets the spatial nature is captured using the correlation of geographically separated markets and the consideration of wheeling administration the model also includes transaction costs and other practical constraints resulting in a mixed integer programming mip model the incorporation of those practical constraints makes the model more attractive than the traditional markowitz portfolio model with continuity a case study is used to illustrate the practical application of the model the results show that the mip portfolio efficient frontier is neither smooth nor concave the paper also considers the possible extension of the model to other energy markets including natural gas and oil markets

optimal replication of contingent claims under portfolio constraints we determine the minimum cost of superreplicating a nonnegative contingent claim when there are convex constraints on portfolio weights we show that the optimal cost with constraints is equal to the price of a related claim without constraints the related claim is a dominating claim that is a claim whose payoffs are increased in an appropriate way relative to the original claim the results hold for a variety of options including some path dependent options constraints on the gamma of the replicating portfolio constraints on portfolio amounts and constraints on the number of shares are also considered article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

delta hedging strategies comparison abstract in this paper we implement dynamic delta hedging strategies based on several option pricing models we analyze different subordinated option pricing models and we examine delta hedging costs using ex post daily prices of s p 500 furthermore we compare the performance of each subordinated model with the black scholes model

benchmarking portfolio insurance and technical analysis a monte carlo comparison of dynamic strategies of asset allocation abstract this paper makes an extensive simulation comparison of popular dynamic strategies of asset allocation for each strategy alternative measures have been calculated for risk return and risk adjusted performance sharpe ratio sortino ratio return at risk moreover the strategies are compared in different market situations bull bear no trend markets and with different market volatility taking into account transaction costs and discrete rebalancing of portfolios the simulations show a dominant role of constant proportion strategies in bear and no trend markets and a preference for benchmarking strategies in bull markets these results are independent of the volatility level and the risk adjusted measure adopted

comparing consumption based asset pricing models we make use of a recently developed method to estimate the intertemporal mar ginal rate of substitution consistent with the fluctuations of asset return data from the toronto stock exchange these estimates are then used to evaluate various parametric specifications for preferences often used in empirical studies of consumption and asset returns in contrast to existing studies we are able to perform a formal statistical comparison of these models we consider six extensions of the usual power utility model and we find that none can be said to be a demonstrable improvement on the standard model

small transaction cost asymptotics and dynamic hedging abstract transaction costs are one of the major impediments to the implementation of dynamic hedging strategies we consider an alternative to utility maximization similar to the good deal pricing framework in incomplete markets we perform a dynamic risk reward analysis for a family of non self financing strategies of practical importance deterministic time hedging i e hedging at predetermined fixed times in the limit of small relative transaction costs we carry out the asymptotic analysis and find that transaction costs affect the hedge ratios and that the time between trades is related in a simple way to the local sensitivities of the replication target

option pricing with transaction costs using a markov chain approximation an efficient algorithm is developed to price european options in the presence of proportional transaction costs using the optimal portfolio framework of davis in dempster m a h pliska s r eds mathematics of derivative securities cambridge university press cambridge uk a fair option price is determined by requiring that an infinitesimal diversion of funds into the purchase or sale of options has a neutral effect on achievable utility this results in a general option pricing formula in which option prices are computed from the solution of the investor s basic portfolio selection problem without the need to solve a more complex optimisation problem involving the insertion of the option payoff into the terminal value function option prices are computed numerically using a markov chain approximation to the continuous time singular stochastic optimal control problem for the case of exponential utility comparisons with approximately replicating strategies are made the method results in a uniquely specified option price for every initial holding of stock and the price lies within bounds which are tight even as transaction costs become large a general definition of an option hedging strategy for a utility maximising investor is developed this involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

on the mean variance tradeoff in option replication with transactions costs this paper analyzes the tradeoff between cost and risk of discretely rebalanced option hedges in the presence of transactions costs i present closed form solutions for expected hedging error transactions costs and variance of the cash flow from a time based hedging strategy similar to that analyzed by leland 1985 furthermore i characterize the cost and risk of a move based hedging strategy without resorting to monte carlo simulations all results are sufficiently general to accommodate the use of a transactions costs adjusted hedging volatility and an asset rate of return that differs from the risk free rate of return

option replication in discrete time with transaction costs option replication is discussed in a discrete time framework with transaction costs the model represents an extension of the cox ross rubinstein binomial option pricing model to cover the case of proportional transaction costs the method proceeds by constructing the appropriate replicating portfolio at each trading interval numerical values of these prices are presented for a range of parameter values the paper derives a simple black scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values

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 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

leverage constraints and the optimal hedging of stock and bond options this paper considers the problem of a financial institution that needs to hedge a stream of state contingent cash flows while facing borrowing and short sales restrictions the study determines analytically the strategy that minimizes the initial cost of hedging the desired cash flow which is also the upper bound on its market price and shows that the impact of leverage constraints on the cost of hedging call and put options is significant and therefore the biases detected by tests of option pricing models may not represent arbitrage opportunities the paper also shows that with credit limits it is optimal to reduce the rate of trading thus these constraints need to be recognized when estimating the trading volume generated in replicating contingent payoffs such as portfolio insurance

continuous time methods in finance a review and an assessment i survey and assess the development of continuous time methods in finance during the last 30 years the subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing term structure theory asset pricing and optimal consumption and portfolio choices during the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance this latter subperiod has seen significant progress in econometric theory computational and estimation methods to test and implement continuous time models capital market frictions and bargaining issues are being increasingly incorporated in continuous time theory the roots of modern continuous time methods in finance can be traced back to the seminal contributions of merton 1969 1971 1973b in the late 1960s and early 1970s merton 1969 pioneered the use of continuous time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting merton 1973b also showed how such a framework can be used to develop equilibrium asset pricing implications thereby significantly extending the asset pricing theory to richer dynamic settings and expanding the scope of applications of continuous time methods to study problems in financial economics 1 within a span of about 30 years from the publication of merton s inf luential papers continuous time methods have become an integral part of financial economics indeed in certain core areas in finance such as e g asset pricing derivatives valuation term structure theory and portfolio selection continuoustime methods have proved to be the most attractive way to conduct research and gain economic intuition the continuous time approach in these areas has produced models with a rich variety of testable implications the econometric theory for testing continuous time models has made rapid strides in the last decade and has thus kept pace with the impressive progress on the theoretical front one hopes that the actual empirical investigations and estimation using the new procedures will follow suit soon

optimal delta hedging under transactions costs this paper examines the problem of delta hedging portfolios of options under transactions costs by maximising expected utility or minimising a loss function on the replication error we extend the work of hodges and neuberger 1989 to study the optimal strategy under a general cost function with fixed and proportional costs a computational procedure for solving this problem is described and we develop an efficient computational method for the case of proportional transaction costs we examine the nature of the solution close to the expiry date and using simulation we compare the performance of the optimal strategies with other common strategies

using tucker s theorem of the alternative to simplify review and expand discrete arbitrage theory abstract for valuing derivatives and other assets in securities and commodities markets arbitrage pricing theory has been a major approach for decades this paper derives fundamental arbitrage pricing results in finite dimensions in a simple unified framework using tucker s theorem of the alternative frictionless results that is perfect market results plus imperfect market results such as those with dividends periodic interest payments transaction costs different interest rates for lending and borrowing shorting costs and constrained short selling are presented while the results are mostly known and appear in various places our contribution is to present them in a coherent and comprehensive fashion with very simple proofs the analysis yields a simple procedure to prove new results and some are presented for cases with imperfect market frictions

pricing methods and hedging strategies for volatility derivatives abstract we explore the valuation and hedging of discretely observed volatility derivatives using three different models for the price of the underlying asset geometric brownian motion with constant volatility a local volatility surface and jump diffusion we begin by comparing the effects on valuation of variations in contract design such as the differences between specifying log returns or actual returns and incorporating caps on the level of realized volatility we then focus on the difficulties associated with hedging these products delta hedging strategies are ineffective for hedging volatility derivatives since they require very frequent rebalancing moreover they provide limited protection in the jump diffusion context we study the performance of a hedging strategy for volatility swaps that establishes small fixed positions in vanilla options at each volatility observation

market making in the options markets and the costs of discrete hedge rebalancing in this paper we provide empirical evidence consistent with the hypothesis that options market makers face risks in managing inventory that are unique to the options markets in particular we show that risks associated with the inability to rebalance an option position continuously and uncertainty about the return volatility of the underlying stock each account for a statistically and economically significant proportion of the bid ask spreads quoted for a sample of chicago board options exchange options it is widely recognized that securities dealers face risk associated with inventory positions taken in the course of their trading activities for the equity dealer this has been shown both theoretically e g stoll 1978a ho and stoll 1983 and empirically e g stoll 1978b to depend on the stock s return volatility and the expected duration of the risk exposure in this paper we recognize that option dealers face an additional dimension of risk as a result of the option s stochastic return volatility and demonstrate that this option characteristic contributes to the cost of liquidity in the options market ho and stoll 1983 show that if the stock return volatility is constant the specialist s risk exposure per dollar of investment is nonstochastic over the interval during which the inventory is held in contrast unless the option dealer is able to trade continuously an option transaction s contribution to the dealer s risk exposure will be stochastic since the volatility of an option is a function of both its stochastic hedge ratio as well as the underlying stock s return volatility the problem that arises is particularly clear in the context of a dealer attempting to maintain a delta neutral exposure a strategy common among market makers in the options markets imagine a market maker who simultaneously buys 10 option contracts with a hedge ratio of 1 4 and sells 5

a note on an interest rate immunization strategy abstract the mechanisms for insuring investments in stocks and bonds against depreciation have grown rapidly in the last decade insuring a portfolio entails managing it in such a way that the left hand tail of the return distribution is truncated the present paper demonstrates how this may be achieved for fixed interest securities discrete time hedging procedures are derived with the inclusion of transaction costs

effectiveness of cppi strategies under discrete time trading abstract the paper analyzes the effectiveness of the constant proportion portfolio insurance cppi method under trading restrictions if the cppi method is applied in continuous time the cppi strategies provide a value above a floor level unless the price dynamics of the risky asset permit jumps the risk of violating the floor protection is called gap risk in practice it is caused by liquidity constraints and price jumps both can be modelled in a setup where the price dynamics of the risky asset are described by a continuous time stochastic process but trading is restricted to discrete time we propose a discrete time version of the continuous time cppi strategies which satisfies three conditions the resulting strategies are self financing the asset exposure is non negative and the value process converges we determine risk measures such as the shortfall probability and the expected shortfall and discuss criteria which ensure that the gap risk does not increase to a level which contradicts the original intention of portfolio insurance in addition we introduce proportional transaction costs and analyze their effects on the risk profile

transactions costs and portfolio choice in a discrete continuous time setting abstract this paper makes the following observation concerning a new formulation of the consumption and portfolio choice model of merton 1971 with transaction costs suppose an investor observes his or her current wealth only when making a transaction that transactions are costly and that decisions to transact can be made at any time based on all current information if at each transaction the agent is charged a fixed fraction of current portfolio value an optimal policy exists and the optimal interval of time between transactions is fixed independent of time and current wealth

sequential entry industry structure and welfare in this paper we reexamine the relationship between potential competition industry structure and welfare in a market subject to a sequential entry threat where firms can make quantity commitments and have access to a constant returns technology it is shown that provided entry is not blockaded the incumbent s will either prevent entry or allow all the potential entrants in furthermore actual entry may decrease but social welfare never goes down with more potential entrants nevertheless with a finite number of potential entrants policies which lower the cost of entry need not be beneficial in welfare terms

utility based option evaluation with proportional transaction costs abstract we examine the problem of finding investors reservation prices of european contingent claims in a continuous time finite horizon economy with proportional transaction costs we derive analytically numerous properties of reservation prices reflecting their dependency on the size of the option position the risk aversion and the initial wealth for the special case of hara utility functions we consider the so called marginal reservation prices i e unit reservation prices of infinitesimal positions of the contingent claim and prove that these are independent of the initial wealth and the parameters of the utility function except for the exponent furthermore we present numerical examples suggesting that the marginal reservation prices are for reasonable parameter values insensitive to the drift of the underlying security and the exponent of the hara utility function

primes and scores an essay on market imperfections this paper investigates the reported relative mispricing of primes and scores to the underlying stock given transaction costs we establish arbitrage based bounds on prime and score prices we then develop a new nonparametric statistical technique to test whether prime and score prices violate these bounds we find that prime and score prices do exceed stock prices and often by a considerable amount we demonstrate that this increased value is most likely due to the score s ability to save on the costs of dynamic hedging we also show how short sale and trust size constraints impede the ability to arbitrage price disparities in an efficient market the price of a security reflects the value of its underlying assets it should not be possible therefore to create value simply by splitting a security into different parts since the underlying assets are unchanged the packaging of the cash flows should not matter the recent introduction of primes and scores suggests that this is not always the case by separating a security s cash flows into a dividend based component the prime and an appreciation or option based component the score developers of these securities have seemingly created two assets whose value separately exceeds that of the original stock since the prime and the score are based on the same underlying asset this raises a puzzling question about the actual efficiency of securities markets this paper investigates this anomaly by examining whether primies and scores are actuauy mispriced and if so why given the costs of transacting in the prime score and stock we establish bounds on prime and score prices that are consistent with no arbitrage opportunities we then develop a new nonparametric statistical technique to test whether prime and score prices violate these bounds this nonparametric procedure is designed both to confront the measurement error problems plaguing the literature i e nonobservable bid ask prices and nonsimultaneous prices see phillips and smith 1980 bhattacharya 1983 and bookstaber 1981 and to avoid the estimation of round trip transaction costs commissions we find the surprising result that prime and score prices exceed the price of the underlying stock often by a considerable amount using time series data we de monstrate that significant price differentials exist for each firm in our sample

tractable hedging an implementation of robust hedging strategies abstract this paper analyzes tractable robust hedging strategies in diffusion type models including stochastic volatility models a robust hedging strategy avoids any losses as long as volatility stays within a given interval it does not depend on the exact specification of the volatility process and therefore mitigates problems caused by model misspecification a tractable hedging strategy is defined as the sum over black scholes strategies for a convex concave payoff the cheapest robust hedge is given by a bs hedge at the upper lower volatility bound thus it is tractable for all other payoffs one has to solve a black scholes barenblatt equation and the cheapest robust hedge is not tractable a tractable hedge can then be found by decomposing the payoff into a convex and a concave function each of which is hedged separately we first give the decomposition that minimizes the initial capital second we show that it may be even cheaper to hedge a dominating payoff and we show explicitly how to determine the optimal dominating payoff we illustrate our results by two examples

misspecification and the pricing and hedging of long term foreign currency options abstract this study examines the effects of stochastic volatility upon the pricing and hedging of long term foreign currency options the traditional method of pricing such options uses a constant volatility option model with an implicit volatility derived from a short term traded option we show that the traditional method leads to small pricing errors for short and medium term options but does a poor job in pricing long term options the traditional method also does a poor job for all maturities in determining the derivatives of the option s value with respect to the exchange rate delta and the volatility vega the errors in calculating these derivatives which are used in forming the replicating portfolio lead to large and costly errors in error hedging

hedging options under transaction costs and stochastic volatility in this paper we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility extensive research has clearly demonstrated that the volatility of most stocks is not constant over time as small changes of the volatility can have a major impact on the value of contingent claims hedging strategies should try to eliminate this volatility risk we propose a stochastic optimization model for hedging contingent claims that takes into account the effects of stochastic volatility transaction costs and trading restrictions simulation results show that our approach could improve performance considerably compared to traditional hedging strategies

or forum the cost of latency in high frequency trading modern electronic markets have been characterized by a relentless drive toward faster decision making significant technological investments have led to dramatic improvements in latency the delay between a trading decision and the resulting trade execution we describe a theoretical model for the quantitative valuation of latency our model measures the trading frictions created by the presence of latency by considering the optimal execution problem of a representative investor via a dynamic programming analysis our model provides a closed form expression for the cost of latency in terms of well known parameters of the underlying asset we implement our model by estimating the latency cost incurred by trading on a human time scale examining nyse common stocks from 1995 to 2005 shows that median latency cost across our sample roughly tripled during this time period furthermore using the same data set we compute a measure of implied latency and conclude that the median implied latency decreased by a

option pricing and replication with transactions costs transactions costs invalidate the black scholes arbitrage argument for option pricing since continuous revision implies infinite trading discrete revision using black scholes deltas generates errors which are correlated with the market and do not approach zero with more frequent revision when transactions costs are included this paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision hedging errors are uncorrelated with the market and approach zero with more frequent revision the technique permits calculation of the transactions costs of option replication and provides bounds on option prices

the american put under transactions costs abstract this paper examines the optimal super replication of american put options with physical delivery of the underlying asset such as stock options by means of a stock plus riskless asset portfolio the framework of the analysis is the binomial model with proportional transactions costs on stock transactions the paper extends the model for european options originally presented in merton geneva papers risk insurance 14 1989 225 and boyle and vorst j of finance 47 1992 271 and generalized in bensaid et al math finance 2 1992 63 the optimizing framework of this latter study is adapted to put options held by investors and perfectly hedged by a market maker and to put options written by investors and both held and hedged perfectly by a market maker it is shown that a unique optimal super replicating portfolio exists at every node of the binomial tree for the long option as well as for the short option when transactions costs are low

robust option pricing hannan and blackwell meet black and scholes we apply methods developed in the literature initiated by hannan and blackwell on robust optimization approachability and calibration to price financial securities rather than focus on asymptotic performance we show how gradient strategies developed to minimize asymptotic regret imply financial trading strategies that yield arbitrage based bounds for option prices these bounds are new and robust in that they do not depend on the continuity of the stock price process complete markets or an assumed pricing kernel they depend only on the realized quadratic variation of the price process which can be measured and importantly hedged in financial markets using existing securities our results also apply directly to a new class of options called timer options finally we argue that the hannan blackwell strategy is path dependent and therefore suboptimal with a finite horizon we improve it by solving for the optimal path independent strategy and compare the resulting bounds with black scholes

dynamic hedging under jump diffusion with transaction costs if the price of an asset follows a jump diffusion process the market is in general incomplete in this case hedging a contingent claim written on the asset is not a trivial matter and other instruments besides the underlying must be used to hedge in order to provide adequate protection against jump risk we devise a dynamic hedging strategy that uses a hedge portfolio consisting of the underlying asset and liquidly traded options where transaction costs are assumed present due to a relative bid ask spread at each rebalance time the hedge weights are chosen to simultaneously i eliminate the instantaneous diffusion risk by imposing delta neutrality and ii minimize an objective that is a linear combination of a jump risk and transaction cost penalty function because reducing the jump risk is a competing goal vis a vis controlling for transaction cost the respective components in the objective must be appropriately weighted hedging simulations of this procedure are carried out and our results indicate that the proposed dynamic hedging strategy provides sufficient protection against the diffusion and jump risk while not incurring large transaction costs

stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs by applying stochastic dominance arguments upper bounds on the reservation write price of european calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security the primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option a tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put these results jointly impose tight upper and lower bounds on the implied volatility

hedging demand and market intraday momentum hedging short gamma exposure requires trading in the direction of price movements thereby creating price momentum using intraday returns on over 60 futures on equities bonds commodities and currencies between 1974 and 2020 we document strong market intraday momentum everywhere the return during the last 30 minutes before the market close is positively predicted by the return during the rest of the day from previous market close to the last 30 minutes the predictive power is economically and statistically highly significant and reverts over the next days we provide novel evidence that links market intraday momentum to the gamma hedging demand from market participants such as market makers of options and leveraged etfs

call option pricing and replication under economic friction in this paper we incorporate multiple transactions costs in the option pricing formula of black and scholes 1972 the effect of introducing economic friction in the equilibrium equation is studied and summarized in some central propositions the analysis provides part of the results needed for capturing the economic effects of transactions costs in the pricing process

optimal replication of options with transactions costs and trading restrictions this paper analyzes the strategy that minimizes the initial cost of replicating a contingent claim in a market with transactions costs and trading constraints the linear programming and two stage backward recursive models developed are applicable to the replication of convex as well as nonconvex payoffs and to a portfolio of options with different maturities the paper s formulation conveniently accounts for fixed and variable transactions costs lot size constraints and position limits on trading the article shows that in the presence of trading frictions it is no longer optimal to revise one s portfolio in each period at the optimum cash flows in excess of the desired ones may be generated the optimal policy trades off the curvature of the payoff that is generated against the terminal slack

hedging demands in hedging contingent claims minimum variance hedging of a contingent claim in discrete time is suboptimal when the contingent claim is hedged for multiple periods and the objective is to maximize the expected utility of cumulative hedging errors this is because the hedging errors are not independent the difference between a minimum variance hedge and the optimal multiperiod hedge is called the hedging demand and depends on the hedger s preferences the characteristics of the contingent claim the trading frequency and horizon and most importantly the joint distribution of the contingent claim and the underlying security prices since modeling this joint distribution is empirically controversial i examine nonparametrically the economic importance of hedging demands in the case of hedging standard poor s 500 index options

performance evaluation of portfolio insurance strategies using stochastic dominance criteria abstract this paper evaluates the performance of the stop loss synthetic put and constant proportion portfolio insurance techniques based on a block bootstrap simulation we consider not only traditional performance measures but also some recently developed measures that capture the non normality of the return distribution value at risk expected shortfall and the omega measure we compare them to the more comprehensive stochastic dominance criteria the impact of changing the rebalancing frequency and level of capital protection is examined we find that even though a buy and hold strategy generates higher average excess returns it does not stochastically dominate the portfolio insurance strategies nor vice versa our results indicate that a 100 floor value should be preferred to lower floor values and that daily rebalanced synthetic put and cppi strategies dominate their counterparts with less frequent rebalancing

the price of options illiquidity the purpose of this paper is to examine the effect of illiquidity on the value of currency options we use a unique dataset that allows us to explore this issue in special circumstances where options are issued by a central bank and are not traded prior to maturity the value of these options is compared to similar options traded on the exchange we find that the nontradable options are priced about 21 percent less than the exchange traded options this gap cannot be arbitraged away due to transactions costs and the risk that the exchange rate will change during the bidding process

option prices under bayesian learning implied volatility dynamics and predictive densities abstract this paper shows that many of the empirical biases of the black and scholes option pricing model can be explained by bayesian learning effects in the context of an equilibrium model where dividend news evolve on a binomial lattice with unknown but recursively updated probabilities we derive closed form pricing formulas for european options learning is found to generate asymmetric skews in the implied volatility surface and systematic patterns in the term structure of option prices data on s p 500 index option prices is used to back out the parameters of the underlying learning process and to predict the evolution in the cross section of option prices the proposed model leads to lower out of sample forecast errors and smaller hedging errors than a variety of alternative option pricing models including black scholes and a garch model

an extension of the black scholes model of security valuation abstract this paper provides a formula for the market value of a security whose dividends and liquidation value depend on securities with diffusion dividend and price processes the solution is in terms of the feynman kac formula solving the partial differential equation determining the derivative sucurity s unique arbitrage free value the interest rate process may be stochastic markets need not be dynamically complete

dollar jump fears 1984 1992 distributional abnormalities implicit in currency futures options abstract deutsche mark and yen futures options over 1984 1992 and 1986 1992 respectively are examined for deviations from the lognormal assumption underlying standard option pricing models two methods are used an atheoretic skewness premium and daily estimates of moments using a model for pricing american foreign currency futures options under systematic exchange rate jump risk substantial variation over time is found in all moments including implicit skewness and kurtosis the implicit abnormalities predict future abnormalities in log differenced dm futures prices but not yen the peso problem implications do not explain standard rejections of uncovered interest parity

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

static hedging of multivariate derivatives by simulation we propose an approximate static hedging procedure for multivariate derivatives the hedging portfolio is composed of statically held simple univariate options optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio the method uses simulated paths to estimate the weights of the hedging portfolio and is related to monte carlo control variates techniques we report numerical results showing the performance of this static hedging procedure on bivariate options on the maximum of two assets and on 2 and 7 dimensional portfolio options it is shown that in the presence of transaction costs value at risk and expected shortfall of the dynamically hedged positions can be higher than the ones obtained by a static hedge

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

option hedging theory under transaction costs abstract the problem of option hedging in the presence of proportional transaction costs can be formulated as a singular stochastic control problem hodges and neuberger 1989 optimal replication of contingent claims under transactions costs review of futures markets 8 222 239 introduced an approach that is based on maximization of the expected utility of terminal wealth we develop a new algorithm to solve the corresponding singular stochastic control problem and introduce a new approach to option hedging which is closer in spirit to the pathwise replication of black and scholes 1973 the pricing of options and corporate liabilities journal of political economy 81 637 654 this new approach is based on minimization of a black scholes type measure of pathwise risk defined in terms of a market delta subject to an upper bound on the hedging cost we provide an efficient backward induction algorithm for the problem of cost constrained risk minimization whose associated singular stochastic control problem is shown to be equivalent to an optimal stopping problem this algorithm is then modified to solve the singular stochastic control problem associated with utility maximization which cannot be reduced to an optimal stopping problem we propose to choose an optimal parameter risk aversion coefficient or lagrange multiplier in either approach by minimizing the mean squared hedging error and demonstrate that with this best choice of the parameter both approaches have similar performance we also discuss the different notions of risk in both approaches and propose a volatility adjustment for the risk minimization approach which is analogous to that introduced by zakamouline 2006 european option pricing and hedging with both fixed and proportional transaction costs journal of economic dynamics and control 30 1 25 for the utility maximization approach thereby providing a unified treatment of both approaches

hedging derivative securities and incomplete markets an e arbitrage approach given a european derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based we solve the optimal replication problem find a self financing dynamic portfolio strategy involving only the underlying securities that most closely approximates the payoff function at maturity by applying stochastic dynamic programming to the minimization of a mean squared error loss function under markov state dynamics we derive recursive expressions for the optimal replication strategy that are readily implemented in practice the approximation error or e of the optimal replication strategy is also given recursively and may be used to quantify the degree of market incompleteness to investigate the practical significance of these e arbitrage strategies we consider several numerical examples including path dependent options and options on assets with stochastic volatility and jumps