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

lp modeling for asset liability management a survey of choices and simplifications dynamic linear programming lp models for asset liability management alm are quite powerful and flexible but face two challenges 1 many modeling choices not all consistent with one another or with finance theory and 2 solution difficulties due to the large number of scenarios obtained from standard interest rate models we first survey these modeling choices with a view to help researchers make self consistent choices next we review how the dynamic lp model for alm and the representation of uncertainty therein have been simplified in the past to motivate new or hybrid models emphasizing tractability to this end we review existing static lp models as extreme modeling simplifications and aggregation as a simplification of uncertainty

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

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

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

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

financial asset pricing theory and stochastic programming models for asset liability management a synthesis practical portfolio investment problems under uncertainty can be modeled well as multiperiod stochastic programs however the numerical optimization methods that need to be used to solve such models seriously limit the level of detail in the uncertainty about future asset rices and returns that can be incorporated somewhat surprisingly the question how this necessarily approximate description of the uncertainty should be constructed has received relatively little attention in the stochastic programming literature moreover many of the descriptions that have been used are not arbitrage free and therefore inconsistent with modern financial asset pricing theory in this paper we will present aggregation methods that can be used in combination with financial asset pricing models to obtain a description of the uncertainty that is arbitrage free consistent with observed market prices as well as concise enough for a stochastic programming model furthermore we will discuss how these aggregation methods can form the basis of an iterative solution approach

pricing and hedging in incomplete markets abstract we present a new approach for positioning pricing and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable by assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure we derive a counterpart to the first fundamental theorem of asset pricing we also derive a counterpart to the second fundamental theorem which leads to unique derivative security pricing and hedging even though markets are incomplete for products that are not spanned by the liquid assets of the economy we show how our methodology provides more realistic bid ask spreads

trading cost the critical link between investment information and results 1983 trading cost the critical link between investment information and results financial analysts journal vol 39 no 3 pp 39 44

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

expected gain loss pricing and hedging of contingent claims in incomplete markets by linear programming abstract we analyze the problem of pricing and hedging contingent claims in the multi period discrete time discrete state case using the concept of a gain loss ratio opportunity pricing results somewhat different from but reminiscent of the arbitrage pricing theorems of mathematical finance are obtained our analysis provides tighter price bounds on the contingent claim in an incomplete market which may converge to a unique price for a specific value of a gain loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade the results are obtained in the simpler framework of stochastic linear programming in a multi period setting and have the appealing feature of being very simple to derive and to articulate even for the non specialist they also extend to markets with transaction costs

an exact solution to a dynamic portfolio choice problem under transactions costs the presence of any friction in financial markets qualitatively changes the nature of the optimization problem faced by an investor it requires one to either act or do nothing an issue which of course does not arise in frictionless situations the investor considered here accumulates wealth without consuming until some terminal point in time when he consumes all his objective is to maximize the expected utility derived from that terminal consumption we postpone the terminal point far into the future to obtain a stationary portfolio rule the portfolio policy is in the form of two control barriers between which portfolio proportions are allowed to fluctuate we show how to calculate them

markets that don t replicate any option abstract it is well known from the work of s ross that a securities market is complete if and only if each call option can be replicated using available securities the present short note announces the following surprising complementary result to ross important contribution if the number of securities is less than half the number of states of the world then generically not a single option can be replicated by traded securities this provides further strong motivation for relaxing the assumption of a perfect market in the theory of option pricing and portfolio insurance

habit persistence and the harberger laursen metzler effect in an infinite horizon model abstract the habit persistence model of ryder and heal is used to examine the harberger laursen metzler h l m effect our results are in contrast to the general view in the literature that the stability requirements preclude the h l m effect in an infinite horizon model we show that if the marginal utility of real consumption is strongly increasing in the habitual standard of living then the h l m effect holds and a terms of trade deterioration reduces savings however if the marginal utility of real consumption is not sufficiently strongly increasing or is decreasing in the habitual standard then the h l m effect is overturned

presidential address does finance benefit society academics view of the benefits of finance vastly exceeds societal perception this dissonance is at least partly explained by an underappreciation by academia of how without proper rules finance can easily degenerate into a rent seeking activity i outline what finance academics can do from a research point of view and from an educational point of view to promote good finance and minimize the bad

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

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

optimality of myopic strategies for multi stock discrete time market with management costs the paper studies multi stock discrete time market models with serial correlations and with some management costs we found a market structure that ensures that the optimal strategy is myopic for the case of either power or log utility function

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

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

pricing options in an extended black scholes economy with illiquidity theory and empirical evidence this article studies the pricing of options in an extended black scholes economy in which the underlying asset is not perfectly liquid the resulting liquidity risk is modeled as a stochastic supply curve with the transaction price being a function of the trade size consistent with the market microstructure literature the supply curve is upward sloping with purchases executed at higher prices and sales at lower prices optimal discrete time hedging strategies are then derived empirical evidence reveals a significant liquidity cost intrinsic to every option copyright 2006 oxford university press

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

effective securities in arbitrage free markets with bid ask spreads at liquidation a linear programming characterization abstract we consider a securities market with bid ask spreads at any period including liquidation although the minimum cost super replication problem is non linear we introduce an auxiliary problem that allows us to characterize no arbitrage via linear programming techniques we introduce the notion of effective new security and show that effectiveness restricts the no arbitrage bid and ask prices of a new security to the interval defined by the minimum cost problem we discuss in detail the cases in which the boundaries of this interval can be reached without violating no arbitrage

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