price adjustment in long term contracts the case of coal in two recent papers i examined the effects of relationship specific investment on the duration of contracts negotiated between electric utilities and coal suppliers that work demonstrated that when relationshipspecific investment is important for a cost minimizing supply relationship contracts are frequently utilized that specify ex ante the terms and conditions of trade over many future years in this article i examine the characteristics of the price adjustment provisions specified in these long term coal contracts i utilize a sample of about 250 coal contracts to analyze the structure of formal price adjustment provisions in coal contracts in order to determine the factors that affect initial negotiated contract prices and to examine actual transaction price behavior over time there has been much recent theoretical work as well as some related empirical work that has focused on the benefits of long term contracts when relationship specific investments are important 2 there has also been some theoretical work that focuses on the contractual arrangements that may be chosen to mitigate opportunism problems and guard against

the early exercise of american puts abstract this paper shows that american puts on dividend paying stocks are most likely to be exercised either just after an ex dividend date or just prior to expiration at any other time the option to exercise an american put early may have less value thus put writers and converters can predict when protection against premature exercise will be most valuable the probability of early exercise is shown to be sensitive to managerial policy regarding the suspension of dividend payments transaction costs and interest rates however dividend payments are demonstrated to be the primary deterrent to early exercise

intellectual property rights strategic technology agreements and market structure the case of gsm this paper investigates the role of intellectual property rights iprs in shaping the gsm industry this industry is an example of a high tech industry in which standards play a large role in the process of designing the gsm standard a lot of attention has been given to iprs mainly to avoid a situation in which a single ipr holder could hamper or even totally block the development of the standard nevertheless the ultimate gsm standard contains a large amount of so called essential iprs i e iprs without which the implementation of gsm products is impossible the paper starts with a general discussion of the development of gsm and the role of firm strategy and iprs in this process next we present a database on the essential iprs in the gsm standard this database has been compiled on the basis of international patent statistics and the data that manufacturers have supplied to etsi the european standardization body re sponsible for defining the gsm standard we use this database to assess the dynamic ipr position of firms in the original gsm standard and its subsequent development in a next part of our analysis we relate the firm s ipr p osition to the trends in strategic technology agreements in the mobile telecommunications field we ask the question whether firms that are powerful in terms of iprs are also the firms that are central in the technology agreements network or vice versa we also investigate whether developments over time in the technology agreements data follow from the dynamic movements in the ipr position of a firm and which other factors play a role in this

static hedging of exotic options this paper develops static hedges for several exotic options using standard options the method relies on a relationship between european puts and calls with different strike prices the analysis allows for constant volatility or for volatility smiles or frowns

computing the constant elasticity of variance option pricing formula this paper expresses the constant elasticity of variance option pricing formula in terms of the noncentral chi square distribution this allows the application of well known approximation formulas and the derivation of a whole class of closed form solutions in addition a simple and efficient algorithm for computing this distribution is presented this paper shows that the constant elasticity of variance cev formula can be expressed as a function of the noncentral chi square distribution a simple and efficient algorithm for computing this distribution is presented approximations to this distribution can be used to estimate accurately the cev formula when the computation of the exact solution is problematic section i discusses theories and some evidence on the association between volatility and price level section ii presents the particular kind of relationship assumed by the cev model and reviews empirical evidence on the model section iii shows that the cev formula can be expressed in terms of the noncentral chisquare distribution a simple algorithm for computing this distribution is derived in section iv section v presents some special closed form solutions to this distribution finally section vi shows that an approximation to the cev formula can be used when the exact solution converges slowly i relationship between volatility and price level several theoretical arguments imply an association between stock price and volatility geske 11 black 3 and christie 5 consider the effects of financial leverage on the variance of the stock an increase in the stock price reduces the debt equity ratio of the firm and therefore reduces the variance of the stock s returns black hypothesizes that price changes may also affect volatility through their impact on operating leverage in addition he proposes a reverse causal relationship whereby an increase in the volatility of stocks causes prices to fall in rubinstein s 171 displaced diffusion model the relation between price and volatility of returns depends on the firm s asset mix and debt equity ratio empirical evidence supports the hypothesis that volatility changes with stock price schmalensee and trippi 19 examining just over a year of weekly data on six stocks find a strong negative relationship between stock price changes and changes in implied volatility black 3 using over ten years of data on thirty stocks finds that a given proportional increase decrease in stock price is

technology as a complex adaptive system evidence from patent data this paper develops a theory of invention by drawing on complex adaptive systems theory we see invention as a process of recombinant search over technology landscapes this framing suggests that inventors might face a complexity catastrophe when they attempt to combine highly interdependent technologies our empirical analysis of patent citation rates supports this expectation our results also suggest however that the process of invention differs in important ways from biological evolution we discuss the implications of these findings for research on technological evolution industrial change and technology strategy 2001 elsevier science b v all rights reserved

pretia ex machina prices and process in long term contracts aimong the primary motives for writing contracts identified in both the law and economics literatures is the desire to protect against the hazards inherent to exchange where one or both parties have invested in reliance or relationship specific assets in support of the transaction because such investments have a higher value in their intended than in their next best use parties have an incentive to engage in haggling or other forms of opportunism in hopes of influencing the distribution of the resulting quasi rents contracts promote efficiency by securing the distribution of those rents ex ante thereby avoiding costly repetitive bargaining over the terms of trade and reducing the risk for each party of relying on the performance of the other in reality this description of the role and functioning of contracting is oversimplified as a number of legal and economic scholars have emphasized contracts are not the precise mechanically enforced documents often encountered in economic theory 2 indeed contracts are extremely

the american put option valued analytically an analytic solution to the american put problem is derived herein the hedge ratio and other derivatives of the solution are presented the formula derived implies an exact duplicating portfolio for the american put consisting of discount bonds and stock sold short the formula is extended to consider put options on stocks paying cash dividends a polynomial expression is developed for evaluating these formulae values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated tabulated and compared with values derived by numerical integration and binomial approximation as with european options evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods finally applications of this american put solution are discussed

entry and competitive dynamics in the mobile telecommunications market abstract we propose an extension of the gans stern gans j s stern s 2003 the product market and the market for ideas commercialization strategies for technology entrepreneurs research policy 32 2 333 350 framework that includes entry by existing firms an incumbent firm possessing complementary assets and strong appropriability is in a formidable position teece d j 1986 profiting from technological innovation implications for integration collaboration licensing and public policy research policy 15 6 285 305 however a de alio entrant can leverage complementary assets to enter along a new technological trajectory and then develop appropriability we illustrate how several mobile telecommunications firms ericsson nokia and samsung pursued this strategy to catch up with the market leader motorola we also identify several shortcomings in motorola s approach it was too inward looking in developing technologies but ironically not inward looking enough in exploiting its most valuable patents

conditioning on one step survival for barrier option simulations pricing financial options often requires monte carlo methods one particular case is that of barrier options whose payoff may be zero depending on whether or not an underlying asset crosses a barrier during the life of the option this paper develops variance reduction techniques that take advantage of the special structure of barrier options and are appropriate for general simulation problems with similar structure we use a change of measure at each step of the simulation to reduce the variance arising from the possibility of a barrier crossing at each monitoring date the paper details the theoretical underpinnings of this method and evaluates alternative implementations when exact distributions conditional on one step survival are available and when not available when these one step conditional distributions are unavailable we introduce algorithms that combine change of measure and estimation of conditional probabilities simultaneously the methods proposed are more generally applicable to terminal reward problems on markov processes with absorbing states

pricing and static hedging of american style options under the jump to default extended cev model abstract this paper prices and hedges american style options through the static hedge approach shp proposed by chung and shih 2009 and extends the literature in two directions first the shp approach is generalized to the jump to default extended cev jdcev model of carr and linetsky 2006 and plain vanilla american style options on defaultable equity are priced the robustness and efficiency of the proposed pricing solutions are compared with the optimal stopping approach offered by nunes 2009 under both the jdcev framework and the nested constant elasticity of variance cev model of cox 1975 using different elasticity parameter values second the early exercise boundary near expiration is derived under the jdcev model

static hedging and pricing american knock in put options abstract this paper extends the static hedging portfolio shp approach of derman et al 1995 carr et al 1998 to price and hedge american knock in put options under the black scholes model and the constant elasticity of variance cev model we use standard european calls puts to construct the shps for american up and in down and in puts we also use theta matching condition to improve the performance of the shp approach numerical results indicate that the hedging effectiveness of a bi monthly shp is far less risky than that of a delta hedging portfolio with daily rebalance the numerical accuracy of the proposed method is comparable to the trinomial tree methods of ritchken 1995 boyle and tian 1999 furthermore the recalculation time the term is explained in section 1 of the option prices is much easier and quicker than the tree method when the stock price and or time to maturity are changed

innovation in israel 1968 1997 a comparative analysis using patent data abstract the israeli high tech sector is widely regarded as a hotbed of cutting edge technologies and as the growth engine of the israeli economy in the 1990s and beyond in this paper we present a close up portrait of innovation in israel for the past 30 years with the aid of highly detailed patent data we use for that purpose all israeli patents taken in the us over 7000 as well as us patents and patents from other countries for comparative purposes the time path of israeli patenting reveals big jumps in the mid 1980s and then again in the early 1990s reflecting underlying shocks in policy and in the availability of relevant inputs israeli ranks high in terms of patents per capita compared to the g7 the asian tigers and a group of countries with similar gdp per capita finland is strikingly similar taiwan s patenting has grown extremely fast and is now on par with israel south korea is rapidly closing the gap the technological composition of israeli innovations reflects quite well worldwide technological trends except that computers and communications the fastest growing field in the us has grown even faster in israel the weak side resides in the composition of israeli assignees the actual owners of the intellectual property rights just 35 of israeli patents were assigned to israeli corporations a much lower percentage than in most other countries relatively large shares went to foreign assignees to universities and the government and to private inventors on the other hand israeli patents are of good quality in terms of citations received and getting better over time us patents command on average more citations but not in computers and communications or in biotechnology and israeli patents are significantly better than those of the reference group of countries

dominance by birthright entry of prior radio producers and competitive ramifications in the u s television receiver industry the u s television receiver industry evolved to be an oligopoly dominated by firms that produced radios prior to tvs data on the experience of all u s radio manufacturers and on the length of survival and rate of innovation of all u s tv entrants are collected to analyze how radio experience influenced entry firm performance and the evolution of market structure in the tv industry consistent with a model of the evolution of an oligopolistic industry more experienced radio firms were more likely to enter tv manufacturing had higher innovation rates and in turn had greater market shares and longer survival suggesting that firm capabilities and the evolution of the tv industry s market structure were critically shaped by firms experience prior to entry copyright 2000 john wiley sons ltd

pricing and hedging path dependent options under the cev process much of the work on path dependent options assumes that the underlying asset price follows geometric brownian motion with constant volatility this paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations we use the so called constant elasticity of variance cev diffusion model where the volatility is a function of the underlying asset price we derive analytical formulae for the prices of important types of path dependent options under this assumption we demonstrate that the prices of options which depend on extrema such as barrier and lookback options can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path dependent options

universal option valuation using quadrature methods abstract this paper proposes and develops a novel simple widely applicable numerical approach for option pricing based on quadrature methods though in some ways similar to lattice or finite difference schemes it possesses exceptional accuracy and speed discretely monitored options are valued with only one timestep between observations and nodes can be perfectly placed in relation to discontinuities convergence is improved greatly in the extrapolated scheme a doubling of points can reduce error by a factor of 256 complex problems e g fixed strike lookback discrete barrier options can be evaluated accurately and orders of magnitude faster than by existing methods

systematic equity based credit risk a cev model with jump to default we use equity as the traded primitive for a detailed analysis of systematic default risk default is parsimoniously represented by equity value hitting the zero barrier so that unlike in reduced form models the explicit linkage to the firm s capital structure is preserved but unlike in structural models restrictive assumptions on the structure are avoided default risk is either jump like or diffusive the equity price can jump to default in line with recent empirical evidence on the jump to default risk price we highlight how reasonable choices of the pricing kernel can imply remarkable differences in the equity price dependent status between the objective default intensity and the risk neutral intensity as equity returns experience negative diffusive shocks their cev type local variance increases and boosts the objective and risk neutral probabilities of diffusive default a parsimonious version of our general model simultaneously enables analytical credit risk management and analytical pricing of credit sensitive instruments easy cross asset hedging ensues

the crash of ʼ87 was it expected the evidence from options markets transactions prices of s p 500 futures options over 1985 1987 are examined for evidence of expectations prior to october 1987 of an impending stock market crash first it is shown that out of the money puts became unusually expensive during the year preceding the crash second a model is derived for pricing american options on jump diffusion processes with systematic jump risk the jump diffusion parameters implicit in options prices indicate that a crash was expected and that implicit distributions were negatively skewed during october 1986 to august 1987 both approaches indicate no strong crash fears during the 2 months immediately preceding the crash attempts to explain what caused the stock market crashes around the world in october 1987 have suffered from the paucity of major economic developments occurring around that time that could have triggered the crashes shifting expectations regarding monetary policy foreign investors fears of a dollar decline increasing riskiness of assets none of these appeared major enough if present at all to explain the magnitude of the crashes and although portfolio insurance strategies could conceivably magnify the effects of a jump in fundamentals the initiating jump in fundamentals appears to be lacking

revisiting corporate growth options in the presence of state dependent cashflow risk abstract given a non trivial market price of risk we study the impact of state dependent cashflow risk on the optimal investment policy and on the ensuing value of an unlevered firm that holds the option of scaling up cashflows from its assets in place upon incurring an irreversible cost the firm s investment decision and value are studied as a function of the market price of risk and of the degree of state dependence in cashflow risk

pricing lookback and barrier options under the cev process this paper examines the pricing of lookback and barrier options when the underlying asset follows the constant elasticity of variance cev process we construct a trinomial method to approximate the cev process and use it to price lookback and barrier options for look back options we find that the technique proposed by babbs for the lognormal case can be modified to value lookbacks when the asset price follows the cev process we demon strate the accuracy of our approach for different parameter values of the cev process we find that the prices of barrier and lookback options for the cev process deviate sig nificantly from those for the lognormal process for standard options the corresponding differences between the cev and black scholes models are relatively small our results show that it is much more important to have the correct model specification for options that depend on extrema than for standard options

pde methods for pricing barrier options abstract this paper presents an implicit method for solving pde models of contingent claims prices with general algebraic constraints on the solution examples of constraints include barriers and early exercise features in this unified framework barrier options with or without american style features can be handled in the same way either continuously or discretely monitored barriers can be accommodated as can time varying barriers the underlying asset may pay out either a constant dividend yield or a discrete dollar dividend the use of the implicit method leads to convergence in fewer time steps compared to explicit schemes this paper also discusses extending the basic methodology to the valuation of two asset barrier options and the incorporation of automatic time stepping

the pricing of leverage products an empirical investigation of the german market for long and short stock index certificates abstract this paper describes the first thorough empirical analysis of the pricing of leverage products in the german retail market these mainly exchange traded products with an impressive trading volume are frequently advertised as long and short futures contracts although they are theoretically equivalent to one sided barrier options issuers daily quotes for stock index products are compared to i theoretical values derived from the prices of eurex options and to ii boundaries obtained from semi static superhedging strategies for the vast majority of products bid and ask quotes significantly exceed both theoretical values and upper hedging boundaries thus providing almost risk free profits for the issuers

are structured products fairly priced an analysis of the german market for equity linked instruments abstract based on a unique data set this paper examines the pricing of equity linked structured products in the german market the daily closing prices of a large variety of structured products are compared to theoretical values derived from the prices of options traded on the eurex european exchange for the majority of products the study reveals large implicit premiums charged by the issuing banks in the primary market a set of driving factors behind the issuers pricing policies is identified for example underlying and type of implicit derivative s for the secondary market the product life cycle is found to be an important pricing parameter

pricing options on scalar diffusions an eigenfunction expansion approach this paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes all contingent claims are unbundled into portfolios of primitive securities calledeigensecurities eigensecurities are eigenvectors eigenfunctions of the pricing operator present value operator all computational work is at the stage of finding eigenvalues and eigenfunctions of the pricing operator the pricing is then immediate by the linearity of the pricing operator and the eigenvector property of eigensecurities to illustrate the computational power of the method we develop two applications pricing vanilla single and double barrier options under the constant elasticity of variance cev process and interest rate knock out options in the cox ingersoll ross cir term structure model

going to extremes correcting simulation bias in exotic option valuation monte carlo simulation is widely used in practice to value exotic options for which analytical formulas are not available when valuing those options that depend on extreme values of the underlying asset convergence of the standard simulation is slow as the time grid is refined and even a daily simulation interval produces unacceptable errors this article suggests approximating the extreme value on a subinterval by a random draw from the known theoretical distribution for an extreme of a brownian bridge on the same interval this approach provides reliable option values and retains the flexibility of simulations in that it allows great freedom in choosing a price process for the underlying asset or a joint process for the asset price its volatility and other asset prices

structure and price adjustments in long term contracts the case of coking coal trade in the asian pacific market abstract much of the trade in resource goods takes place within a framework of long term contracts in this paper contract structure and price adjustments are analysed by using samples of long term coking coal supply contracts between japanese importers and coal mines in australia canada and the usa long term contracts have been widely used in japan s coking coal imports although the contracts signed in recent years have been shortened and are more flexible the empirical analyses show that while in general contract prices have tracked market prices japan s coking coal import prices have been considerably stabilized by using long term contracts

bounds and prices of currency cross rate options abstract this paper derives the pricing bounds of a currency cross rate option using the option prices of two related dollar rates via a copula theory and presents the analytical properties of the bounds under the gaussian framework our option pricing bounds are useful because 1 they are general in the sense that they do not rely on the distribution assumptions of the state variables or on the selection of the copula function 2 they are portfolios of the dollar rate options and hence are potential hedging instruments for cross rate options and 3 they can be applied to generate bounds on deltas the empirical tests suggest that there are persistent and stable relationships between the market prices and the estimated bounds of the cross rate options and that our option pricing bounds obtained from the market prices of options on two dollar rates and the historical correlation of two dollar rates are highly informative for explaining the prices of the cross rate options moreover the empirical results are consistent with the predictions of the analytical properties under the gaussian framework and are robust in various aspects

tight bounds on american option prices in contrast to the constant exercise boundary assumed by broadie and detemple 1996 broadie m detemple j 1996 american option valuation new bounds approximations and comparison of existing methods review of financial studies 9 1211 1250 we use an exponential function to approximate the early exercise boundary then we obtain lower bounds for american option prices and the optimal exercise boundary which improve the bounds of broadie and detemple 1996 with the tight lower bound for the optimal exercise boundary we further derive a tight upper bound for the american option price using the early exercise premium integral of kim 1990 kim i j 1990 the analytic valuation of american options review of financial studies 3 547 572 the numerical results show that our lower and upper bounds are very tight and can improve the pricing errors of the lower bound and upper bound of broadie and detemple 1996 by 83 0 and 87 5 respectively the tightness of our upper bounds is comparable to some best accurate efficient methods in the literature for pricing american options moreover the results also indicate that the hedge ratios deltas and gammas of our bounds are close to the accurate values of american options

customer power strategic investment and the failure of leading firms why might firms be regarded as astutely managed at one point yet subsequently lose their positions of industry leadership when faced with technological change we present a model grounded in a study of the world disk drive industry that charts the process through which the demands of a firm s customers shape the allocation of resources in technological innovation a model that links theories of resource dependence and resource allocation we show that established firms led the industry in developing technologies of every sort even radical ones whenever the technologies addressed existing customers needs the same firms failed to develop simpler technologies that initially were only useful in emerging markets because impetus coalesces behind and resources are allocated to programs targeting powerful customers projects targeted at technologies for which no customers yet exist languish for lack of impetus and resources because the rate of technical progress can exceed the performance demanded in a market technologies which initially can only be used in emerging markets later can invade mainstream ones carrying entrant firms to victory over established companies

the valuation of american barrier options using the decomposition technique in this paper we propose an alternative approach for pricing and hedging american barrier options speci cally we obtain an analytic representation for the value and hedge parameters of barrier options using the decomposition technique of separating the european option value from the early exercise premium this allows us to identify some new put call symmetry relations and the homogeneity in price parameters of the optimal exercise boundary these properties can be utilized to increase the computational e ciency of our method in pricing and hedging american options our implementation of the obtained solution indicates that the proposed approach is both e cient and accurate in computing option values and option hedge parameters our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and e ciency in particular the method is free of the di culty that existing

american capped call options on dividend paying assets this article addresses the problem of valuing american call options with caps on dividendpaying assets since early exercise is allowed the valuation problem requires the determination of optimal exercise policies options with two types of caps are analyzed constant caps and caps with a constant growth rate for constant caps it is optimal to exercise at the first time at which the underlying asset s price equals or exceeds the minimum of the cap and the optimal exercise boundary for the corresponding uncapped option for caps that grow at a constant rate the optimal exercise strategy can be

pricing derivatives on financial securities subject to credit risk this article provides a new methodology for pricing and hedging derivative securities involving credit risk two types of credit risks are considered the first is where the asset underlying the derivative security may default the second is where the writer of the derivative security may default we apply the foreign currency analogy of jarrow and turnbull 1991 to decompose the dollar payoff from a risky security into a certain payoff and a spot exchange rate arbitrage free valuation techniques are then employed this methodology can be applied to corporate debt and over the counter derivatives such as swaps and caps the purpose of this article is to provide a new theory for pricing and hedging derivative securities involving credit risk two sources of credit risk are identified and analyzed the first is where the asset underlying the derivative security may default paying off less than promised this is the case for example with imbedded options on corporate debt the second is the credit risk introduced by the writer of the derivative security who may also default examples include over the counter writers of options on eurodollar futures swaps and swaptions for pricing derivative securities involving credit risk there are currently two approaches the first views these derivatives as contingent claims not on the financial securities themselves but as compound options on the assets underlying the financial securities this is the case for example with the pricing of imbedded options on corporate debt see merton 1974 1977 black and cox 1976 ho and singer 1982 chance 1990 and kim ramaswamy and sundaresan 1993 or the pricing of vulnerable options see johnson and stulz 1987 in practice however this valuation methodology is difficult to use first the assets underlying the financial security are often not tradeable and therefore their values are not observable this makes application of the theory and estimation of the relevant parameters problematic second as in the case of corporate debt all of the other liabilities of the firm senior to the corporate debt must first and simultaneously be valued this generates significant computational difficulties as a result this approach has not

preemptive patenting and the persistence of monopoly this article takes a different tack and inquires whether institutions such as the patent system create opportunities for firms with monopoly power to maintain their monopoly power the results apply to other situations such as brand identification spatial location and capacity expansion which share the characteristic that early or preemptive actions may lower the returns to potential competitors

the adaptive mesh model a new approach to efficient option pricing abstract most derivative securities must be priced by numerical techniques these models contain distribution error and nonlinearity error the adaptive mesh model amm sharply reduces nonlinearity error by grafting one or more small sections of fine high resolution lattice onto a tree with coarser time and price steps three different amm structures are presented one for pricing ordinary options one for barrier options and one for computing delta and gamma efficiently the amm approach can be adapted to a wide variety of contingent claims for some common problems accuracy increases by several orders of magnitude with no increase in execution time

pricing american options under the constant elasticity of variance model and subject to bankruptcy this paper proposes an alternative characterization of the early exercise premium that is valid for any markovian and diffusion underlying price process as well as for any parameterization of the exercise boundary this new representation is shown to provide the best pricing alternative available in the literature for medium and long term american option contracts under the constant elasticity of variance model moreover the proposed pricing methodology is also extended easily to the valuation of american options on defaultable equity and possesses appropriate asymptotic properties

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

pricing exotic options with l stable pade schemes abstract in this paper we develop a strongly stable l stable and highly accurate method for pricing exotic options the method is based on pade schemes and also utilizes partial fraction decomposition to address issues regarding accuracy and computational efficiency due to non smooth payoffs which cause discontinuities in the solution or its derivatives standard a stable methods are prone to produce large and spurious oscillations in the numerical solutions which would mislead to estimating options accurately the proposed method does not suffer these drawbacks while being easy to implement on concurrent processors numerical results are presented for digital options butterfly spread and barrier options in one and two assets in addition the methods are tested on the heston stochastic volatility model

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

pricing and static hedging of american style knock in options on defaultable stocks abstract this paper applies the static hedge portfolio approach shp of chung et al 2013 in two new directions first the shp approach is generalized from the constant elasticity of variance cev model of cox 1975 to the jump to default extended cev jdcev framework of carr and linetsky 2006 for this purpose the recovery value of the american style down and in put is hedged through the one attached to a european style plain vanilla contract whereas for an up and in put it is necessary to use the recovery component of the corresponding european style up and in option second the shp methodology is adapted from single to double barrier american style knock in options by matching the value of the hedging portfolio along both lower and upper barriers finally and to benchmark the accuracy of the novel shp pricing solutions the optimal stopping approach of nunes 2009 is also extended to price american style double knock in options under the jdcev framework such extension highlights the relevant credit derivative component embedded in american style knock in equity puts

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

robust pricing of the american put option a note on richardson extrapolation and the early exercise premium this paper presents a detailed analysis of the numerical implementation of the american put option decomposition into an equivalent european option plus an early exercise premium kim 1990 jacka 1991 carr et al 1992 it subsequently introduces a new algorithm based upon this decomposition and richardson extrapolation this new algorithm is based upon a the derivation of the correct order for the error term when applying richardson extrapolation which is used to control the error of the extrapolated prices b an innovative adjustment of kim s 1990 discrete time early exercise premium so that these premiums monotonically converge and therefore it is appropriate to use them in extrapolation and c the optimal exercise frontier can be quickly computed through newton s method permitting the efficient implementation of the decomposition formula in practice numerical experiments show that this new algorithm is accurate efficient easy to implement and competitive in comparison with other methods finally it can also be applied to other american exotic securities