valuation of foreign currency options some empirical tests this paper investigates the efficiency of the market for foreign currency options with the help of a modified version of the black scholes model the evidence in the ex post tests is inconsistent with this hypothesis since we find a large number of opportunities for abnormal profits a second set of tests is conducted on an ex ante basis to determine whether these profit opportunities exist even if the execution of the strategy is delayed by one day the evidence from these tests provides more support for the hypothesis of market efficiency

regional bias in new firm formation in the uk whittington r c 1984 regional bias in new firm formation in the uk reg studies 18 253 256 theories explaining regional differences in new firm formation rates are tested and refining previous theory a model is constructed the major influences on new firm formation rates are found to be the regional proportions of manual workers and home ownership and the change in the rate of regional unemployment in the preceding year new firm formation rates are measured by new vat registrations the implications of these results for government small firm policy are discussed

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

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

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

the skew risk premium in the equity index market we develop a new method for measuring moment risk premiums we find that the skew premium accounts for over 40 of the slope in the implied volatility curve in the s p 500 market skew risk is tightly related to variance risk in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium this provides a new testable restriction for asset pricing models trying to capture in particular disaster risk premiums we base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments

the value of the option to wait and see abstract this note shows a very simple way to incorporate the effects of uncertainty about the accuracy of present value estimates into the firm s option to delay irreversible investment it is shown that if the firm s priors about the distribution of present value are sufficiently diffuse a reduction in the accuracy of present value estimates will increase the value of delay while learning will reduce its value

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

the valuation of sequential exchange opportunities sequential exchange opportunities are valued using the techniques of modern option pricing theory the vehicle for analysis is the concept of a compound exchange option this security is shown to exist implicitly in several contractual settings a valuation formula for this option is derived the formula is shown to generalize much previous work in option pricing several applications of the formula are presented

monte carlo methods for security pricing the monte carlo approach has proved to be a valuable and flexible computational tool in modern finance this paper discusses some of the recent applications of the monte carlo method to security pricing problems with emphasis on improvements in efficiency we first review some variance reduction methods that have proved useful in finance then we describe the use of deterministic low discrepancy sequences also known as quasi monte carlo methods for the valuation of complex derivative securities we summarize some recent applications of the monte carlo method to the estimation of partial derivatives or risk sensitivities and to the valuation of american options we conclude by mentioning other applications

on the market risk involved in the public financial system in japan a theoretical and numerical investigation abstract treating the postal savings system and the fiscal investments and loans program in japan as an integrated financial institution this paper analyzes the market risk involved in this system for this purpose the paper pays particular attention to options embedded in both assets and liabilities this paper finds that 1 the current rule for determining interest rates on the postal savings account well reflects the values of the embedded put options and 2 due to the flexible options the system tends to entail high market risks in particular as spot rates go up the duration of liabilities becomes extremely short with anticipation of early withdrawal

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

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

hedging using simulation a least squares approach abstract this paper presents a new and flexible computational approach to derivative hedging it is based on the use of least squares regression in order to compute the hedging portfolio this nonparametric methodology can be readily applied to any derivative contract written on a single underlying risky asset in a complete market with continuous markov price paths we illustrate this technique computing sensitivities on plain vanilla and exotic options with both european and american exercise style the achieved numerical accuracy is always comparable with the best simulation and semianalytic techniques presented in the literature

valuation of capped variable rate loan commitments abstract the early exercise of capped variable rate loan commitments is formalized as the first passage time to a critical boundary in a compound option model as early exercised commitment puts are american style options numerical procedures are used to obtain simulated values it appears from the latter that the value of the early exercise premium is nontrivial and increasing with the terms to option expiry put values are also sensitive to the volatility of credit market rates as these affect the variance of the borrower s indebtedness value

monte carlo valuation of american options through computation of the optimal exercise frontier this paper introduces a monte carlo simulation method for pricing multidimensional american options based on the computation of the optimal exercise frontier we consider bermudan options that can be exercised at a finite number of times and compute the optimal exercise frontier recursively we show that for every date of possible exercise any single point of the optimal exercise frontier is a fixed point of a simple algorithm once the frontier is computed we use plain vanilla monte carlo simulation to price the option and obtain a low biased estimator we illustrate the method with applications to several types of options

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

entrepreneurship and regional development some conceptual issues o farrell p n 1986 entrepreneurship and regional development some conceptual issues reg studies 20 565 574 this paper attempts to clarify and improve understanding of the concept of entrepreneurship in national and regional development the nature of entrepreneurship is discussed and it is shown that the entrepreneur and the capitalist are conceptually distinct that it is useful to differentiate between the entrepreneurial and managerial functions and that the essence of the concept is the initiation of entrepreneurial acts when the individual is behaving in an innovative way under uncertainty the distinction between entrepreneurship and arbitrage is briefly clarified and the relationship between entrepreneurship and large organizations is discussed our understanding of spatial variations in entrepreneurial behaviour is currently insufficient for the purpose of explanation and policy prescription

new firms and rural industrialization in east anglia gould a and keeble d 1984 new firms and rural industrialization in east anglia reg studies 18 189 201 the paper analyses key aspects of the formation of new independent manufacturing firms in east anglia between 1971 and 1981 special attention is paid to trends in formation rates over time to the spatial bias of new firm origins towards both rural areas and the cambridge region and to the location character and impact of high technology new firms original findings include the contention that spatial variations chiefly reflect variation in the occupational structure of the resident workforce together with industrial mix plant size and previous industrial immigration some implications for government policy to new firms are discussed

is the 2007 u s sub prime financial crisis so different an international historical comparison the first major financial crisis of the twentyfirst century involves esoteric instruments unaware regulators and skittish investors it also follows a well trodden path laid down by centuries of financial folly is the special prob lem of sub prime mortgages really different our examination of the longer historical record which is part of a larger effort on cur rency and debt crises finds stunning qualitative and quantitative parallels across a number of standard financial crisis indicators to name a few the run up in us equity and housing prices that graciela l kaminsky and reinhart 1999 find to be the best leading indicators of crisis in countries experiencing large capital inflows closely tracks the average of the previous 18 post world war ii banking crises in industrial countries so too does the inverted v shape of real growth in the years prior to the crisis despite widespread concern about the effects on national debt of the tax cuts of the early 2000s the run up in us public debt is actually some what below the average of other crisis episodes in contrast the pattern of us current account deficits is markedly worse at this juncture the book is still open on how the current dislocations in the united states will play out the precedent found in the aftermath of other episodes suggests that the strains can be quite severe depending especially on the initial degree of trauma to the financial system and to some extent the policy response the average drop in real per capita output growth is over 2 percent and it typically takes two years to return to trend for the five most catastrophic cases which include episodes in finland japan

pricing and exercising american options an asymptotic expansion approach abstract this paper proposes and implements a novel asymptotic expansion approach for pricing discretely monitored american options and approximating their optimal early exercise boundaries under a generic class of multivariate derivative pricing models incorporating both stochastic volatility and levy driven jumps in asset return the price and the critical value can be expanded up to any arbitrary order around those under a simple constant volatility jump diffusion model the expansion terms are then efficiently implemented by exactly solving some backward inductions via closed form fourier transforms where a substantial extension of the hilbert transform method of feng and linetsky 2008a 2009 plays an important role the efficiency of our method is illustrated through some representative examples as applications we analyze the impacts of various model parameters on the optimal early exercise boundary compare the optimal early exercise boundaries under different models and propose a derivative proxy based method for practically exercising american options under models with stochastic volatility and jumps

nonparametric estimation of american options exercise boundaries and call prices abstract unlike european type derivative securities there are no simple analytic valuation formulas for finite lived american options even when the underlying asset price has constant volatility the early exercise feature considerably complicates the valuation of american contracts the strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries a comparison is made with parametric constant volatility model based prices and exercise boundaries the paper focuses on assessing the adequacy of conventional formulas by comparing them to nonparametric estimates we use daily market option prices and exercise data on the s p100 contract the most actively traded american option contract we find large discrepancies between the parametric and nonparametric call prices and exercise boundaries we also find remarkable similarities of the nonparametric estimates before and after the crash of october 1987

a moving boundary approach to american option pricing this paper describes a method to solve the free boundary problem that arises in the pricing of american options most numerical methods for american option pricing exploit the representation of the option price as the expected pay off under the risk neutral measure and calculate the price for a given time to expiration and stock price they do not solve the related free boundary problem explicitly the advantage of solving the free boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly our approach which we term the moving boundary approach is based on using a boundary guess and the value associated with the guess to construct an improved boundary it is also shown that on iteration the sequence of boundaries converge monotonically to the optimal exercise boundary examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented finally we compare runtimes and speeds with other methods that solve the free boundary problem and compute the optimal boundaries explicitly like the front fixing method penalty method method based on the integral representations and the method by brennan and schwartz 1977 the valuation of american put options journal of finance 32 2 449 462

naive diversification strategies in defined contribution saving plans there is a worldwide trend toward defined contribution saving plans and growing interest in privatized social security plans in both environments individuals are given some responsibility to make their own asset allocation decisions raising concerns about how well they do at this task this paper investigates one aspect of the task namely diversification it is shown that some investors follow the 1 n strategy they divide their contributions evenly across the funds offered in the plan consistent with this naive notion of diversification it is found that the proportion invested in stocks depends strongly on the proportion of stock funds in the plan

an analytic approximation for the american put price black and scholes 1 derived the pricing equation for a european put when the stock price follows geometric brownian motion for this same case merton 5 derived the pricing equation for an american put with infinite time to maturity brennan and schwartz 2 rubinstein and cox 7 and parkinson 6 have developed numerical solutions for the price of an american put numerical solutions are expensive and do not provide much intuition naturally an analytic solution would be much preferred unfortunately pricing the american put requires solving a formidable and presumably intractable boundary value problem

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

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

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

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

baby boomer retirement security the roles of planning financial literacy and housing wealth abstract we compare wealth holdings across two cohorts of the health and retirement study the early baby boomers in 2004 and individuals in the same age group in 1992 levels and patterns of total net worth have changed relatively little over time though boomers rely more on housing equity than their predecessors most important planners in both cohorts arrive close to retirement with much higher wealth levels and display higher financial literacy than non planners instrumental variables estimates show that planning behavior can explain the differences in savings and why some people arrive close to retirement with very little or no wealth

the home pension savings and risk aversion intentions of the defined contribution pension plan participants of a london based investment bank at the peak of the bubble in the lead up to the peak of the financial bubble and before the onset of the global financial crisis property was regularly promoted as a ready made alternative to private pensions this paper explores the importance of owner occupied housing for the retirement savings strategies of defined contribution dc pension plan members based upon a unique survey of over 2300 participants in the dc pension scheme of a london based international bank an assessment is made of the statistical significance of respondents socioeconomic status and risk preference in predicting the significance or otherwise of their home for retirement saving relatively few respondents indicated that they were likely to rely on their home those that indicated reliance were relatively older higher paid and married employees the paper concludes with implications for understanding the connection between savings behaviour and housing before and after the global financial crisis

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

understanding the competitive process a guide to effective intervention in the small firms sector abstract the paper describes a project undertaken within the economic and social research council s competitiveness of british industry research programme the aim of the project was to assist agencies who intervene in a local economy to try to help individual small firms guidance currently available to such agencies was considered to lack an adequate theoretical basis in relation to either the choice of firms who should be granted assistance or the form of assistance which might be given in particular there is a lack of recognition that there is scope for management strategy among smaller firms affecting the way they compete in the market place and having a clear bearing on their revealed performance from a study of 100 small firms located in telford new town criteria were derived for classifying the competitive stance of small firms this was identified as the key to the potential performance of the small firm the extent to which it reveals a potential for future growth can determine whether a firm is or not a suitable candidate for assistance and the strengths and weakness in an individual firm s stance can determine the most suitable form of assistance to give the survey and analysis exercise leading to the identification of components of competitive stance are described and the classification of firms into a range of stance types then the usefulness of the competitive stance classification as a guide to selection of firms and choice of form of assistance is considered

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

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

numerical valuation of high dimensional multivariate european securities we consider the problem of pricing a contingent claim whose payoff depends on several sources of uncertainty using classical assumptions from the arbitrage pricing theory the theoretical price can be computed as the discounted expected value of future cash flows under the modified risk neutral information process although analytical solutions have been developed elsewhere for a few particular option pricing problems computing the arbitrage prices of securities under several sources of uncertainty is still an open problem in many instances in this paper we present efficient numerical techniques based upon monte carlo simulation for pricing european contingent claims depending on an arbitrary number of risk sources we introduce in particular the method of quadratic resampling qr a new powerful error reduction technique for monte carlo simulation quadratic resampling can be efficiently combined with classical variance reduction methods such as importance sampling our numerical experiments show th

an empirical examination of the pricing of american put options this study is an ex post performance test comparing the accuracy of an american model to a european model for valuing listed options specifically the geske and johnson american put valuation model is compared with the black and scholes european put model on average both models undervalue relative to market prices put options however the geske and johnson model values are significantly closer to market prices than are the black and scholes values

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

an fft network for levy option pricing abstract this paper develops a simple network approach to american exotic option valuation under levy processes using the fast fourier transform fft the forward shooting grid fsg technique of the lattice approach is then generalized to expand the fft network to accommodate path dependent variables this network pricing approach is applicable to all levy processes for which the characteristic function is readily available in other words the log value of the underlying asset can follow finite activity or infinite activity levy processes with the powerful computation of fft the proposed network has a negligible additional computational burden compared to the binomial tree approach the early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach numerical examples using american style barrier lookback and asian options demonstrate that the fft network is accurate and efficient

the pricing of call and put options on foreign exchange this paper derives pricing equations for european puts and calls on foreign exchange the call and put pricing formulas are unlike the black scholes equations for stock options in that there are two relevant interest rates interest rates are stochastic and boundary constraints differ in addition it is shown that both american call and put options have values larger than their european counterparts

a monte carlo approach for the american put under stochastic interest rates abstract this paper presents a new approach for the valuation of an american put option under stochastic interest rates the paper combines a monte carlo simulation approach for the valuation of bermudan options and the valuation technique for american options proposed by geske and johnson 1984 the american put option valued analytically journal of finance 39 5 1511 1524 numerical results show that the price estimates are accurate with very low standard errors the simulation algorithm used to generate the price estimates is fast and easy to implement the effect of stochastic interest rates is clearly reflected in the option prices especially under regimes where interest rate volatility is high this effect can be important to incorporate also for long lived options this can be an important extension

exponential growth bias and household finance exponential growth bias is the pervasive tendency to linearize exponential functions when assessing them intuitively we show that exponential growth bias can explain two stylized facts in household finance the tendency to underestimate an interest rate given other loan terms and the tendency to underestimate a future value given other investment terms bias matters empirically more biased households borrow more save less favor shorter maturities and use and benefit more from financial advice conditional on a rich set of household characteristics there is little evidence that our measure of exponential growth bias merely proxies for broader financial sophistication what drives household financial decisions the canonical economic model assumes that consumers choose to consume borrow or save based on their preferences their expectations and the costs and benefits of borrowing and saving a growing body of work applies insights from psychology to enrich specifications of three of the model s key pieces preferences expectations and problem solving conditional on parameter values 1 in this paper we bring psychological evidence to bear on a fourth specification issue how consumers perceive the costs and benefits of borrowing and saving we begin by tying together existing and new evidence on these cost perceptions to show that most consumers err systematically when given information commonly available in the market on the saving side consumers display future value bias a systematic tendency to underestimate a future value given

options on the maximum or the minimum of several assets using an intuitive approach that also provides new intuition concerning the black and scholes equation this paper extends the results of johnson and stulz to the pricing of options on the minimum or the maximum of several risky assets

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

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

returns of claims on the upside and the viability of u shaped pricing kernels abstract when the pricing kernel is u shaped then expected returns of claims with payout on the upside are negative for strikes beyond a threshold determined by the slope of the u shaped kernel in its increasing region and have negative partial derivative with respect to strike in the increasing region of the kernel using returns of i s p 500 index calls ii calls on major international equity indexes iii digital calls iv upside variance contracts and v a theoretical construct that we denote as kernel call we find broad support for the implications of u shaped pricing kernels a possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short selling

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

on the pricing of european and american foreign currency call options abstract this study uses cox ross analysis and dynamic programming techniques to price foreign currency call options we show that under certain conditions the american call price will exceed its european counterpart while under other conditions the two prices will be identical we find that the american premium is a complex function of the degree to which an option is in or out of the money and that this premium is greatest when an option is near in or out we present empirical evidence which shows that the american model significantly improves upon a european model however significant pricing errors associated with the american model remain

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 valuation of american options for a class of diffusion processes we present an integral equation approach for the valuation of american style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic our contribution is fourfold first we show that the exercise region is determined by a single exercise boundary under very general conditions on the interest rate and the dividend yield second based on this result we derive a recursive integral equation for the exercise boundary and provide a parametric representation of the american option price third we apply the results to models with stochastic volatility or stochastic interest rate and to american bond options in one factor models for the cases studied explicit parametric valuation formulas are obtained finally we extend results on american capped options to general diffusion prices numerical schemes based on approximations of the optimal stopping time such as approximations based on a lower bound or on a combination of lower and upper bounds are shown to be valid in this context

the valuation of options on futures contracts rational restrictions are derived for the values of american options on futures contracts for these options the optimal policy in general involves premature exercise a model is developed for valuing options on futures contracts in a constant interest rate setting despite the fact that premature exercise may be optimal the value of this american feature appears to be small and a european formula due to black serves as a useful approximation finally a model is developed to value these options in a world with stochastic interest rates it is shown that the pricing errors caused by ignoring the location of the interest rate relative to its long run mean range from 5 to 7 when the current rate is 200 basis points from its long run value the role of interest rate expectations is therefore crucial to the valuation optimal exercise policies are found from numerical methods for both models in recent years there has been a steady growth in the number of financial assets which one might properly call derivative assets that are available for trading on the organized exchanges among these the most recent and notable are options contracts written on available futures contracts options are now traded on the futures contracts on stock market indexes on the futures contracts on treasury instruments on the futures contracts on foreign exchange rates and on the futures contracts on some metals in design these options contracts do not differ substantially from the well known options contracts on common stock except that the underlying asset is a futures contract the received theory of the valuation of these options suggests that such contracts provide a direct vehicle for investors to alter the terminal payoffs on their portfolios to a desired distribution in the absence of these contracts investors would be forced to pursue a dynamic portfolio policy at the expense of considerable transactions in order to achieve a similar distribution indeed the availability of put options on the futures contracts on stock market indexes now enables well diversified investors to purchase portfolio insurance in his seminal work black 1 provided a complete description of forward and futures contracts as well as the description and valuation of european options on forward contracts and on spot commodities breeden 3 has examined the use of commodity options in a theoretical framework and courtadon 6 has studied the valuation of options on treasury bond futures french 13 cox