barrier option pricing under the 2 hypergeometric stochastic volatility model abstract we investigate the pricing of financial options under the 2 hypergeometric stochastic volatility model this is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data using a regular perturbation method from asymptotic analysis of partial differential equations we derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2 hypergeometric stochastic volatility model the asymptotic convergence of the method is proved under appropriate regularity conditions and a multi stage method for improving the quality of the approximation is discussed numerical examples are also provided

asymptotically optimal optical orthogonal codes with new parameters optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks an n w a c ooc with size l is a family of l 0 1 sequences with length n weight w maximum autocorrelation a and maximum cross correlation c in this paper we present two new constructions for oocs with a c 1 which are asymptotically optimal with respect to the johnson bound we first construct an asymptotically optimal mpn m 1 1 ooc with size pn 1 m by using the structure of zpn the ring of integers modulo pn where p is an odd prime with m p 1 and n is a positive integer we then present another asymptotically optimal mp1 pk m 1 1 ooc with size p1 pk 1 m from a product of k finite fields where pi is an odd prime and m is a positive integer such that m pi 1 for 1 i k in particular it is optimal in the case that k 1 and m 1 2 p1 1

spectral gmm estimation of continuous time processes abstract this paper derives a methodology for the estimation of continuous time stochastic models based on the characteristic function the estimation method does not require discretization of the stochastic process and it is simple to apply in practice the method is essentially generalized method of moments on the complex plane hence it shares the efficiency and distribution properties of gmm estimators we illustrate the method with some applications to relevant estimation problems in continuous time finance we estimate a model of stochastic volatility a jump diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump diffusion model we find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution while stochastic volatility is important to capture the overall level of this kurtosis positive jumps are not statistically significant once we allow for stochastic volatility in the model we also estimate a non affine model of stochastic volatility and find that the power of the diffusion coefficient appears to be between one and two rather than the value of one half that leads to the standard affine stochastic volatility model however we find that including jumps into this non affine stochastic volatility model reduces the power of the diffusion coefficient to one half finally we offer an explanation for the observation that the estimate of persistence in stochastic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model

optical orthogonal codes with unequal auto and cross correlation constraints an optical orthogonal code ooc is a collection of binary sequences with good auto and cross correlation properties they were defined by salehi and others as a means of obtaining code division multiple access on optical networks up to now all work on oocs have assumed that the constraint placed on the autocorrelation and that placed on the cross correlation are the same we consider codes for which the two constraints are not equal specifically we develop bounds on the size of such oocs and demonstrate constriction techniques for building them the results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross correlation constraint these results suggest that for a given performance requirement the optimal ooc may be one with unequal constraints this paper also views oocs with unequal auto and cross correlation constraints as constant weight unequal error protection uep codes with two levels of protection the bounds derived are interpreted from this viewpoint

parallel binary adders with a minimum number of connections an n bit parallel binary adder consisting of nor gates only in single rail input logic is proved to require at least 17n 1 connections for any value of n such an adder is proved to require at least 7n 2 gates an adder that attains these minimal values is shown also it is concluded that some of the parallel adders with the minimum number of nor gates derived by lai and muroga have the minimum number of connections as well as the minimum number of gates except for the two modules for the two least significant bit positions

new constructions of optimal cyclically permutable constant weight codes three new constructions for families of cyclic constant weight codes are presented all are asymptotically optimum in the sense that in each case as the length of the sequences within the family approaches infinity the ratio of family size to the maximum possible under the johnson upper bound approaches unity

efficient implementation of markov chain monte carlo when using an unbiased likelihood estimator summary when an unbiased estimator of the likelihood is used within a metropolis hastings chain it is necessary to trade off the number of monte carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain using many monte carlo samples will typically result in metropolis hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples however the computing time required to construct the likelihood estimator increases with the number of samples under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated we provide guidelines on the number of samples to select we illustrate our results by considering a stochastic volatility model applied to stock index returns

discrete and continuous maxima in multicarrier communication the ratio between the discrete and continuous maxima of signals used in multicarrier communications is analyzed an exact expression up to an additive term is obtained for the considered ratio when the number of uniformly distributed samples is equal to the number of carriers a more accurate upper estimate on the continuous maximum from discrete samples of the signal and its derivative is suggested finally a tight upper bound is given for the value of the continuous maximum via discrete values of samples when the number of samples is greater than the number of carriers

european option pricing with transaction costs the authors consider the problem of pricing european options in a market model similar to the black scholes one except that proportional transaction charges are levied on all sales and purchases o

threshold bipower variation and the impact of jumps on volatility forecasting this study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility this result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent but also scarcely plagued by small sample bias with the aim of achieving this we introduce the concept of threshold bipower variation which is based on the joint use of bipower variation and threshold estimation we show that its generalization threshold multipower variation admits a feasible central limit theorem in the presence of jumps and provides less biased estimates with respect to the standard multipower variation of the continuous quadratic variation in finite samples we further provide a new test for jump detection which has substantially more power than tests based on multipower variation empirical analysis on the s p500 index individual stocks and us bond yields shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

frequency hopping code sequence designs having large linear span in frequency hopping spread spectrum multiple access communication systems it is desirable to use sets of hopping patterns that in addition to having good hamming correlation properties and large period are also derived from sequences having large linear span here two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented the hamming correlation properties of the designs are optimal in the first case and close to optimal in the second in terms of the alphabet size p required to be prime in both cases the period and family size of the two designs are given by p sup 2 p and p sup n p sup n 2 1 n an even integer respectively the finite field sequences underlying the patterns in the first design have linear span exceeding p whereas still larger linear spans when compared to the sequence period can be obtained using the second design method

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

single precision multiplier with reduced circuit complexity for signal processing applications when two numbers are multiplied a double wordlength product is produced in applications where only the single precision product is required the double wordlength result is rounded to single precision hence in single precision applications it is not necessary to compute the least significant part of the product exactly instead it is only necessary to estimate the carries generated in the computation of the least significant part that will ripple into the most significant part of the product this will produce a single precision multiplier with significantly reduced circuit complexity three novel methods for realizing this class of reduced complexity single precision multipliers are introduced and their performance analyzed

pricing formula for european currency option and exchange option in a generalized jump mixed fractional brownian motion with time varying coefficients abstract in this paper a new framework for pricing the european currency option is developed in the case where the spot exchange rate follows a generalized mixed fractional brownian motion with jumps hereafter gjmfbm in addition we consider a general case that the coefficients of the model are time varying to capture the behaviors of exchange rate the combination of poisson jumps and generalized mixed fractional brownian motion is introduced to derive the pricing formula for some options we firstly derive a generalized mixed fractional girsanov theorem and some results regarding the quasi conditional expectation that we will need for the rest of the paper then analytic pricing formulas for european currency option and exchange option are obtained using the equivalent martingale measure finally through some numerical experiments and discussion we show that the gjmfbm model is different with the other previous ones

exact simulation of stochastic volatility and other affine jump diffusion processes the stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated discretization methods can be used for simulating security prices under these models however discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level this paper suggests a method for the exact simulation of the stock price and variance under hestons stochastic volatility model and other affine jump diffusion processes the sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security we compare our method with the more conventional euler discretization method and demonstrate the faster convergence rate of the error in our method specifically our method achieves an o s 1 2 convergence rate where s is the total computational budget the convergence rate for the euler discretization method is o s 1 3 or slower depending on the model coefficients and option payoff function

financial asset returns direction of change forecasting and volatility dynamics we consider three sets of phenomena that feature prominently in the financial economics literature 1 conditional mean dependence or lack thereof in asset returns 2 dependence and hence forecastability in asset return signs and 3 dependence and hence forecastability in asset return volatilities we show that they are very much interrelated and explore the relationships in detail among other things we show that 1 volatility dependence produces sign dependence so long as expected returns are nonzero so that one should expect sign dependence given the overwhelming evidence of volatility dependence 2 it is statistically possible to have sign dependence without conditional mean dependence 3 sign dependence is not likely to be found via analysis of sign autocorrelations runs tests or traditional market timing tests because of the special nonlinear nature of sign dependence so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments 4 sign dependence is not likely to be found in very high frequency e g daily or very low frequency e g annual returns instead it is more likely to be found at intermediate return horizons and 5 the link between volatility dependence and sign dependence remains intact in conditionally non gaussian environments for example with time varying conditional skewness and or kurtosis

on a bit serial input and bit serial output multiplier a recent paper by chen and willoner 1 forwarded a bit sequential input and output lsbfirst multiplier for positive numbers this multiplier for n bit operands requires 2n clocks and 2n number of five input adder modules in this correspondence after a brief discussion on the different claims made by the authors of 1 and their limitations we show that this multiplier can be realized with only n adder modules the technique is extended to two s complement number system also a more complete picture of the actual implementation is depicted finally we bring to the attention an already existing multiplier which fits into the bit sequential multiplier category

a multidimensional exponential utility indifference pricing model with applications to counterparty risk this paper considers exponential utility indifference pricing for a multidimensional nontraded assets model subject to intertemporal default risk and provides a semigroup approximation for the utility indifference price the key tool is the splitting method whose convergence is proved based on the barles souganidis monotone scheme and the convergence rate is derived based on krylov s shaking the coefficients technique we apply our methodology to study the counterparty risk of derivatives in incomplete markets

logic networks with a minimum number of nor nand gates for parity functions of n variables design of logic networks in single rail input logic with a minimum number of nor gates for parity functions of an arbitrary number of variables is described this is partly based on minimum networks for parity functions of a small number of variables which are designed by the integer programming logic design method although it is generally difficult to design minimum networks for functions of an arbitrarily large number of variables we have previously designed minimum networks for adders of an arbitrary number of variables the minimum networks for parity functions of an arbitrary number of variables discussed in this paper is another case many unique properties of minimum nor networks for parity functions are shown minimum networks with nand gates for parity functions can be easily obtained from those with nor gates because of duality relationship between nand and nor

two dimensional spatial signature patterns an optical orthogonal signature pattern code oospc is a collection of 0 1 two dimensional 2 d patterns with good correlation properties i e high autocorrelation peaks with low sidelobes and low cross correlation functions such codes find applications for example to parallelly transmit and access images in multicore fiber code division multiple access cdma networks up to now all work on oospcs has been based on an assumption that at most one pulse per column or one pulse per row and column is allowed in each two dimensional pattern however this restriction may not be required in such multiple access networks if timing information can be extracted from other means rather than from the autocorrelation function a new class of oospcs is constructed without the restriction the relationships between two dimensional binary discrete auto and cross correlation arrays and their corresponding sets for oospcs are first developed in addition new bounds on the size of this special class of oospcs are derived afterwards four algebraic techniques for constructing these new codes are investigated among these constructions some of them achieve the upper bounds with equality and are thus optimal finally the codes generated from some constructions satisfy the restriction of at most one pulse per row or column and hence can be used in applications requiring for example frequency hopping patterns

constructions for optimal spl upsi 4 1 optical orthogonal codes four direct constructions three of which are by way of skew starters are given in this correspondence for optimal spl upsi 4 1 optical orthogonal codes ooc s these improve the known existence results concerning optimal spl upsi 4 1 oocs in particular it is shown that an optimal spl upsi 4 1 ooc exists for all positive integers spl upsi spl equiv 6 mod 12 or spl upsi spl equiv 24 mod 48 it is also shown that an optimal 12 spl upsi 4 1 ooc exists for any positive integer spl upsi whose prime factors are all congruent to 1 modulo 4

a reduced form framework for modeling volatility of speculative prices based on realized variation measures abstract building on realized variance and bipower variation measures constructed from high frequency financial prices we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility we decompose the total daily return variability into the continuous sample path variance the variation arising from discontinuous jumps that occur during the trading day as well as the overnight return variance our empirical results based on long samples of high frequency equity and bond futures returns suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long memory har garch model while the overnight returns may be modeled by an augmented garch type structure the dynamic dependencies in the non parametrically identified significant jumps appear to be well described by the combination of an ach model for the time varying jump intensities coupled with a relatively simple log linear structure for the jump sizes finally we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out of sample forecasts for the total return volatility

increased correlation among asset classes are volatility or jumps to blame or both abstract we develop estimators and asymptotic theory to decompose the quadratic covariation between two assets into its continuous and jump components in a manner that is robust to the presence of market microstructure noise using high frequency data on different assets classes we find that the recent financial crisis led to an increase in both the quadratic variations of the assets and their correlations however we find little evidence to suggest a change between the relative contributions of the brownian and jump components as both comove co jumps stem from surprising news announcements that occur primarily before the opening of the us market and are also accompanied by an increase in brownian driven correlations

a new general construction for generalized bent functions a simple yet general method of constructing bent functions is presented for certain applications it is of interest to minimize the size of the image of a bent function in this study a tight lower bound on the number of elements in the image is established under certain conditions

smc 2 an efficient algorithm for sequential analysis of state space models we consider the generic problem of performing sequential bayesian inference in a state space model with observation process y state process x and fixed parameter theta an idealized approach would be to apply the iterated batch importance sampling ibis algorithm of chopin 2002 this is a sequential monte carlo algorithm in the theta dimension that samples values of theta reweights iteratively these values using the likelihood increments p y t y 1 t 1 theta and rejuvenates the theta particles through a resampling step and a mcmc update step in state space models these likelihood increments are intractable in most cases but they may be unbiasedly estimated by a particle filter in the x dimension for any fixed theta this motivates the smc 2 algorithm proposed in this article a sequential monte carlo algorithm defined in the theta dimension which propagates and resamples many particle filters in the x dimension the filters in the x dimension are an example of the random weight particle filter as in fearnhead et al 2010 on the other hand the particle markov chain monte carlo pmcmc framework developed in andrieu et al 2010 allows us to design appropriate mcmc rejuvenation steps thus the theta particles target the correct posterior distribution at each iteration t despite the intractability of the likelihood increments we explore the applicability of our algorithm in both sequential and non sequential applications and consider various degrees of freedom as for example increasing dynamically the number of x particles we contrast our approach to various competing methods both conceptually and empirically through a detailed simulation study included here and in a supplement and based on particularly challenging examples

power efficient pipelined reconfigurable fixed width baugh wooley multipliers in this paper we propose a pipelined reconfigurable fixed width baugh wooley multiplier design framework that provides four configuration modes cms n n fixed width multiplier two n 2 n 2 fixed width multipliers n 2 n 2 full precision multiplier and two n a n a full precision multipliers furthermore low power schemes including gated clock and zero input techniques are employed to achieve the power efficient pipelined reconfigurable design the presented power efficient pipelined reconfigurable fixed width multiplier design not only generates a family of widely used multipliers but also leads to 10 59 21 7 28 84 and 31 58 percent power saving on average for n 8 16 24 and 32 respectively compared with that of the pipelined reconfigurable fixed width multiplier without using the low power schemes on the other hand compared with non reconfigurable pipelined multiplier we can save 0 81 12 46 17 93 and 23 2 percent power consumption respectively for n 8 16 24 and 32

incremental computation of squares and sums of squares an incremental algorithm for computation of sums of squares is presented that is suitable for both most significant bit msb first and least significant bit lsb first bit sequential operation by exploiting symmetry properties of numerical values and evaluation times in the bit product matrix it is shown how incremental multipliers can be converted to perform squaring at reduced hardware cost and sum of squaring at a hardware cost to that of scalar multiplication by the elimination of redundant computation existing hardware modules are either reduced in size or assigned to the evaluation of a second squaring computation the corresponding hardware architectures are derived from a simple conversion of existing incremental scalar multipliers this conversion process is less practical on standard serial parallel or serial pipeline multipliers a digit on line algorithm is outlined for magnitude extraction operations on plane vectors

combinatorial constructions of optimal optical orthogonal codes with weight 4 a v k spl lambda optical orthogonal code c is a family of 0 1 sequences of length v and weight k satisfying the following correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda for any x x sub 0 x sub 1 x sub v 1 spl isin c and any integer i spl ne 0 mod v 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda for any x x sub 0 x sub 1 x sub v 1 spl isin c y y sub 0 y sub 1 y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v a v k spl lambda optical orthogonal code ooc with spl lfloor 1 k spl lfloor v 1 k 2 spl lfloor v 2 k 2 spl lfloor spl middot spl middot spl middot spl lfloor v spl lambda k spl lambda spl rfloor m spl rfloor spl rfloor spl rfloor codewords is said to be optimal oocs are essential for success of fiber optic code division multiple access cdma communication systems the use of an optimal ooc enables the largest possible number of asynchronous users to transmit information efficiently and reliably in this paper various combinatorial constructions for optimal v 4 1 oocs such as those via skew starters and weil s theorem on character sums are given for v spl equiv 0 mod 12 these improve the known existence results on optimal oocs in particular it is shown that an optimal v 4 1 ooc exists for any positive integer v spl equiv 0 mod 24

bootstrapping realized multivariate volatility measures we study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations for these measures of covariation the monte carlo simulation results of barndorff nielsen and shephard 2004 show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent this motivates our use of the bootstrap as an alternative tool of inference for covariation measures we consider an i i d bootstrap applied to the vector of returns we show that the finite sample performance of the bootstrap is superior to the existing first order asymptotic theory nevertheless and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term the edgeworth expansion for the i i d bootstrap that we develop here shows that this method is not second order accurate we argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility

optimal 2 d n times m 3 2 1 optical orthogonal codes optical orthogonal codes are commonly used as signature codes for optical code division multiple access systems so far research on 2 d optical orthogonal codes has mainly concentrated on the same autocorrelation and cross correlation constraints in this paper we are concerned about optimal 2 d optical orthogonal codes with the autocorrelation a and the cross correlation 1 some combinatorial constructions for 2 d n m k a 1 optical orthogonal codes are presented when k 3 and a 2 the exact number of codewords of an optimal 2 d n m 3 2 1 optical orthogonal code is determined for any positive integers n 0 1 3 6 9 10 mod 12 and m 2 mod 4

stochastic volatility with leverage fast and efficient likelihood inference this paper is concerned with the bayesian analysis of stochastic volatility sv models with leverage specifically the paper shows how the often used kim et al 1998 stochastic volatility likelihood inference and comparison with arch models review of economic studies 65 361 393 method that was developed for sv models without leverage can be extended to models with leverage the approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten component mixture of bivariate normal distributions the resulting posterior distribution is summarized by mcmc methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure the overall procedure is fast and highly efficient we illustrate the ideas on daily returns of the tokyo stock price index finally extensions of the method are described for superposition models where the log volatility is made up of a linear combination of heterogenous and independent autoregressions and heavy tailed error distributions student and log normal

integrated variance forecasting model based vs reduced form abstract this paper compares model based and reduced form forecasts of financial volatility when high frequency return data are available we derived exact formulas for the forecast errors and analyzed the contribution of the wrong data modeling and errors in forecast inputs the comparison is made for feasible forecasts i e we assumed that the true data generating process latent states and parameters are unknown as an illustration the same comparison is carried out empirically for spot 5 min returns of dm usd exchange rates it is shown that the comparison between feasible reduced form and model based forecasts is not always in favor of the latter in contrast to their infeasible versions the reduced form approach is generally better for long horizon forecasting and for short horizon forecasting in the presence of microstructure noise

singular perturbations in option pricing after the celebrated black scholes formula for pricing call options under constant volatility the need for more general nonconstant volatility models in financial mathematics motivated numerous works during the 1980s and 1990s in particular a lot of attention has been paid to stochastic volatility models in which the volatility is randomly fluctuating driven by an additional brownian motion we have shown in derivatives in financial markets with stochastic volatility cambridge university press cambridge uk 2000 internat j theoret appl finance 13 2000 pp 101 142 that in the presence of a separation of time scales between the main observed process and the volatility driving process asymptotic methods are very efficient in capturing the effects of random volatility in simple robust corrections to constant volatility formulas from the point of view of pdes this method corresponds to a singular perturbation analysis the aim of this paper is to deal with the nonsmoothness of the payoff

a fast serial parallel binary multiplier a fast serial parallel fsp multiplier design is derived from the carry save add shift csas multiplier structure the csas technique accepts multiplier bits serially lsb first and produces outputs serially lsb first multiplication of two n bit unsigned numbers requires 2n clock cycles to complete the process out of which n clocks are used for n row carry save additions and the other n clocks are utilized only to propagate the remaining carries this csas structure is modified so that it operates as a csas unit for the first n clocks and reconfigures itself as an n bit ripple carry parallel adder at the n 1 st clock thus allowing the carries to ripple through eliminating the delay due to storage elements during the last n clocks it is shown that this modification results in an about one third increase in speed for an approximately one third increase in hardware the technique is extended to signed numbers represented in 2 s complement form also it is shown how these implementations can be modularized

stochastic volatility asymptotics of stock loans valuation and optimal stopping abstract a stock loan or equity security lending service is a loan which uses stocks as collateral the borrower has the right to repay the principal with interest and regain the stock or make no repayment and surrender the stock therefore the valuation of stock loan is an optimal stopping problem related to a perpetual american option with a negative effective interest rate the negative effective interest rate makes standard techniques for perpetual american option pricing failure using a fast mean reverting stochastic volatility model we applied a perturbation technique to the free boundary value problem for the stock loan price an analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

econometric analysis of jump driven stochastic volatility models abstract this paper introduces and studies the econometric properties of a general new class of models which i refer to as jump driven stochastic volatility models in which the volatility is a moving average of past jumps i focus attention on two particular semiparametric classes of jump driven stochastic volatility models in the first the price has a continuous component with time varying volatility and time homogeneous jumps the second jump driven stochastic volatility model analyzed here has only jumps in the price which have time varying size in the empirical application i model the memory of the stochastic variance with a carma 2 1 kernel and set the jumps in the variance to be proportional to the squared price jumps the estimation which is based on matching moments of certain realized power variation statistics calculated from high frequency foreign exchange data shows that the jump driven stochastic volatility model containing continuous component in the price performs best it outperforms a standard two factor affine jump diffusion model but also the pure jump jump driven stochastic volatility model for the particular jump specification

asymptotically optimal optical orthogonal signature pattern codes optical orthogonal signature pattern codes oospcs have played an important role in a novel type of optical code division multiple access network for 2 d image transmission in this paper we give four direct constructions for oospcs based on polynomials and rational functions over finite fields we also use r simple matrices to present a recursive construction for oospcs these constructions yield new families of asymptotically optimal oospcs

neglecting parameter changes in garch models if a garch model is estimated on a time series that contains parameter changes in the conditional volatility process and these parameter changes are not accounted for a distinct error in the estimation occurs the sum of the estimated autoregressive parameters of the conditional variance converges to one in finite samples the sum of the estimated autoregressive parameters is heavily biased towards one this paper shows that this convergence holds for all common estimators of garch simulations of the garch model show that the effect occurs for realistic parameter changes and sample sizes for financial volatility data

realised quantile based estimation of the integrated variance in this paper we propose a new jump robust quantile based realised variance measure of ex post return variation that can be computed using potentially noisy data the estimator is consistent for the integrated variance and we present feasible central limit theorems which show that it converges at the best attainable rate and has excellent efficiency asymptotically the quantile based realised variance is immune to finite activity jumps and outliers in the price series while in modified form the estimator is applicable with market microstructure noise and therefore operational on high frequency data simulations show that it has superior robustness properties in finite sample while an empirical application illustrates its use on equity data

bounds and asymptotic approximations for utility prices when volatility is random this paper is a contribution to the valuation of derivative securities in a stochastic volatility framework which is a central problem in financial mathematics the derivatives to be priced are of european type with the payoff depending on both the stock and the volatility the valuation approach uses utility based criteria under the assumption of exponential risk preferences this methodology yields the indifference prices as solutions to second order quasilinear pdes two sets of price bounds are derived that highlight the important ingredients of the utility approach namely nonlinear pricing rules with dynamic certainty equivalent characteristics and pricing measures depending on correlation and the sharpe ratio of the traded asset the problem is further analyzed by asymptotic methods in the limit of the volatility being a fast mean reverting process the analysis relates the traditional market selected volatility risk premium approach and the preference based valuation techniques

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

reprojecting partially observed systems with application to interest rate diffusions abstract we introduce reprojection as a general purpose technique for characterizing the dynamic response of a partially observed nonlinear system to its observable history reprojection is the third step of a procedure wherein first data are summarized by projection onto a hermite series representation of the unconstrained transition density for observables second system parameters are estimated by minimum chi squared where the chi squared criterion is a quadratic form in the expected score of the projection and third the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of the estimated system onto a hermite series representation of the constrained transition density for observables the constrained transition density can be used to study the response of the system to its observable history we utilize the technique to assess the dynamics of several diffusion models for the short term interest rate that have been proposed and to compare them to a ne

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

large families of asymptotically optimal two dimensional optical orthogonal codes nine new two dimensional optical orthogonal codes 2 d oocs are presented here all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature each of these constructions is either optimal or asymptotically optimal with respect to either the original johnson bound or else a nonbinary version of the johnson bound introduced in this paper the first five codes are constructed using polynomials over finite fields the first construction is optimal while the remaining four are asymptotically optimal the next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal the last two codes also asymptotically optimal are constructed by composing two of the above codes with a constant weight binary code also presented is a three dimensional optical orthogonal code 3 d ooc that exploits the polarization dimension finally phase encoded optical cdma is considered and construction of two efficient codes are provided

analytical calculation of the maximum error for a family of truncated multipliers providing minimum mean square error a truncated multiplier is a multiplier with two n bit operands that produces a n bit result truncated multipliers discard some of the partial products of a complete multiplier to trade off accuracy with hardware cost compared with a conventional multiplier a truncated multiplier introduces an error on the output whose magnitude depends on the input bits the maximum value of the error is hardly computable since it isn t possible to test every possible input and nonexhaustive simulations are very unlikely to provide the actual maximum absolute error value it is therefore extremely useful to develop methods that provide the maximum error for a truncated multiplier this paper presents a closed form analytical calculation for every bit width of the maximum error for a previously proposed family of truncated multipliers the considered family of truncated multipliers is particularly important since it is proved to be the design that gives the lowest mean square error for a given number of discarder partial products with the contribution of this paper the considered family of truncated multipliers is the only architecture that can be designed for every bit width using an analytical approach that allows the a priori knowledge of the maximum error

exact and asymptotic tests for possibly non regular hypotheses on stochastic volatility models abstract we study the problem of testing hypotheses on the parameters of one and two factor stochastic volatility models sv allowing for the possible presence of non regularities such as singular moment conditions and unidentified parameters which can lead to non standard asymptotic distributions we focus on the development of simulation based exact procedures whose level can be controlled in finite samples as well as on large sample procedures which remain valid under non regular conditions we consider wald type score type and likelihood ratio type tests based on a simple moment estimator which can be easily simulated we also propose a c type test which is very easy to implement and exhibits relatively good size and power properties besides usual linear restrictions on the sv model coefficients the problems studied include testing homoskedasticity against a sv alternative which involves singular moment conditions under the null hypothesis and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors which raises identification difficulties three ways of implementing the tests based on alternative statistics are compared asymptotic critical values when available a local monte carlo or parametric bootstrap test procedure and a maximized monte carlo mmc procedure the size and power properties of the proposed tests are examined in a simulation experiment the results indicate that the c based tests built upon the simple moment estimator available in closed form have good size and power properties for regular hypotheses while monte carlo tests are much more reliable than those based on asymptotic critical values further in cases where the parametric bootstrap appears to fail for example in the presence of identification problems the mmc procedure easily controls the level of the tests moreover mmc based tests exhibit relatively good power performance despite the conservative feature of the procedure finally we present an application to a time series of returns on the standard and poor s composite price index

generalized spectral testing for multivariate continuous time models we develop an omnibus specification test for multivariate continuous time models using the conditional characteristic function which often has a convenient closed form or can be accurately approximated for many multivariate continuous time models in finance and economics the proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context a class of easy to interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification our tests are also applicable to discrete time distribution models simulation studies show that the tests provide reliable inference in finite samples

is the diurnal pattern sufficient to explain intraday variation in volatility a nonparametric assessment abstract in this paper we propose a nonparametric way to test the hypothesis that time variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern we assume that noisy high frequency data from a discretely sampled jump diffusion process are available the test is then based on asset returns which are deflated by the seasonal component and therefore homoskedastic under the null to construct our test statistic we extend the concept of pre averaged bipower variation to a general ito semimartingale setting via a truncation device we prove a central limit theorem for this statistic and construct a positive semi definite estimator of the asymptotic covariance matrix the t statistic after pre averaging and jump truncation diverges in the presence of stochastic volatility and has a standard normal distribution otherwise we show that replacing the true diurnal factor with a model free jump and noise robust estimator does not affect the asymptotic theory a monte carlo simulation also shows this substitution has no discernable impact in finite samples the test is however distorted by small infinite activity price jumps to improve inference we propose a new bootstrap approach which leads to almost correctly sized tests of the null hypothesis we apply the developed framework to a large cross section of equity high frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility but important sources of heteroskedasticity remain present in the data

geometric orthogonal codes of size larger than optical orthogonal codes the class of geometric orthogonal codes gocs was introduced by doty and winslow 2016 for more robust macrobonding in dna origami they observed that gocs are closely related to optical orthogonal codes oocs it is possible for gocs to have size greater than oocs of corresponding parameters due to slightly more relaxed constraints on correlations however the existence of gocs exceeding the size of optimal oocs of corresponding parameters has never been demonstrated this paper gives the first infinite family of gocs of size greater than optimal oocs

bit serial multipliers and squarers traditional bit serial multipliers present one or more clock cycles of data latency in some situations it is desirable to obtain the output after only a combinational delay as in serial adders and subtracters a serial multiplier and a squarer with no latency cycles are presented here both accept unsigned or sign extended two s complement numbers and produce an arbitrarily long output they are fully modular and thus good candidates for introduction in vlsi libraries

out of sample forecasts of quadratic variation we compare the forecasts of quadratic variation given by the realized volatility rv and the two scales realized volatility tsrv computed from high frequency data in the presence of market microstructure noise under several different dynamics for the volatility process and assumptions on the noise we show that tsrv largely outperforms rv whether looking at bias variance rmse or out of sample forecasting ability an empirical application to all djia stocks confirms the simulation results

a new recursive construction for optical orthogonal codes we present a new recursive construction for n spl omega spl lambda sub a spl lambda sub c optical orthogonal codes for the case of spl lambda sub a spl lambda sub c spl lambda this recursive construction enlarges the original family with spl lambda unchanged and produces a new family of asymptotically optimal codes if the original family is asymptotically optimal we call a code asymptotically optimal following the definition of o moreno et al see ibid vol 41 p 448 55 1995 if as n the length of code goes to infinity the ratio of the number of codewords to the corresponding johnson bound approaches unity

a generalized bose chowla family of optical orthogonal codes and distinct difference sets a new construction of optical orthogonal codes is provided in this correspondence which is a generalization of the well known construction of distinct difference set dds by bose and chowla this construction is optimal with respect to the johnson bound and has parameters n qa 1 omega q and lambda 1

constructions of binary constant weight cyclic codes and cyclically permutable codes a general theorem is proved showing how to obtain a constant weight binary cyclic code from a p ary linear cyclic code where p is a prime by using a representation of gf p as cyclic shifts of a binary p tuple based on this theorem constructions are given for four classes of binary constant weight codes the first two classes are shown to achieve the johnson upper bound on minimum distance asymptotically for long block lengths the other two classes are shown similarly to meet asymptotically the low rate plotkin upper bound on minimum distance a simple method is given for selecting virtually the maximum number of cyclically distinct codewords with full cyclic order from reed solomon codes and from berlekamp justesen maximum distance separable codes two correspondingly optimum classes of constant weight cyclically permutable codes are constructed it is shown that cyclically permutable codes provide a natural solution to the problem of constructing protocol sequence sets for the m active out of t users collision channel without feedback

singular perturbations for boundary value problems arising from exotic options we study the pricing of three exotic derivative securities barrier lookback and passport options which can be characterized by boundary value pde problems in the context of popular markovian sv models of stock prices by extending the fast mean reverting asymptotic analysis in j p fouque g papanicolaou and k r sircar derivatives in financial markets with stochastic volatility cambridge university press london 2000 the usual greek correction to the black scholes prices of these contracts is further corrected by a boundary integral term that is rapidly computed numerically in the case of the passport option the asymptotic method is effective in accounting for sv effects in a simple and robust fashion even in the presence of a highly nonlinear embedded stochastic control problem

estimating stochastic differential equations efficiently by minimum chi squared summary we propose a minimum chi squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state we prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi squared criterion increases and as the number of past observations entering each moment function increases the minimised criterion is asymptotically chi squared and can be used to test system adequacy when a fitted system is rejected inspecting studentised moments suggests how the fitted system might be modified to improve the fit the method and diagnostic tests are applied to daily observations on the u s dollar to deutschmark exchange rate from 1977 to 1992

alternative models for stock price dynamics abstract this paper evaluates the role of various volatility specifications such as multiple stochastic volatility sv factors and jump components in appropriate modeling of equity return distributions we use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns we consider two broad families of models 1 the multifactor loglinear family and 2 the affine jump family both classes of models have attracted much attention in the derivatives and econometrics literatures there are various tradeoffs in considering such diverse specifications if pure diffusion sv models are chosen over jump diffusions it has important implications for hedging strategies if logarithmic models are chosen over affine ones it may seriously complicate option pricing comparing many different specifications of pure diffusion multifactor models and jump diffusion models we find that 1 log linear models have to be extended to two factors with feedback in the mean reverting factor 2 affine models have to have a jump in returns stochastic volatility or probably both models 1 and 2 are observationally equivalent on the data set in hand in either 1 or 2 the key is that the volatility can move violently as we obtain models with comparable empirical fit one must make a choice based on arguments other than statistical goodness of fit criteria the considerations include facility to price options to hedge and parsimony the affine specification with jumps in volatility might therefore be preferred because of the closed form derivatives prices

estimation of stochastic volatility models with diagnostics abstract efficient method of moments emm is used to fit the standard stochastic volatility model of various extensions to several daily financial time series emm matches to the score of the model determined by data analysis called the score generator discrepancies reveal characteristics of data that stochastic volatility models cannot approximate the two score generators employed here are semiparametric arch and nonlinear nonparametric with the first the standard model is rejected although some extensions are accepted with the second all versions are rejected the extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient

multiple wavelength optical orthogonal codes under prime sequence permutations for optical cdma a new family of two dimensional 2 d wavelength hopping time spreading codes which employs wavelength hopping algebraically under prime sequence permutations on top of time spreading optical orthogonal codes is studied and analyzed different from other 2 d codes our new codes allow the number of wavelengths and code length to be chosen independently and at the same time the code cardinality is a quadratic function of the number of wavelengths without sacrificing the maximum cross correlation value i e still at most one they are particularly suitable for high bit rate optical code division multiple access systems with broadband mode locked lasers in which the number of time slots is very limited and system capacity can only be grown by increasing the number of wavelengths rather than code length finally a novel wavelength aware detector for wavelength hopping time spreading codes is discussed and shown to provide improved code performance

partial differential equation pricing of contingent claims under stochastic correlation in this paper we study a partial differential equation pde framework for option pricing where the underlying factors exhibit stochastic correlation with an emphasis on computation we derive a multidimensional time dependent pde for the corresponding pricing problem and present a numerical pde solution we prove a stability result and study numerical issues regarding the boundary conditions used moreover we develop and analyze an asymptotic analytical approximation to the solution leading to a novel computational asymptotic approach based on quadrature with a perturbed transition density numerical results are presented to verify second order convergence of the numerical pde solution and to demonstrate its agreement with the asymptotic approximation and monte carlo simulations the effect of certain problem parameters on the pde solution as well as on the asymptotic approximation solution is also studied

optimization of gaussian random fields many engineering systems are subject to spatially distributed uncertainty i e uncertainty that can be modeled as a random field altering the mean or covariance of this uncertainty will in general change the statistical distribution of the system outputs we present an approach for computing the sensitivity of the statistics of system outputs with respect to the parameters describing the mean and covariance of the distributed uncertainty this sensitivity information is then incorporated into a gradient based optimizer to optimize the structure of the distributed uncertainty to achieve desired output statistics this framework is applied to perform variance optimization for a model problem and to optimize the manufacturing tolerances of a gas turbine compressor blade

efficient hedging currency options in fractional brownian motion model with jumps abstract this paper deals with the problem of efficient hedging for european currency option and exchange option in case that exchange rate is driven by a fractional brownian motion with jumps in a complete market as long as a seller receives a price of the option equal to the expectation under the risk neutral probability measure of the discounted payoff the seller can hedge this payoff perfectly as the price is often quite expensive the investors need partial hedges which require less capital and reduce the risk the efficient hedge is one of partial hedges the efficient hedging results for options are obtained under fractional brownian motion model with jumps using the equivalent martingale measure simulation results and empirical studies confirm the theoretical findings and show that the fractional brownian motion model with jumps is reasonable

constructions of optimal 2 d optical orthogonal codes via generalized cyclotomic classes optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks in this paper a bound on the code size of 2 d oocs with both at most one pulse per wavelength am oppw and at most one pulse per time slot am oppts is derived accordingly two constructions of optimal 2 d oocs with both am oppw and am oppts are proposed via the generalized cyclotomic classes furthermore optimal 2 d ooc with am oppw can be also constructed by adding more codewords into the 2 d oocs with both am oppw and am oppts

comments on a signed bit sequential multiplier by t rhyne and n r strader ii with reference to the above mentioned paper see ibid vol c 35 p 896 901 1986 it is stated that the authors introduction in which they claim that the references all deal with algorithms for processing unsigned operands is erroneous one of their references most certainly does not deal with unsigned operands as a two s complement number system is one of the module interfacing conventions germane to r lyon s 1981 methodology moreover in the authors conclusions they state that they have now extended bit sequential multiplication to signed two s complement binary operands which may give the doubtless unintended impression that this has not been done before

a discrete time model for daily s p500 returns and realized variations jumps and leverage effects abstract we develop an empirically highly accurate discrete time daily stochastic volatility model that explicitly distinguishes between the jump and continuous time components of price movements using nonparametric realized variation and bipower variation measures constructed from high frequency intraday data the model setup allows us to directly assess the structural inter dependencies among the shocks to returns and the two different volatility components the model estimates suggest that the leverage effect or asymmetry between returns and volatility works primarily through the continuous volatility component the excellent fit of the model makes it an ideal candidate for an easy to implement auxiliary model in the context of indirect estimation of empirically more realistic continuous time jump diffusion and levy driven stochastic volatility models effectively incorporating the interdaily dependencies inherent in the high frequency intraday data

pricing of options in the singular perturbed stochastic volatility model the pricing of options in the fast mean reverting stochastic volatility model using the singular perturbation method has received a considerable amount of attention in the last two decades however it is not to easy to estimate the accuracy of the approximation if the payoff function is not smooth or bounded as is the case for european call options in this article we introduce a new novel approach for pricing options in the fast mean reverting stochastic volatility model combinations of fourier analysis and singular perturbation methods enable us to estimate the accuracy easily we also show that this method allows us to derive the price of european and bermudan options in the fast mean reverting stochastic volatility environment with jumps

the design of easily testable vlsi array multipliers array multipliers are well suited for vlsi implementation because of the regularity in their iterative structure however most vlsi circuits are difficult to test this correspondence shows that with appropriate cell design array multipliers can be designed to be very easily testable an array multiplier is called c testable if all its adder cells can be exhaustively tested while requiring only a constant number of test patterns the testability of two well known array multiplier structures is studied in detail the conventional design of the carry save array multiplier is modified the modified design is shown to be c testable and requires only 16 test patterns similar results are obtained for the baugh wooley two s complement array multiplier a modified design of the baugh wooley array multiplier is shown to be c testable and requires 55 test patterns the c testability of two other array multipliers namely the carry propagate and the trw designs is also presented

matching asymptotics in path dependent option pricing abstract the valuation of path dependent options in finance creates many interesting mathematical challenges among them are a large delta and gamma near the expiry leading to a big error in pricing those exotic options as well as european vanilla options also the higher order corrections of the asymptotic prices of the derivatives in some stochastic volatility models are difficult to be evaluated in this paper we use the method of matched asymptotic expansions to obtain more practical values of lookback and barrier option prices near the expiry our results verify that matching asymptotics is a useful tool for pde methods in path dependent option pricing

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

combinatorial constructions of optimal three dimensional optical orthogonal codes in this paper we study three dimensional u x v x w k lambda optical orthogonal codes oocs with at most one optical pulse per wavelength time plane am opp restriction which is denoted by am opp 3 d u x v x w k lambda ooc we build an equivalence relation between such an ooc and a certain combinatorial subject called a w cyclic group divisible packing of type vw u by this link the upper bound of the number of codewords is improved and some new combinatorial constructions are presented as an application the exact number of codewords of an optimal am opp 3 d uxvxw 3 1 ooc is determined for any positive integers v w and u sic 2 mod 6 with some possible exceptions

testing for jumps when asset prices are observed with noise a swap variance approach abstract this paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps formally the test follows by a direct application of ito s lemma to the semi martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments intuitively the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps simulations show that the jump test has nice properties and is generally more powerful than the widely used bi power variation test an important feature of our test is that it can be applied in analytically modified form to noisy high frequency data and still retain power as a by product of our analysis we obtain novel analytical results regarding the impact of noise on bi power variation an empirical illustration using ibm trade data is also included

empirical reverse engineering of the pricing kernel abstract this paper proposes an econometric procedure that allows the estimation of the pricing kernel without either any assumptions about the investors preferences or the use of the consumption data we propose a model of equity price dynamics that allows for i simultaneous consideration of multiple stock prices ii analytical formulas for derivatives such as futures options and bonds and iii a realistic description of all of these assets the analytical specification of the model allows us to infer the dynamics of the pricing kernel the model calibrated to a comprehensive dataset including the s p 500 index individual equities t bills and gold futures yields the conditional filter of the unobservable pricing kernel as a result we obtain the estimate of the kernel that is positive almost surely i e precludes arbitrage consistent with the equity risk premium the risk free discounting and with the observed asset prices by construction the pricing kernel estimate involves a highly nonlinear function of the contemporaneous and lagged returns on the s p 500 index this contradicts typical implementations of capm that use a linear function of the market proxy return as the pricing kernel hence the s p 500 index does not have to coincide with the market portfolio if it is used in conjunction with nonlinear asset pricing models we also find that our best estimate of the pricing kernel is not consistent with the standard time separable utilities but potentially could be cast into the stochastic habit formation framework of campbell and cochrane j political economy 107 1999 205

new construction of multiwavelength optical orthogonal codes we investigate multiwavelength optical orthogonal codes mwoocs for optical code division multiple access particularly we present a new construction method for mn spl lambda 2 spl lambda mwoocs with the number of available wavelengths m codeword length n and constant hamming weight spl lambda 2 that have autocorrelation and cross correlation values not exceeding spl lambda in the proposed scheme there is no constraint on the relationship between the number of available wavelengths and the codeword length and it is also possible to use an arbitrary spl lambda we show that the constructed code is optimal especially for spl lambda 1 finally we analyze the bit error rate of the new code and compare it with that of other optical codes