P. Glasserman P. Boyle, M. Broadie. Monte carlo methods for security pricing. Journal of Economic Dynamics and Control, pages 1267--1321, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to generate each random number twice instead of once. For machines with limited memory, we can now use larger values of M and N to improve the accuracy in pricing the options. 1 Introduction Monte Carlo method is one of the main methods for computing American style options, see for instance [10, 1, 2, 7]. These algorithms are computationally inefficient because they require the storage of all asset prices at all simulation times for all simulated paths. Thus the total storage requirement grows like O(MN) where M is the number of simulated paths and N is the number of time steps. The accuracy of ....

P. Boyle, M. Broadie, and P. Glasserman, Monte Carlo Methods for Security Pricing, J. Econom. Dynam. Control, 21 (1997), 1267--1321.

.... depending on the development of interest rates For simple cases analytical formulas are available, but for a range of products, whose cash flows depend on a value of a financial variable in the past so called path dependent products Monte Carlo simulation techniques have to be applied [6], 10] By utilizing massively parallel architectures very efficient implementations can be achieved [29] 46] For a detailed description of the technique implemented see [37] HPF PROCESSORS : PR(NUMBER OF PROCESSORS( HPF DISTRIBUTE (BLOCK) ONTO PR : VALUE . TYPE(BOND) B ....

P. Boyle, M. Broadie, and P. Glasserman. Monte carlo methods for security pricing. Journal of Economic Dynamics and Control, pages 1267--1321, 1997.

....model, together with some discrete numerical method. A tremendous number of di erent nancial models are used today (e.g. Black Scholes, Ho Lee, etc. but only three families of numerical methods are widely used in industry: partial di erential equations [Willmot et al. 1993] Monte Carlo [Boyle et al. 1997] and lattice methods [Cox et al. 1979] This approach is strongly reminiscent of the way in which a compiler is typically structured. The program is rst translated into a low level but machineindependent intermediate language; many optimisations are applied at this level; and then the program ....

Boyle, P., Broadie, M., and Glasserman, P. (1997). Monte carlo methods for security pricing. Journal of Economic Dynamics and Control, 21:1267-1321.

....lower triangular matrix. The original Faure sequence is obtained by taking b prime and A j as 14 the identity matrix for all j = 1; s. By allowing the matrices A j to be di erent from the identity matrix, point sets that avoid some of the defects observed on the original Faure sequence [81, 6, 110] can be built. For instance, the Generalized Faure sequence of Tezuka and Tokuyama [115] amounts to take A j = P j 1 . Recently, Faure suggested another form of Generalized Faure sequence that consists in taking A j equal to the lower triangular matrix with all nonzero entries equal to 1, for ....

....by using a method that gives a lot of importance to a few uniform numbers. As an illustration, we describe in the example below the Brownian bridge technique, which can be used to generate the sample paths of a Brownian motion. Example 3 As this often happens in nancial simulations (see e.g. [6, 11]) suppose we want to generate the sample path of a Brownian motion at s di erent times B(t 1 ) B(t s ) using s uniform numbers u 1 ; u s . For instance, this Brownian motion might be driving the price process of an asset on which an option has been written [22] Instead of ....

P. Boyle, M. Broadie, and P. Glasserman. Monte Carlo methods for security pricing. Journal of Economic Dynamics & Control, 21(8-9):1267-1321, 1997. Computational nancial modelling.

....(3) e.g. with M i.i.d. random shifts) and then computing the sample variance. 4 Reducing the Variance and or the Dimension To increase the e#ciency of MC simulations, many variance reduction techniques are available [24, 23] and can be applied for financial simulations; see the survey [6] for an overview. A good example of such technique is for pricing an Asian option on the arithmetic average; one can then use as a control variable the price of the same option but taken on the geometric average [21] This can reduce the Quasi Monte Carlo Methods in Finance 7 variance by very ....

P. Boyle, M. Broadie, and P. Glasserman. Monte Carlo methods for security pricing. Journal of Economic Dynamics & Control, 21(8-9):1267--1321, 1997.

....can be applied. More recently, the use of low discrepancy sequences has also helped in certain cases. Several papers have described and analyzed the use of Monte Carlo techniques in finance [1, 11, 3] Improvements in the efficiency using variance reduction techniques is thoroughly discussed in [2]. The MC method relies on the use of a pseudo random number generator (RNG) to produce its results. The generation of random numbers is known to be di#cult since deterministic algorithms are used to obtain random quantities. Bad RNGs are detrimental to MC simulations. The sequence of an ideal ....

Boyle, P., M. Broadie and P. Glasserman (1997). "Monte Carlo methods for security pricing", Journal of Economic Dynamics and Control 21, 1267--1321.

....the model for the purpose of pricing options on the index. We set aside the last year of data (1995) in order to perform the out of sample tests. To adjust for dividends of the S P 500 index, a continuously compound rate of 2# was used for simplicity, which is consistent with the practice in Boyle, Broadie Glasserman (1997). To estimate the spot interest rate model, the US 3 month T bill rates are used as proxy of the instantaneous rates. The data are also daily, covering the same sampling period 1980 to 1995. As justified in Jiang (1998) the use of a 3 month rate is a necessary compromise between literately ....

....to estimate model parameters. In our simulation, 100,000 sampling paths are simulated to reduce the Monte Carlo error and to reflect accurately the fat tail behaviour of the asset return distributions, and the antithetic variable technique is used to reduce the variation of option prices; see Boyle et al. 1997). The results show that option prices generated using different methods are almost the same, with the largest differences less than a penny for even long term deep ITM options. The accuracy is further reflected in the small standard derivations of the simulated option prices. Option pricing ....

Boyle, P., Broadie, M. & Glasserman, P. (1997), `Monte Carlo methods for security pricing', Journal of Economic Dynamics and Control 21, 1267--1321.

....of interest rates For simple cases analytical formulas are available, but in general numerical techniques have to be applied. Products, whose cash flows depend on a value of a financial variable in the past (path dependent products) are priced with Monte Carlo simulation techniques (see [5], 7] Instruments without path The work described in this paper was partially supported by the Special Research Program SFB F011 AURORA of the Austrian Science Fund and by NEC Europe Ltd. within the co operation project ADVANCE of the C C Research Laboratories, St. Augustin, Germany, with the ....

P. Boyle, M. Broadie, P. Glasserman. Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control, 21: 1267 - 1321. 1997.

....Pricing contingent claims where no closed form solution exists essentially amounts to do a numerical integration. In the general case with multiple state variables, Monte Carlo simulation is superior to other methods such as lattices trees. Monte Carlo simulation is a very general subject on which [BBG97] give an excellent overview. Contingent claims with European decision features can be priced easily using MonteCarlo simulation even when there are multiple state variables and or multiple stochastic factors. Bermudan and American claims cannot be priced correctly using straightforward ....

P Boyle, M Broadie, and P Glasserman, Monte Carlo Methods for Security Pricing, J. Economic Dynamics and Control 2 (1997), no. 8--9, 1267--1321.

....in some cases (such as for conditional Monte Carlo and lattice rules) the total work (CPU time) is also reduced, so the efficiency improvement factors are even larger than the variance reduction factors that we just mentioned. The use of simulation for pricing financial derivatives is surveyed by Boyle, Broadie, and Glasserman (1997). Among the recent papers where variance reduction methods are studied in that context, we cite Glasserman, Heidelberger, and Shahabuddin (1999) Lemieux and L Ecuyer (1998) and Willard (1997) For general overviews of variance reduction, see, e.g. Bratley, Fox, and Schrage (1987) Fishman (1996) ....

.... Bratley, Fox, and Schrage (1987) Fishman (1996) and L Ecuyer (1994) Quasi Monte Carlo (QMC) methods have also been used successfully to evaluate financial products (e.g. Paskov and Traub 1995; Joy, Boyle, and Tan 1996; Caflish, Morokoff, and Owen 1997; Acworth, Broadie, and Glasserman 1997; Boyle, Broadie, and Glasserman 1997; Willard 1997; Tezuka 1998; Lemieux and L Ecuyer 1998; Lemieux and L Ecuyer 1999a) In particular, the empirical results obtained in Paskov and Traub (1995) for problems related to mortgage backed securities have shown that QMC can work even for large dimensional problems (up to 360 in their ....

Boyle, P., M. Broadie, and P. Glasserman. 1997. Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control, 21:1267--1321.

....has opened the possibility to price more complex and also more realistic derivatives. From a computational point of view, the representation of a nancial instrument s price as an expectation value naturally provides a way to evaluate the price of the derivative by Monte Carlo simulation, e.g. [3]) This is usually achieved by simulating sample paths of the underlying variables and averaging the discounted cash ow of the security on each simulated path. This is equivalent to computing a multidimensional integral, the dimension of which can become quite large. Various methods have been ....

....but as the other methods are not able to give us a good error estimate, this is even an advantage. The method described so far is the crude Monte Carlo and one expect this one to converge very slowly with the relative accuracy being reduced at 1= p K with K the numbers of paths simulated. [3] discuss several methods to speed up the convergence of Monte Carlo methods using di erent variance reduction techniques. A very simple one is the use of so called antithetic variables. In this approach not all paths are chosen purely randomly, but they are correlated in a way to reduce the ....

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Boyle, P., Broadie, M. and P. Glasserman, 1997. Monte Carlo Methods for Security Pricing, Journal of Economic Dynamics and Control 21, 1267{ 1321.

.... security, e.g. stock prices or interest rates For simple cases analytical formulas are available, but for a range of products, whose cash flows depend on a value of a financial variable in the past so called path dependent products Monte Carlo simulation techniques have to be applied [38, 35]. By utilizing massively parallel architectures very efficient implementations can be achieved [31, 47] 15 0 100 200 300 400 500 600 N 0 10 20 30 40 50 secs measured predicted Figure 6. Measured versus predicted computation times of the Cholesky factorization for various problem ....

P. G. P. Boyle, M. Broadie. Monte carlo methods for security pricing. Journal of Economic Dynamics and Control, pages 1267--1321, 1997.

....however, which may involve multiple assets, complex payo# functions, possibilities of early exercise, stochastic time varying model parameters, etc. analytic formulas are unavailable. These derivatives are usually priced either via Monte Carlo simulation or via numerical methods. e.g. Boyle, Broadie, and Glasserman 1997, Hull 2000, Wilmott, Dewynne, and Howison 1993, and other references given there) An important class of options for which no analytic formula is available even under the standard Black Scholes GBM model is the class of Asian options, for which the payo# is a function of the arithmetic average ....

Boyle, P., M. Broadie, and P. Glasserman, "Monte Carlo methods for Security Pricing," Journal of Economic Dynamics and Control, 21 (1997), 1267--1321.

....Until this point, we have concentrated on connections focussing on communications, cryptography, and networking. In this final section, we examine combinatorial tools that have found recent application to computation of definite integrals. This has had particular impact in the area of finance [143]. The principal current application is in the financial arena, where they are used to price exotic options. Nevertheless, the connection described affords a technique of general applicability. Indeed, Niederreiter [154] provides applications for the same combinatorial tools in pseudo random number ....

P.P. Boyle, M. Broadie & P. Glasserman, Monte Carlo methods for security pricing, J. Economic Dynamics Control , in press.

....course significant improvements may be possible over straightforward implementations. For some results along these lines, see Andersen and Brotherton Ratcliffe [3] 8 We also tested low discrepancy (quasi Monte Carlo) methods using Faure and Sobol sequences; see Boyle, Broadie, and Glasserman [11] for an introduction and references on low discrepancy methods. These methods do not provide simple error estimates and, in this application, converged erratically. Using the Faure sequence, a rough estimate of the uncertainty after 10 million points (which took 70 minutes on an Intel Pentium ....

Boyle, P., Broadie, M., Glasserman P.: Monte carlo methods for security pricing. J. Econ. Dynamics Control 21, 1267--1321 (1997)

.... methods for enhancing the precision of the Monte Carlo estimates and in our implementation we have employed one of the simplest the antithetic variable technique, which is described in e.g. Hull (1997) The reader is also referred to the pioneering article by Boyle (1977) the recent survey by Boyle, Broadie, and Glasserman (1997), and the excellent book by Gentle (1998) for further details and more advanced techniques. The simulation framework is also well suited for the analysis of issues such as optimal reserving, the distribution of the future solvency degree, and default probabilities at the individual contract level. ....

Boyle, P. P., M. Broadie, and P. Glasserman (1997): "Monte Carlo Methods for Security Pricing," Journal of Economic Dynamics and Control, 21:1267--1321.

....[17, 11] in a di#erent context estimating the steady state mean of a real valued Markov chain. Glasserman [14] analyzes a continuous time version of this idea. An example of using one step 2 conditional distributions in barrier option simulations appears in Boyle, Broadie, and Glasserman [7]. Independent of our work, Ross and Shanthikumar [29] combine two examples from Boyle et al. to arrive at an estimator similar to the simplest one considered here; they do not consider the case of unknown conditional probabilities for which we propose several alternative estimators. For other ....

Boyle, P., M. Broadie, and P. Glasserman. "Monte Carlo methods for security pricing," J. Economic Dynamics and Control, 21, pp. 1267-1321 (1997).

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P. Glasserman P. Boyle, M. Broadie. Monte carlo methods for security pricing. Journal of Economic Dynamics and Control, pages 1267--1321, 1997.

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P. P. Boyle, M. Broadie, and P. Glasserman. Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control, 21:1267--1321, 1997.

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P. G. P. Boyle, M. Broadie. Monte carlo methods for security pricing. Journal of Economic Dynamics and Control, pages 1267--1321, 1997.

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Boyle, P., M. Broadie and P. Glasserman, 1997, \Monte Carlo Methods for Security Pricing," Journal of Economic Dynamics and Control, 21, 1267-1321.

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Boyle, P., M. Broadie and P. Glasserman, 1997, Monte Carlo Methods for Security Pricing, Journal of Economic Dynamics and Control 21, 1263-1321.

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P. Boyle, M. Broadie, and P. Glasserman, Monte Carlo Methods for Security Pricing, Journal of Economic Dynamics and Control 21 (1997), 1267-1321.

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P. Boyle, M. Broadie, and P. Glasserman "Monte Carlo Methods for Security Pricing" Journal of Economic Dynamics and Control 8-9 1267--1322, 1997.

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Boyle, P., M. Broadie and P. Glasserman, "Monte Carlo Methods for Security Pricing," J. Econom. Dynam. Control, 21, 8-9 (1997), 1267-1321.

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