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Convergence of the crude Monte Carlo is slow to the order of 1/ M To increase the accuracy 10 times, we need to run 100 times more simulations of sample paths. On the other hand, decreasing the variance 2 by a factor of 10 does as much for error reduction as increasing the number of simulations by a factor of 100. The simplest variance reduction procedure is use of antithetic variates. For each path simulated with k (denoted as the ith deviate, i = 1 . . . N on the kth path, i k = 1 . . . M) an identical path is simulated with ik . The payoff Fk for the path is ^ calculated with ik , and also the payoff Fk for the path with k. Then the average is i taken: 1 (Fk + Fk ) 2 Although k s are samples from a standard normal distribution with mean 0, in a i sample you will get some nonzero mean. The antithetic variates procedure corrects this bias by averaging out the deviations and centers the mean at 0. Another variance reduction technique is to use control variates. Control variates are random variables, whose expected value (mean) that we know is correlated with the variable we are trying to estimate (i.e., the derivative security we want to value).14 The principle underlying this technique is to use what you know. Suppose you are trying to simulate an estimate for the price of a complex security. Suppose also that you know a closed-form analytical formula for the price of a similar, but simpler, security. The price of the complex security can be represented as: fcomplex = fsimple + (fcomplex fsimple) (2.16)

In the Java community, the MVC design pattern is widely recognized as the way to go for developing medium to large-scale enterprise Web applications. The MVC design pattern is associated with the JSP Model 2 development approach. In JSP Model 2 development, the JavaServer Page is used strictly to render the output of a Web page. A servlet is used to act as a controller, determining which page to generate and gathering the information to be rendered into HTML by the JSP. Someone just being introduced to application frameworks will naturally want to know answers to questions such as, What does a framework do for

See www.linuxtoys.net for hardware URLs. Of course, all of the items you see here are likely to be offered at different prices from a variety of vendors.

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After you have Fedora Core or another Linux operating system installed, you just have to add the software that is specific to each Linux Toys II project you want to build All of the software needed to create the Linux Toys II projects is included on the CD that comes with this book (or is easily downloaded) in the following forms: RPMs Pre-built binaries for each of the Linux Toys II projects are included on the CD in the form of RPM Package Management (RPM) files These RPMs were created specifically to run on Fedora Core or Red Hat Enterprise Linux systems However, it might be possible to use them on other systems that support RPM packages or by extracting the software from these packages and installing them on other Linux systems RPM packages can be installed and managed using the rpm command.

You don t need to change any of these settings. If you don t however, here is what you get by default: Layout Each new album will have images appear in three columns and three rows per page. Appearance Each image will have a black border 1 pixel wide and Arial font type. Image processing and display Each image added to an album will have a thumbnail size of 150 pixels and an intermediate image size of 640 pixels. By default, JPEG and

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You can also use software packaging tools such as yum or apt to install and maintain software packages over the network Tarballs A tarball is a single file that contains a whole set of files The name comes from the tar command, which is used to make the tarballs Tar stands for Tape ARchiver, because when tar was created back in the old UNIX days, magnetic tape was the primary medium for archiving software The tar command has many, many options for creating, comparing, listing, appending, and extracting tar files For the projects in this book, you are most interested in extracting files from a project s tarball directory, and then possibly compiling and installing the software to use on a Linux system.

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