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11.10 The delta of an option is the hedge ratio between an option and the underlying instrument. Because the option confers the right but not the obligation to buy or sell, it can gain or loss money more slowly than an outright position in the underlying instrument. Under most circumstances, an option will move no faster than the underlying instrument from which it derives its value. For deep-in-the-money European options, the maximum hedge ratio is the present value of the delta (hedge ratio) 1.00 because any payoffs on the option are received only in the future. 11.11 You could overweight the ve-year by 25 percent. If the relationship between the two-year and ve-year follows the past pattern, your positions will not show gain or loss from changes in the yields of the underlying instruments. Alternatively, you could underweight the two-year position by 20 percent because the the unadjusted ve-year, at 100 percent of the duration-based weighting, is 125 percent of the two-year that represents only 80 percent of the unadjusted amount. 11.12 Modi ed duration represents the percent change in value for the position for a change in yield. The formula for modi ed duration was derived from the present value formula before accrued interest is subtracted. Modi ed duration will underestimate price changes if applied to the net price instead of the full or dirty price, which includes accrued interest. When applied to trade weightings, the price sensitivity of both the long and short positions will be too low.

Figure 31-37

9. Save the file. Click the Save button and your comments are saved. You can quit Acrobat and later go online again and publish or retrieve additional comments.

FIGURE 2-27

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The commands available include: Insert: Inserts the clip on the active slide. This is the same as clicking the clip, which also inserts it. Copy: Copies the clip to the Clipboard. You can then paste it (Ctrl+V) onto any slide. Delete from Clip Organizer: Available only if the clip is stored on your hard disk; removes it from your hard disk. The clip may still be available online, so it may continue to show up in searches if you allow Of ce.com to be searched. See Deleting Clips from the Clip Organizer later in this chapter. Make Available Of ine: Stores a copy of the clip on your hard disk. This enables you to re-access it when you are not connected to the Internet, and also to change the clip s properties and keywords. See the section Making Clips Available Of ine later in this chapter. Move to Collection: Available only if the clip is stored on your hard disk; it places the clip in another clip collection. See the section Moving Clips Between Collections later in this chapter.

Sunday Servers Tina Kayli Mikayla Heather *Phase means that the level of business has slowed down enough for some staff to clock out. 3 to 11 Monday 3 to 11 Tuesday 3 to 11 Wednesday off 3 to phase* 6 to 11 Thursday off 3 to phase* 5 to 11 Friday 3 to 11 5 to phase* 6 to phase* Saturday 3 to 11 5 to phase* 6 to phase* 6 to phase*

PROBLEMS 8.1 Deconvolution and Coded Apertures. Consider again Problem 2.10. (a) Decode your image using the Wiener lter corresponding to your coded aperture. Assume normally distributed independent noise in each measurement pixel. What is the noise spectral density Assume uniform image spectral density. Plot Wiener lter reconstructed images for various SNR levels. How do your results compare with results using the decoding lter of 2 (b) Decode your image using Richardson Lucy deconvolution. Assume normally distributed independent noise in each measurement pixel. What is the noise spectral density Assume uniform image spectral density. Plot reconstructed images for various SNR levels. Hadamard Coding. Consider the measurement system g H f n with f, g [ R127 and H a 127 127 matrix. The zero-mean noise n may be drawn from a normal distribution or may be Poisson distributed about the expected values gij. 2 Assuming that in the normal case the measurement variance is 10 4 h fij i and in 2 the Poisson case that h fij i 1000, use Monte Carlo simulations to characterize the least-squares estimation variance for H corresponding to (a) The order 128 Hadamard S matrix (b) A random 127 127 matrix with values uniformly drawn from [21, 1] (c) The level 3 Haar wavelet transform of f Regularizaton. Operating from the left and right on a 127 127 natural image using the measurement matrices of Problem 8.2, nd the mean-square error for least-squares image estimation, truncated SVD estimation, and Tikhonov regularization. Make sure to use the same random matrix in all experiments and document your regularization parameters. Deconvolution. Using a 256 256 monochrome natural image sampled by a 3 3 shift-coded downsampling operator, compare the Wiener lter and Richardson Lucy deconvolution assuming that s2 1023k f 2 l normally

Conversely, if G satisfies (29.17), then H*HG = -H*HD*y or, equivalently,

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