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The list of ingredients (see Figure 6-1 for an example of such a list) notes the constituents of a product. (If you re like us, at times you ll find yourself surprised to see how much an otherwise healthy product has of an unexpected ingredient like sugar or oil.) The items are listed in descending order by weight. Therefore, the first item in the list is present in the product in the greatest amount by weight, the second item in the list is present in the second greatest amount by weight, and so on. In other words, the list of ingredients tells you both the ingredients in a product and their relative amounts. Although the list of ingredients doesn t tell you the actual (absolute) amount of a product s ingredients (this information is revealed in the Nutrition Facts table, which we discuss in a moment), it does give a pretty good sense of whether the product contains lots or little of a substance. For example, if salt (sodium) is listed as one of the first three ingredients in the list, the product is probably fairly rich in sodium. Another important role of the list of ingredients is to help people who have food allergies to identifiy whether a product contains the food they re allergic to. Also, people who avoid certain foods because of religious or other beliefs are able to determine whether the product contains these ingredients.

Many portfolios are set up to fund a speci c liability, for example the future payment of bene ts promised by a corporate de ned-bene t pension plan. Insurance companies have xed income portfolios designed to fund the liabilities created by their products. One of the main considerations in the management of these portfolios is that the growth in liabilities is matched with the growth in assets. The main in uence of price change in xed income portfolios is the change in interest rates. The value of the assets will vary inversely to the change in liabilities as interest rates uctuate. To monitor the change in assets versus the change in liabilities, we can benchmark these portfolios against a custom liability benchmark comprised of zero coupon government bonds or treasury strips that match the dollar and time to maturity characteristics of the liability structure. The custom benchmark is a portfolio that is constructed and valued in a similar way as a market index. The portfolio is valued periodically and single-period returns are calculated in the same manner as for a market benchmark. The relative performance of the portfolio versus the custom benchmark will indicate whether the portfolio is structured to neutralize the effects of interest rate changes.4

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13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 13.15 13.16 LIBOR Market Models Speci cations of the Instantaneous Volatility of Forward Rates Implementation of Hull-White LIBOR Market Model Calibration of LIBOR Market Model to Caps Pricing Swaptions with Lognormal Forward-Swap Model Approximate Swaption Pricing with Hull-White Approach LFM Formula for Swaption Volatilities Monte Carlo Pricing of Swaptions Using LFM Improved Monte Carlo Pricing of Swaptions with a Predictor-Corrector Incompatibility between LSM and LSF Instantaneous and Terminal Correlation Structures Calibration to Swaption Prices Connecting Caplet and S 1-Swaption Volatilities Including Caplet Smile in LFM Stochastic Extension of LIBOR Market Model Computing Greeks in Forward LIBOR Models

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