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his chapter focuses on the pricing of various exotic interest rate derivatives including Bermudan swaptions, constant maturity swaps, trigger swaps, index amortizing swaps, and quantos. These interest rate derivatives are heavily traded by many nancial institutions and an understanding of them is essential for any quant working with traders on a xed income trading desk. In section 14.1, we discuss the characteristics and method to price Bermudan swaptions. In section 14.2, we give a practical implementation for pricing Bermudan swaptions. In section 14.3, we discuss Andersen s (1999) method for pricing Bermudan swaptions. In section 14.4, we discuss the least-squares Monte Carlo (LSMC) technique, developed by Longstaff and Schwartz. In section 14.5, we discuss the stochastic mesh method as a technique for building lattices to value interest rate derivatives. In section 14.6, we discuss the valuation of range notes and provide an implementation using the HJM model. In section 14.7, we discuss the valuation of index amortizing swaps and provide an implementation using the HJM model. In section 14.8, we discuss the pricing of trigger swaps. In section 14.9, we discuss pricing quanto (multicurrency) derivatives including quanto caps, oors, and swaptions. Finally, in section 14.10, we discuss the Gaussian quadrature procedure for numerically evaluating integrals for valuation of derivatives.

5

9.1.5.2 i)

For this example, the following formula returns $312,500.00:

The value of the xed-strike lookback put option is $7.45 using = 3/ 2 Figure 6.6 shows the trinomial tree generated using = 3/ 2 For a more detailed discussion of lookback options, see Goldman, Sosin, and Gatto (1979) (who rst introduced lookback options), Conze and Viswanathan (1991), and Dewynne and Wilmott (1993). For variations of lookbacks such as double lookbacks, see He, Keirstead, and Rebholz (1998). For a discussion of pricing lookbacks (and barrier options) using a constant elasticity of variance process, see Boyle and Tian (1999).

The following example displays the value in sixteenths, with a quotation mark appended to the right. This format string is useful when you deal with inches (for example, 2/16 ).

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Power flux-density values to facilitate the application of RR Article 14 for the FSS in Region 2 in relation to the BSS in the band 11.7-12.2 GHz Ways of reducing the interference from the broadcasting-satellite service of one Region into the fixed-satellite service of another Region around 12 GHz Ways of reducing the interference from the broadcasting-satellite service into the fixed-satellite service in adjacent frequency bands around 12 GHz Fixed-satellite and radiolocation/radionavigation services sharing in the band 13.75-14 GHz Compatibility between the fixed-satellite service and the space science services in the band 13.75-14 GHz Sharing between the inter-satellite service involving geostationary satellites in the fixed-satellite service and the radionavigation service at 33 GHz Sharing between feeder links for the mobile-satellite service and the aeronautical radionavigation service in the Earth-to-space direction in the band 15.4-15.7 GHz Sharing between feeder links for the mobile-satellite service and the aeronautical radionavigation service in the space-to-Earth direction in the band 15.4-15.7 GHz and the protection of the radio astronomy service in the band 15.35-15.4 GHz Feasibility of sharing between spaceborne passive sensors of the earth exploration-satellite service and inter-satellite links of geostationary-satellite networks in the range 50 to 65 GHz Feasibility of sharing between the inter-satellite service and the fixedsatellite service in the frequency band 50.4-51.4 GHz Requirements and suitable bands for operation of the inter-satellite service within the range 50.2-71 GHz

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