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Unformatted text preview: 192 Answers to Questions and Problems 1. Explain the relationship among mortgagebacked securities, mortgage passthroughs, and collateralized mortgage obligations. The mortgagebacked security (MBS) is a security that gives the security owner rights to cash flows from mortgages that underlie the MBS. The MBS comes in two basic types: mortgage passthrough securities and collateralized mortgage obligations. The owner of a passthrough owns a fractional share of the entire pool of mortgages that underlie the passthrough security. The owner of a passthrough participates in all the cash flows from the underlying mortgage pool. A collateralized mortgage obligation (CMO) is another type of MBS. A CMO is created by decomposing the cash flows from a pool of mortgages. For example, some CMOs are backed by interestonly payments from a pool of mortgages, while other CMOs might be backed by principalonly payments from the same mortgage pool. 2. Explain the similarities and differences between the zerocoupon yield curve and the implied forward yield curve. Both the zerocoupon yield curve and the forward yield curve show rates of interest that apply to single future payments. The rates from both curves can be used to discount a single payment from a distant future date to an earlier date. The zerocoupon yield curve gives discount rates for discounting a distant payment to the present. The rates from the forward curve are essentially rates for discounting a distant payment from its payment date to a time one period earlier. For example, if the forward curve has annual rates, the forward rate for a period from year 7 to year 8 could be used to discount a payment to be received at year 8 back to year 7. Together, the singleperiod forward rates that constitute the forward yield curve can be used to discount a distant payment back to any earlier time. 3. Given the zerocoupon yield curve, explain how to find the implied forward yield curve. The forward rate between any two periods is a function of the zerocoupon discount rates for a horizon from the present to the initiation point of the forward rate and the zerocoupon rates for a horizon from the present to the termination date of the forward rate. For example, consider a singleperiod forward rate from year 5 to year 6. This forward rate can be found by using the zerocoupon yield curve to find the zerocoupon factors for years 5 and 6, Z 0, 5 and Z 0, 6 . The forward rate factor for this period, FRF 5, 6 , is given by: FRF 5, 6 5 Z 0, 6 Z 0, 5 19 Interest Rate Options ANSWERS TO QUESTIONS AND PROBLEMS 193 Given the set of oneperiod FRF s, the elements of the forward yield curve can be found quite easily, because the oneperiod forward rate is simply the oneperiod FRF minus 1: In general, for any forward rate factor for a period beginning at time x and ending at time y , we have: 4. Given the implied forward yield curve, explain how to find the zerocoupon yield curve....
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 Spring '08
 Danısoglu
 Interest, Interest Rate, Options, Yield Curve, Forward rate

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