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For example, in the following spreadsheet below, I conjectured five coupon-bearing bonds (yellow background indicates inputs). The first bond is a zero (no coupon) paying par in six months. Since this bonds price is $98, its discount factor is 0.98.
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Now let's bootstrap the one-year (theoretical) spot rate. The price of the 4% coupon one-year bond is $99.00. If d(1) is the one-year discount factor, then the following must be true: $99 = $2(0.98) + $102[d(1)]. Make sure you see how the price of the one year bond is a function of two cash flows: the discounted $2 coupon [$2 x d(0.5)] and the discounted final cash flow [$102 x d(1.0]. 天下金融网
Solving for d(1) gives 0.9514, the one-year discount factor. Now this d(1) discount factor will be used for all coupons that are paid in one year. 21jrr.com
Translate discount factor to spot rate
Below the discount function (i.e., the series of discount factors) are the spot rates. The spot rate is given by:
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..and we could rearrange to solve for the discount rate...
Knowing our d(1) = 0.9514, the one-year theoretical spot rate is 5.05% because 5.05% = 2* [(1/0.9514)^(1/2)-1].
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Term structure of interest rates
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The spreadsheet below repeats this for each maturity. The set of spot rates produces the term structure of interest rates:
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The average rate on a 30-year fixed rate mortgage returned to a point near record lows during the we...
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