**Bond Pricing**

Thats what this option does. Note that to get the very best performance, you should use this function as an array function which always calculates the whole curve. In other words: It does not affect the calculations, just the speed of processing. Option 0 is optimal for one or two calls to ZeroCoupon, because it only calculates the part of the curve that is needed.

Option 1 says, OK, we are going to use the curve alot over many calls, so lets calculate the whole curve, and, provided we get the same set of inputs, we will not calculate the curve again, but use the curve we have stored internally. On the whole, Option 1 is what most people would want. Performance The function has to create a zero coupon curve internally using the bootstrap method.

The formula says that if the tenor of the grid as shown in column A [cash flows] exceeds the tenor of the bond [row 14] then a zero value will be returned otherwise:.

## Business Functions Library for Excel

If the tenor of the grid equals the tenor of the bond the cash flow will equal the coupon and principal amount due on the maturity of the bond, i. If the tenor of the grid is less than the tenor of the bond the cash flow will equal the coupon of the bond, i. The price of the bond is equivalent to the sum of the present value of each cash flow discounted using the relevant zero rates over the respective tenors.

For a quarterly payment frequency this means that:.

## Bootstrapping the Zero Curve and Forward Rates

Under the assumption of par bonds, the bond price, at time 0 is equal to it face value, which we will assume is As you can see from the formula above, the discounted values are functions of zero rates and we have yet to derive these rates. This issue is solved when we take into account the par bond assumption and the iterative process.

This is illustrated in the steps that follow. Let us start with the shortest tenor bond, the 0. Its cash flows are coupon and principal payable at maturity of The present value of the 0.

Hence, according to the price formula we have:. We have labelled this derivation of the discount factor as df 0.

The value of df is based on the discounted final cash flow and the final cash flow at maturity of a given bond. The value of the zero-coupon bonds must equal the coupon bond; otherwise, an arbitrageur could strip the bond and sell the zeros for a profit, as they sometimes do. The forward rates thus calculated are not forecasts of future interest rates, since future interest rates are unknown.

Rather, the forward rates are simply calculated from current bond prices; hence, they are sometimes referred to as implied forward rates , because they are implied by the market prices of the bonds in the same way that implied volatility is determined by market option prices. Treasuries are the ideal bond to use in constructing a yield curve because they are devoid of credit risk, so Treasury prices depend more on market interest rates.

Treasuries define a risk-free yield curve, but the market prices also imply forward rates, which are yields for certain periods in the future. Because Treasury notes and bonds are generally issued as coupon bonds, their prices cannot simply be used to construct the spot rate curve or to calculate forward rates.

### 3 -Ways to Bootstrap Spot Rates for the Treasury Yield Curve

Instead, a theoretical spot rate curve and implied forward rates are constructed through the process of bootstrapping which calculates the forward rates by considering the value of the zero coupon bonds that are equivalent to the Treasury bond. The calculated forward rates can then construct the spot-rate curve by adding the yields for each term to the desired maturity. The bootstrapping technique is based on the price-yield equation using different rates for each of the 6-month terms, as determined by market prices:. The interest rate is 1 st calculated for the 6-month bond that has a known market price, which has only a single payment, consisting of the coupon payment and the principal repayment, at its maturity.

After the rate is calculated for the 1 st period with the 6-month bond, then that rate is used to calculate the rate for the 2 nd period of a 1-year bond, and so on, until all the rates for the desired number of terms for which there are market prices available have been determined.

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This is referred to as the bootstrapping technique, because the prior calculated spot rates are used to calculate later spot rates in successive steps.