Zero Coupon Swap

8/10/2019 Zero Coupon Swap

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HOW TO PRICE A ZERO

COUPON SWAP USING

SWPM

10 March 2010Version: 1.00


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How to price a Zero coupon swapusing SWPM

SWPM is the main interest rate derivatives pricing function in the Bloombergprofessional System, allowing users to price a wide range of vanilla and exotic interestrate swaps, interest rate options, swaptions and interest rate and hybrid structurednotes.

In a plain vanilla swap, counterparties will exchange cash flows during the life of theswap in the frequency that was pre-established. For zero-coupon swapsthe onlychange is that there will be only one exchange of cash flow at the maturity date.

Although the payment occurs only at maturity, the rates compound according to the pay

frequency tab.

In this document we will show how to use SWPM to price a Zero Coupon interest rateswap transaction, how to store it in the system, how to retrieve it and calculate a mark tomarket price with current markets or historical curves.

To do this we will use as example a 5 year EUR Zero coupon swap where user receivesa fixed rate of 2.54526% against paying 6M EURIBOR compounded and paid atmaturity.


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New ScreensThe screens have been redesigned for easier navigation. You can click on the tabs atthe bottom of the screen for quick access to the various screens. The Leg Detail tab

now consolidates screens for date generation, amortization and payoffs .

Click on the Configure field in the upper right corner to display the DateGeneration, Amortization or Payoff screens. You can use the payoffscreens to do step up fixed coupons or increasing spreads for floating legs.TheAmortization section allows you to add various amortization balancepayoffs using a loan or security. For more details on amortization, please

see DOCS #2052082 .

The Date Configure section regenerates dates based on different first/lastpayment dates and roll conventions. Click on Export to Excel to export thedata from these screens to Microsoft Excel. You can also drag and dropdata from Excel for specific columns in the detail section for custom payoffsand amortization.


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The Leg Detailtab can also be launched when you click on the buttonfrom Leg section in the top half of the screen. To switch between legs, clickon the radio buttons next to Leg1 or Leg2.

Current market value is calculated based on the selected curves andappears in the Market Value section in the bottom of the screen. You canmodify interest rate curve defaults for each currency via SWDF .

For Mark to Market using historical curves with a backdated evaluation(mark to market at a specific date in the past), select the desired Curve andValuation Date from the Valuation section. The Market Value that appearsis calculated using the selected curve at the market close of the day,indicated in Curve field. The Valuation Date is the date at which future cashflows are discounted.

Use of SolversUsing the Calculate Menu in the lower part of the main screen, you canselect the variable to solve for. The following is a list of variables:

Fixed Coupon:Calculates a fixed coupon that has to be used tohave a market value divided by the notional equal to premium in thePremium field.

Notional:Calculates a notional amount based on your Dv01 input.

Spread:Calculates the floating leg spread that has to be used inorder to have a market value divided by notional equal to thepremium indicated in the Premium field.

Premium:Calculates the market value of the swap.

Par shift function: The Par Shift Quick calculator is a scenarioanalysis on the relationship between the discount curve and thepremium. The cashflows are presumed unchanged. Only the discount

curve is shifted. As such, par shift is the shift on the par curve (notstripped).

You can either enter a spread to calculate the premium or enter apremium to calculate the spread.


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Function Output Description Output fields in each leg:

Market Value:The sum of the present values of the leg cash flows.

Accrued:The amount of interest accrued on the leg since the last legcash flow date, calculated as leg coupon * day count fraction.

Premium = Leg Principal / Leg Notional

Net Valuation Section:

Principal:market value minus accrued.

Accrued: the amount of net interest accrued, calculated as the sumof the accrued interest for both legs. Each legs accrued interest iscalculated as the leg coupon *day count fraction.

Market Value:Market Value of the Receive Leg - Market Value of thePay Leg.

Premium:Principal / Notional

Unwind PV:sum of present value of existing transaction and of anhypothetical unwinding transaction where user pay (receives) acoupon specified in Unwind Coupon field in fixed leg section(unwinding coupon is considered paid if in the base transaction userreceives a fixed coupon or received if in the base transaction userpays a fixed rate).

Par coupon: the fixed coupon rate that results in a swap with zeronet market value.

Net DV01:Receive Leg DV01 - Pay Leg DVO1


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Deal Main Details and Saving FunctionalityYou can save the deal using the Save Deal button, with the ability tospecify:

On the main screen, first line: Counterparty name, a ticker and a

series numbers.

Deal Detail button located on the main screen, first line: Privilegetype, presence of exchange on notional and if timing of eventualprincipal exchange, Custom ID number and deal notes.

When saving a deal, a deal number is automatically assigned and the dealis stored as a (F3 key) transaction.

To evaluate a saved deal:

Use the Options/Listall deals option and select User or Firmprivileged from the dropdown menu that appears.

Type deal number, followed by , then type SWPM .

An Excel file is available to evaluate portfolios of swaps and interest ratestructured notes saved in the system using the SWPM function. To access

the file, type XIRS .


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Curves ScreenIn Curves Screen you can:

Visualize and export in Excel the par or zero coupon curve used for

swap evaluation.

Manually override curve values and apply shifts to the whole curve orto defined buckets.

Choose the interpolation method.


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Cash Flow ScreenUse the Cashflow screen to visualize and export deal cash flows to anExcel spreadsheet. You can choose between Net, Payor Receivefrom theCashflowfield. For existing deals, you click on show historical cashflows.

The fixed and float section now displays the number of days in eachcoupon period for validating your cash flows with counterparties.


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Risk ScreenThe Risk screen displays some key risk measures for each leg:

DV01:The dollar value of a 1-basis-point negative shift in the curve.

Risk:The risk for each leg and the deal is calculated according to thefollowing equations: Risk = [DV01 / Notional] x 10,000

Modified Duration[DV01 / (Notional + Market Value)] x 10000

Key Rate Risk:The change in the market value of the deal for abasis point change on a particular swap rate. For example, if the parcurve is shifted up or down by one basis point at a particular termpoint, and the rest of points on the par curve remains the same, the

dollar change in market value divided by 2 is the key rate risk for thatparticular term.

Grid Point Delta:The measure of the price change when a particularterm rate changes. For example, if the spot curve is tent shifted up ordown one basis point at a particular term point, it indicates the shift istent-shaped, rising linearly from zero at the previous term point,peaking at one basis point at a particular term point, and decliningback down to zero at the following term point.


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Horizon ScreenUse the Horizon screen to perform what-if analysis using differentscenarios of curves and evaluation dates:

Horizon Curve Date:Can be historical, today, or in the future. If thedate is historical, then historical data from that date for the curveselected (which can be a discount, forecast, or basis curve) is appliedin the valuation. If the date is today, then the most recent curve isused. If the date is in the future, then a snapshot of the most recentcurve is applied for that future valuation date.

Horizon Settle Date:The date to which future cash flows arediscounted.

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Zero Coupon Swap