This topic explains three zone digital swaps and then describes how to use the associated template in SWPM to price a three zone digital swap.
Three zone digital payoff securities are popular financial instruments that are traded as both OTC three zone digital swaps with a funding leg and as structured notes (three zone digital bonds/options).
The receiver of the triple digital exotic payoff obtains one of the determined alternative payoffs. The payoff for each coupon date depends on the level of the observation index immediately before the coupon payment date:
• If the index is above a pre-determined level, an “A” payoff occurs. • If the index is between the two barriers, a “B” payoff occurs. • If the index is below a pre-determined level, a “C” payoff occurs.
273 1.) In the Calculate drop-down menu, calculates the market value based on your inputs. The Market Value appears in the
Valuation section. 2.) The premium, calculated as (Market Value / Notional) x 100.00. 3.) In the Solver drop-down menu,
calculates the net present value (NPV) based on your inputs. The NPV appears in the Results section.
274 The option-adjusted spread. To value this structure with a spread (OAS), enter an appropriate bps amount in the OAS
cell on the main screen valuation section. When you launch SWPM, the premium should be calculated at an OAS of
zero. When the OAS is changed, the premium is re-computed and the PV of cashflows is adjusted accordingly.
275 Displays the Par Shift Quick Calculator, a scenario analysis tool that allows you to analyze the relationship between the
discount curve and the premium. The Par Shift Quick Calculator presumes that cashflows are unchanged and shifts only
the discount curve. Par shift is the shift on the par curve (not stripped).
276 Displays the Z-Spread Quick Calculator, a scenario analysis tool that allows you to analyze the relationship between the
discount curve and the premium. The Z-Spread Quick Calculator presumes that cashflows are unchanged and shifts
only the discount curve. The Z-Spread is the spread of the stripped, zero-coupon curve that makes the multi-leg deal
premium match the value specified in the Premium field.
277 The percentage price change of the deal for a given change in yield. The higher the duration of the deal, the higher its
risk.
278 The percentage duration change of the deal for a given change in yield. The convexity is the second derivation of the
deal's price with respect to yield, divided by the price. The deal exhibits positive convexity when its price rises more for a
downward move in yield than its price declines for an equal upward move in yield.
279 The vega for the swaptions priced by the HW1F model is the change in market value for a 1% shift in volatilities of the
swaptions to which one calibrates.
You can use the shortcut SWPM -TZD <Go> to access the three zone digital template from the command line. Since three zone digitals are often traded OTC as a swap and with a funding leg, you can use a “two-legged” structure as well. You can use the shortcuts SWPM -TZD -FLT <Go> or SWPM -TZD -FIX <Go> to access the two-leg structure from the command line. Alternatively, you can click the Products toolbar button to choose a template from a menu.
• For more information about shortcuts, see Shortcuts.
• For information about how to load templates from the toolbar, see Choosing a Template.
SWPM's three zone digital template is organized into tabs that allow you to set up and analyze the swap. You can structure and value your swap on the Main tab of the template, which is divided into two sections. You can input details of the swap in the three zone digital leg section, and then evaluate the swap in the valuation section.
• Control Area: Allows you to navigate between tabs, analyze deals, and configure your default settings.
• Three Zone Digital Details: Allows you to configure your settings for the deal. You can enter, for example, the notional amount, currency, effective date, and maturity, for the deal, along with the observation index and the threshold that determines the payoff for the deal. The DiscountCrv/Forward Crv fields allow you to update the curve that SWPM uses to discount/project cashflows when calculating the Market Value of the swap. The deal's stochastic features are priced using a customized volatility cube. The Vol Cube drop-down menu allows you to choose between Flat volatility (manual input) and volatilities from the Volatility Cube (VCUB) function. You can customize the deal coupon by coupon by selecting View >
Detail > Custom from the toolbar.
— For definitions of the fields on the template, see Definitions.
— For information about how to update the curves that appear by default, see Setting a Source Curve. — For information about VCUB, see VCUB <Help>.
• Valuation: Allows you to backdate the curve, so you can price swaps as of a historical date. SWPM calculates the market
value using the selected curve at the market close of the day indicated in the Curve field. The Valuation date is the date at which future cashflows are discounted.
Note: By default, SWPM prices swaps as of today, i.e., the default curve date is the current date. To price swaps as of a historical date, you must backdate both the Curve and Valuation fields. For example, to mark to market at quarter's end,
you can enter the historical quarter-end date in both the Curve Date and Valuation fields. You can visualize, customize, and apply shifts to the selected curve by selecting View > Curve from the toolbar.
The Valuation section allows you to make a note callable, as well as select the variable you want to solve for and evaluate the swap. You can calculate the market value of the deal (the sum of the present values of the receive leg minus the sum of the present values of the pay leg), or you can customize the valuation by choosing a variable from the Calculate drop-down menu. You can solve for the following variables: Premium281, OAS282, Par Shift...283, Z-Spread...284. DV01285, Delta286
, and Vega287 values appear, along with the value of the note without callability and the value of the call option. For definitions of the fields on the template, see Definitions.
You can further analyze three zone digital swaps by selecting another tab from the control area. Additionally, you can save your deal by selecting Actions > Save from the toolbar. Once you save the deal, you can access it from other Bloomberg functions or through Bloomberg's API by entering the deal number followed by the <CORP> key. For example, this allows you to download the cashflow schedule for an individual leg to Microsoft® Excel with Bloomberg's API.
• For information about the other tabs that appear on the template, see SWPM Tabs. • For more information about saving deals, see Saving Deals.
• For examples of using the template to price a plain vanilla swap, see Example: Solving for Spread and Example: Solving for
Price.
• For information about Bloomberg's API, see DAPI <Help>.