Bloomberg Fair Value Market Curves

1. Bloomberg Fair Value Market Curves Michael Lee Fixed Income Specialist, Bloomberg LP International Bond Market Conference 2007, Taipei 2007 Bloomberg L.P. All rights reserved.

2. What Are BFV Curves? • Bloomberg generates BFV (Bloomberg Fair Value) curves, aka fair market sector curves, or best fit curves, for many bond sectors, grouped by currency, sovereign, agency, corporate, industry, issuer, and credit ratings. • Currently, Bloomberg provides 483 BFV curves, covering 37 different currencies: - USD 148 - EUR 106 - CAD 45 - JPY 42 - GBP 20 - AUD 17 - KRW 17 • BFV curves are used to generate Bloomberg Fair Values (BFV) for bonds under different bond sectors. 2007 Bloomberg L.P. All rights reserved.

3. BFV Curve for USD Industrial A 2007 Bloomberg L.P. All rights reserved.

4. Sector Bonds for BFV Curve on USD Industrial A 2007 Bloomberg L.P. All rights reserved.

5. Definition of Bloomberg Fair Value • The Bloomberg Fair Value (BFV) model generates two sub-products: - An option-free, par coupon yield curve, and - An objective price for a bond that may or may not be priced by a market maker. • A BFV price is a model or derived price of a bond. It indicates where the price of a bond should trade based on where comparably rated bonds with comparable maturities actually trade. • The BFV price is derived by utilizing well-priced bonds with similar characteristics i.e., currency, market type, industry, and credit rating. A yield curve is built daily for each sector based on the population of bonds directed to that sector or curve. • The model derives a price for a bond based on the BFV market curve. Many bonds will have a BFV price without the bond’s physical presence on a sector curve. 2007 Bloomberg L.P. All rights reserved.

6. In Search of High Quality BFV Curves • Lack of Market Transparency - Most bonds are traded over-the-counter - High quality executable prices generally unavailable • Lack of Liquidity - In many bond markets, liquidity tends to concentrate on a handful of bonds - Pricings are unavailable for the illiquid bonds • Need reliable prices for mark-to-market, bond portfolio risk management and relative value comparison. • The current system for search of optimal BFV curves was first developed during1995-1997 by Ralph Birnbaum, David Klein and Eric Berger of our Tel Aviv Bloomberg Quantitative team. • The goal of the BFV project was to use the OAS framework to create a reference pricing curve for each credit sector. 2007 Bloomberg L.P. All rights reserved.

7. Mapping Bonds to a Sector • Bonds are mapped into different bond sectors, differentiated by the following: - currency denomination - country - supranational (e.g. World Bank, ADB etc.) - Sovereign - Agency (e.g. GNMA, FNMA etc.) - Industry sector (e.g. bank, industrial, utilities etc.) - Issuer (e.g. Ford Motors) 2007 Bloomberg L.P. All rights reserved.

8. Identifying Credit Sectors • All credit sectors are grouped into clusters that usually contain 1 or more similar sectors. • For instance, for industrial sector, 9 different credit sectors {AAA, AA1, AA2, AA3, A1, A2, A3, BBB1, BBB2, BBB} are grouped into 4 clusters as follows: AAA = {AAA}, AA = {AA1, AA2, AA3}, A = {A1, A2, A3}, BBB = {BBB1, BBB2, BBB3} • Major reason for the clustering is that there might not be enough bonds in a given credit sector. • Bloomberg Composite Rating system is adopted for the credit sectors • Bloomberg Composite Ratings are averages of Moody’s, Standard and Poor’s and Fitch. 2007 Bloomberg L.P. All rights reserved.

9. Gathering Price Data • Only bonds with Bloomberg Generic (BGN) prices are included. • BGN price is the simple average price of all kinds of prices, including indicative prices and executable prices, quoted by our price contributors over a specified time window. • The availability of BGN price for a bond is an indication of good liquidity for that bond. • In some cases, bond prices from a specific pricing source are used in lieu of BGN prices (e.g. fixing prices). • Outliers (i.e. bonds whose OAS are significantly higher or lower than OAS of comparable bonds) are excluded. 2007 Bloomberg L.P. All rights reserved.

10. Yield Curve modeling • The zero yield curve is modeled and all other curves ( par coupon curve and forward curve ) are derived from the zero curve. • We use a piecewise linear function to estimate the zero coupon yield curve. • The advantage of a piecewise model is that it contains more points (parameters) than parameterized smooth curve (which only contains 4-5 parameters). More parameters can better fit a sector yield curve. • One disadvantage of piecewise function is that it could result in unstrippable zero curves and negative forward rates as well. • The smoothed curve function , though never generates unstrippable curve and always has positive forward rates, can’t in general fit the sector curve as well as a high parameter piecewise linear curve. • An additional disadvantage of the smoothed curve function is that, when the curves have complex parameterizations, it is hard to analytically specify the cross sector constraints, and thus hard to enforce them in the optimization of the curves. 2007 Bloomberg L.P. All rights reserved.

11. Constraints • Pure parameters constraints - the upper and lower bounds imposed on each parameter to ensure the optimization engine would work properly • Yield constraints - Credit constraints: Forward curvefi(T) > fj(T) if credit sector i is risk than j for any T  0; - Positive forward rates constraints: Forward curve fi(T) should be positive for any sector I for any T  0; - Technical constraints: Zero curve Zi(T) must be in the functional set suitable for the current bond price – OAS pricing engine. - Continuity constraint: the yield curve is continuous at all points on the curve, including the yields adjacent to the maturity points. 2007 Bloomberg L.P. All rights reserved.

12. Interest Rate Model • The interest rate model used in the yield curve modeling is the lognormal model. • Any interest rate options embedded in callable and puttable bonds are valued with the lognormal interest rate model. • Zero curve Zi(T) and yield volatility σ are the parameters of the lognormal interest rate model. 2007 Bloomberg L.P. All rights reserved.

13. Optimization Process • The bonds within the same credit sector are broken down into zero coupon cash flows • A constant OAS spreadis added to the zero curve Zi(T) to generate a set of discount rates which are used to discount cash flows of any bond into its present value. The present value of a bond’s future cash flows is the estimated market value of that bond. • For any given set of zero curve Zi(T), OASi is determined such that the estimated market value of the bond i is equal to the BGN full price of that bond. • If a bond has embedded option, as in a callable bond or puttable bond, both implied volatility and ∆OAS are determined for the bond. • The optimized zero curve, or the best fitted zero curve, is the curve that minimizes the sum of squares of OASi. • Par coupon curves are derived from the optimized zero curves. 2007 Bloomberg L.P. All rights reserved.

14. OAS of Bonds in USD Industrial A 2007 Bloomberg L.P. All rights reserved.

15. Unstrippable Zero Curve and Negative Forward Rates • The piecewise linear zero curve model was chosen back in 1995 because of its computational efficiency. This was an important consideration given the fact that there were more than half a million bonds in Bloomberg’s bond database and there were close to 400 sector curves to be built by then. • However, a major drawback of this model is the possibility of generating unstrippable zero curve and negative implied forward rates. When this occurs, manual overriding of the curve with be performed by our team of curve experts in Princeton. • One solution to this problem is to consider switching to a forward rate model from a zero curve model. • The drawback of forward rate model is computation efficiency. However, with computation speed and power increasing at exponential rates and computational costs dropping sharply in recent years, forward rate model is becoming a viable option. 2007 Bloomberg L.P. All rights reserved.

16. Quality of Bond Pricing • Bond prices we receive from our price providers can be categorized into: - Indicative prices - Executable prices - Traded prices • Indicative prices account for nearly 90% of the bond prices available on the Bloomberg bond database. Since market makers have no obligation to execute trades at indicative prices, it is not unusual to find indicative prices being way off the actual market prices. • Executable prices are available only for bonds traded at some electronic trading platforms. However, most electronic trading platforms offer executable prices to non-competitors only and the subscription costs for executable prices could be very expensive. • Providing a free platform on the Bloomberg for electronic trading is one of our major bond initiatives in recent years. Currently, more than 10,000 bonds out of 510,000 bonds on Bloomberg database have CBBT prices, which are BGN prices based on executable prices. 2007 Bloomberg L.P. All rights reserved.

17. Availability of Credit Rating • Mapping bonds into credit sectors relies on availability of credit ratings by the rating agencies. • BFV cannot be determined for bonds without credit ratings. • One solution is to derive a Shadow Rating based on market prices available. The credit rating associated with the credit sector curve that generates the lowest OAS for the bond is considered as the Shadow Rating. 2007 Bloomberg L.P. All rights reserved.

18. Structured Products • The issuance of structured bonds linked to interest rates, credit, equities, FX and commodities has increased dramatically over the past few years, requiring complex and sophisticated models to derive model prices. • Currently, almost all of the structured products have been issued by highly rated banks (with AA rating or better). • Bloomberg provides pricing models to our users for the following types of structured products: - Interest rate structured products - Equity linked structured notes - Convertible valuation model - Pricing models for single name CDS, FTD baskets and CDOs - FX option pricing models for pricing FX options embedded in FX structured products 2007 Bloomberg L.P. All rights reserved.

19. Default Probability • The phenomenal growth of the credit derivatives market witnessed over the past few years has yielded an additional dimension for curve pricing. • Currently, we have CDS spreads provided by our contributors for over 1,800 reference entities. • CDS spreads provide information related to default probabilities of reference entities. • Information on default probability and recovery rate can help us price corporate bonds with different collateral structures. 2007 Bloomberg L.P. All rights reserved.

20. End of Presentation 2007 Bloomberg L.P. All rights reserved.