are readily identified with portfolio positions of duration, flattening/steepening, butterfly, etc.
● It is flexible and can be easily applied to mortgage prepayment models, emerging markets, multi-currency portfolios, inflation linked bonds, derivatives analysis, etc.
● It can be used as an indicator of relative value or relative curve positions in a consistent way across currencies and credits.
● The model is easily applied to all global rates, term structure of Libor, term structure of real rates and term structure of credit rates.
● The model is very stable and, unlike cubic splines, can be easily differentiated multiple times if necessary.
Throughout this book we have provided detailed examples of the applications of our model to risk measurement, performance attribution and portfolio management. We first introduce the concept of linear and non-linear time space and then construct the components of our term structure model and forward rates. Next, we derive duration and convexity components and calculate performance attribution from duration components.
In Chapter 6 Libor and interest rate swaps are covered and the model is applied to the term structure of Libor rates. It is shown that interest rate swaps have a structural problem that makes them subject to arbitrage. In Chapters 7 and 8 trading and portfolio optimization and security selection are examined. In Chapter 9 a model for the term structure of volatility surface is developed, and in Chapter 10 the effects of convexity and volatility on the shape of the TSIR are analyzed and the convexity adjusted TSIR model is developed. The convexity adjustment to eurodollar futures is also covered and potential arbitrage opportunities are pointed out. In Chapter 11 there is a very detailed and precise coverage of inflation linked bonds along with the application of the term structure of real rates to global inflation linked bonds as well as inflation swaps.
In Chapter 12 credit securities are analyzed and the term structure of credit rates (TSCR) with its application to performance attribution and risk measurement is analyzed. In Chapter 13 default and recovery or cash flow guarantees of credit securities are analyzed and for the first time the TSCR is used to estimate the market implied recovery rate. The application of the TSCR to credit default swaps and construction of performance attribution for complex portfolios are also analyzed in this chapter.
Analysis of global bond futures and their hedging, replication, arbitrage and performance attribution are covered in Chapter 14. Bond options and callable bonds are covered in Chapter 15 along with a very detailed analysis of American bond options with accuracy approaching closed form solutions. The weaknesses of the Black-76 model are pointed out and the model is applied to corporate bond options and exotic securities. It is shown that credit bond prices cannot follow the efficient market hypothesis and there are long term opportunities in the credit markets for fund managers.
In Chapter 16 currencies as an asset class along with their options and futures are covered and models to take advantage of currencies in a portfolio are explored. Chapters 17 and 18 cover the application of the TSIR to prepayments and development of mortgage analysis. In Chapter 19 product design and portfolio construction are covered and a method is developed to analyze the competitive universe of a bond fund. Chapter 20 covers detailed mathematical derivations of the parameters of the TSIR and TSCR and estimation of recovery value, and Chapter 21 covers implementation notes and short-cuts.
Chapter 1
Review of Market Analytics
This chapter reviews some of the basic analytics for fixed income securities and provides evidence for the inadequacies of the existing models. The simplest and most straightforward fixed income instrument is a bond. A bond is a security that pays interest at prescribed intervals, called coupon dates, and pays back the principal and final coupon on the maturity date.
Consider a company or a government that borrows $100 million for a period of 5 years at a rate of 7 % per year payable at semi-annual intervals. The borrower, also known as the bond issuer, will have to make coupon payments equal to 3.5 % of the borrowed amount or $3.5 million every 6 months to lenders, also known as bond holders or investors. At the end of 5 years, the borrower pays $3.5 million of interest plus the $100 million principal back to the lenders.
The above example is a typical bond, where the borrower, unlike mortgage borrowers, cannot pay back the principal earlier than scheduled. The bond holder can usually sell the bond in the secondary market and receive a fair price for it.
The primary risk of a bond holder, other than default, is a rise in interest rates. If inflation expectations increase, bond investors demand higher interest rates to compensate them for anticipated inflation that will lower their future buying power. Likewise, if inflationary expectations fall, interest rates are likely to fall as well. During rapid economic growth, demand for money rises, which can lead to higher interest rates. During recessions or low economic activity, demand for money falls, usually resulting in lower interest rates.
1.1 BOND VALUATION
If interest rates fall, the value of an existing bond increases since investors will pay a premium price for a bond that has a higher coupon payment than a newly issued bond with a lower coupon. This brings us to the simplest and most fundamental of all pricing formulas in the fixed income market, namely the present value of a bond, defined with a principal amount of 100 as
1.1
where p is the present value of the bond, ym is the market yield or effective interest rate of the bond, m is the frequency of coupon payment (if the bond pays semi-annual interest, then m = 2, if it pays quarterly, then m = 4), c is the periodic coupon payment, and n is the number of interest payments. It can be easily shown that if the present value of the bond on issue date is equal to 100, then the following relationship holds:
1.2
In our prior example, the semi-annual coupon payment per 100 of principal would be 3.5. Inserting this value for c, and using m = 2, leads to a yield of 0.07 or 7 %. Thus, on issue date, the yield of a bond priced at 100 (par) is equal to the annual coupon payment of the bond per 100 principal amount divided by 100. At all other times, the price/yield function of a bond is a little more complicated.
Nearly all bonds in the market are traded on the basis of what is known as the clean price. The clean price does not include the amount of interest that has been accrued but not paid to the bond holder. Accrued interest is the pro rata share of the next coupon payment that is due the seller at the time of the trade settlement. In our previous example, if after 3 months the bond holder sells his bonds, then the buyer has to pay half of the next coupon payment to the seller for holding the bonds for half the period of coupon payment.
Different
