Choudhry. Fixed Income Securities Derivatives Handbook

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Deacon, M., and A. Derry. 1994. Deriving Estimates of Inﬂ ation Expectations

From the Prices of U.K. Government Bonds. Bank of England Working Paper

no. 23, July.

———. 1998. Inﬂ ation Indexed Securities. London: Prentice Hall.

Fisher, T. 1930. The Theory of Interest. London: Pickering & Chatto Ltd.

Foresi, S., A. Penati, and G. Pennacchi. 1997. Reducing the Cost of Govern-

ment Debt: The Role of Index-Linked Bonds. In de Cecco, M., L. Pecchi,

and G. Piga, eds. Public Debt: Index-Linked Bonds in Theory and Practice.

Cheltenham: Edward Elgar.

James, J., and N. Webber. 2000. Interest Rate Modeling. Chichester: John Wiley

& Sons.

Waggoner, D. 1997. Spline Methods for Extracting Interest Rate Curves From

Coupon Bond Prices. Federal Reserve Bank of Atlanta Working Paper, 97–10.

Wojnilower, A. 1997. Inﬂ ation–Indexed Bonds: Promising the Moon. New York:

Clipper Group.

Chapter 14—Securitization and Mortgage-Backed Securities

Ames, L. 1997. Mortgage Backed Securities Analysis, in Fabozzi, F., Handbook of

Fixed Income Securities, 4th ed. New York: McGraw Hill.

Anderson, G., J. Barber, and C. Chang. 1993. Prepayment Risk and the Duration

of Default-Free Mortgage-Backed Securities. Journal of Financial Research 16,

1–9.

Arora, A., D. Heike, and R. Mattu. 2000. Risk and Return in the Mortgage

Market: Review and Outlook. Journal of Fixed Income, June, 5–18.

Bear Stearns. 1994. Asset-Backed Securities Special Report, 5 December.

Bhattacharya, A., and F. Fabozzi, eds. 1996. Asset-Backed Securities. New Hope,

PA: FJF Associates.

Fabozzi, F. J. 1997. Fixed Income Mathematics: Analytical and Statistical Tech-

niques, 3rd ed. New York: McGraw-Hill.

———. 2000. The Handbook of Mortgage-Backed Securities. New Hope, PA: FJF

Associates.

———, ed. 1998. The Handbook of Structured Financial Products. New Hope,

PA: FJF Associates.

———, ed. 1987. Mortgage-Backed Securities: New Strategies, Applications and

Research. London: Probus Publishing.

Fabozzi, F., and D. Jacob. 1996. The Handbook of Commercial Mortgage-Backed

Securities. New Hope, PA: FJF Associates.

Fabozzi, F., C. Ramsey, and F. Ramirez. 1994. Collateralized Mortgage Obligations.

New Hope, PA: FJF Associates.

Hayre, L., and C. Mohebbi. 1989. Mortgage Pass-Through Securities. In Fabozzi,

F., ed. Advances and Innovations in the Bond and Mortgage Markets. Probus

Publishing, 259–304.

342 References

Hayre, L., S. Chaudhary, and R. Young. 2000. Anatomy of Prepayments. Journal

of Fixed Income June, 19–49.

Morris, D. 1990. Asset Securitization: Principles and Practices. New York:

Executive Enterprise.

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18.

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Chapter 16—The Yield Curve, Bond Yield, and Spot Rates

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chap. 10–14.

Chapter 17—Approaches to Trading

Neftci (2000) is an excellent introduction to bond pricing and its relationship to spot

and forward rates. Campbell, Lo, and MacKinley (1997) is a very readable book,

worth purchasing for Chapter 10 alone, which is an excellent and readable study of

term structure, providing proofs of some of the results discussed in this chapter.

Brennan, M., and E. Schwartz. 1979. A Continuous Time Approach to the Pric-

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———. 1980. Conditional Predictions of Bond Prices and Returns. Journal of

Finance 35, 405 ff.

Choudhry, M. 2001. Bond Market Securities. London: FT Prentice Hall.

Campbell, J., A. Lo, and A. MacKinley. 1997. The Econometrics of Financial

Markets. Princeton: Princeton University Press.

Fisher, L., and M. Leibowitz. 1983. Effects of Alternative Anticipations of Yield

Curve Behaviour on the Composition of Immunized Portfolios and on Their

Target Returns. In Kaufmann, G., eds. Innovations in Bond Portfolio Manage-

ment. Greenwich, CT: JAI Press.

Neftci, S. 2000. An Introduction to the Mathematics of Financial Derivatives, 2nd

ed. Oxford: Academic Press.

“Out of Debt,” The Economist February 12, 2000.

References 343

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345

accreting (step-up) swap, 121

accrued interest, 17, 27–29

ACE Securities Corp, Home Eq-

uity Loan Trust, Series 2004,

276–277

agency mortgage-backed securities

(AMBSs), 249

American options, 137, 138,

160–161, 191

amortizing swap, 121

annualized interest rates, 7

annuity bonds, 35

annuity indexation, 215

arbitrage CDOs, 279, 285–286

arbitrage-free pricing, 194, 196

arbitrage models, 79

Asset-Backed Alert, 256

asset-backed securities (ABSs), 241

asset-linked swaps, 125

asset-swap pricing, 187–188

at-the-money, 138, 160, 191

backwardation, 102

balance sheet CDOs, 279, 285

Bank for International Settlement,

280

Barone-Adesi Whaley (BAW)

model, 157

barrier credit option, 179–180

Basel rules, 280

basis, 101–104

basis points, 37–38

basis point value (BPV), 38–40

basis risk, 104, 120

basis swap, 120–121

Bermudan options, 137

binomial interest rate trees,

193–194, 195, 196

Black-Derman-Toy model, 157

Black model, 152, 154–155

Black-Scholes

Microsoft Excel model, 331–

332

option model, 144–156, 192

pricing model, 122–124

Bloomberg YA screen, 128, 182,

294

bond equivalent yield, 26

bond futures, 96

Bond Market Association, 250

bond pricing

accrued interest, 17, 27–29

Black-Scholes model, 149–152

callable, 200–204

clean, 17, 27–28

consideration, calculating, 18

in continuous time, 51–56

dirty, 17, 27–28

INDEX

346 Index

fair, 15–16

present value and discounting,

6–15

principles of, 4–15

traditional approach, 15–19

bonds

See also inﬂ ation-indexed bonds

basic features and deﬁ nitions,

5–6

bond yield

levels, 3

traditional approach, 19–27

bootstrapping, 14, 84, 115, 303,

307–308

Brace-Gatarek-Musiela model, 157

Brennan-Schwartz model, 76

British Bankers Association, 6

B-splines, 90

bullet bonds, 5

butterﬂ y spread, 319

buyer, 138

call, 138, 228

callable bonds, pricing, 200–204

call feature, 6

call option, 191

call swaption, 122

Canadian Real Return Bonds, 214

capital indexation, 214

capital structure arbitrage, 184,

185

caplets, 171

cap level, 170

caps, 170–172, 228

cash amount, 5

cash ﬂ ow waterfall, 288

cash reserve funds, 265

CBOT, 319

Centauri, 232

charting, 316

cheapest to deliver, 104

Chicago Board Options Exchange

(CBOE), 139

Chicago Mercantile Exchange

(CME), 316, 317, 319

Citibank, 228

Citigroup, 232

clean bond prices, 17, 27–28

collar, 172

collared FRNs, 231

collateralized bond obligations

(CBOs), 279

collateralized debt obligations

(CDOs)

analysis of, 286–289

arbitrage, 279, 285–286

balance sheet, 279, 285

cash ﬂ ow, 286–287

conventional, structures, 280,

281–282

credit enhancements, 288

emerging market, 279

expected loss, 289

growth of, 279

legal structure, 288–289

objectives of, 280

originator’s credit quality, 287

portfolio characteristics, 286

reasons for issuing, 284–286

synthetic, structures, 283–284

collateralized loan obligations

(CLOs), 279

collateralized mortgage-backed

securities, 249

collateralized mortgage obliga-

tions (CMOs)

deﬁ ned, 249

features of, 257

growth of, 255–256

interest-only (IO), 245, 250,

261–263

nonagency, 264–265

planned amortization classes

(PACs), 256, 258–260

Index 347

principal-only (PO), 250,

261–263

sequential pay, 257–258

targeted amortization classes

(TACs), 256, 260

whole loan, 256

Z-class, 261

commercial mortgage-backed secu-

rities (CMBSs)

deﬁ ned, 249

issuing, 265–266

types of structures, 266–267

commodity futures, 96

commodity options, 133

compounding, 7–10

conduits, 267

constant maturity swap (CMS),

121

constant maturity Treasury

(CMT), 121

constant prepayment rate (CPR),

250–255

Consumer Price Index, 213,

216–221

contang, 102

continuously compounded rates,

continuous time, bond price in,

51–56

conventional bonds, 5

conventional CDO structures,

280, 281–282

conversion factor, 104

convertible bonds, 6

convexity, 41–45, 127, 208–209,

262

of mortgage-backed securities,

262, 271–272

corridor FRNs, 231

cost of carry, 101–102

Cost of Funds Index (COFI), 247

coupon, 5

coupon bonds, 47, 49, 51, 56

coupon frequency, 214

coupon payments, 5

coupon yield spreads, low- and

high-, 323–326

Cox-Ingersoll-Ross (CIR) model,

74–75

extended, 76–77

credit default swap, 178–179

credit derivatives

applications, 177–178, 184–

186

instruments, 178–183

pricing, 186–188

risk, 173, 175

role of, 175–177

credit enhancements, 264–265,

288

credit-linked notes (CLNs),

180–181

credit options, 179–180

credit rating, 5

credit spreads, 184–185

pricing models, 188

cross-default, 267

cubic polynomials, 87–88

current pay bonds, 215

current yield, 21, 35

day-count conventions, 28–29

default, technical versus actual,

173

default-free bonds, 4

delivered into, 96

delivery basket, 96

delta, 161–163

delta hedging, 162

delta neutral, 162

differential swap, 121

digital credit option, 180

dirty bond prices, 17, 27–28, 295

discount factors, 12–15

348 Index

discount function, 12, 55, 62

discounting, 6–15

discount rate, 4

calculating forward rate from

spot rate, 113–117

dividends, ex- or cum, 27–28

doji, 97

dollar value of a basis point

(DVBP), 127

Dorada Corp., 232

duration

calculating, 32–36

deﬁ ned, 32, 215

modiﬁ ed, 33–35, 37–41

of mortgage-backed securities,

271–272

properties of, 36–37

dynamic hedging, 162, 167

Eleventh Federal Home Loan Bank

Board District Cost of Funds

Index, 247

embedded options

arbitrage-free pricing, 194, 196

basic features, 190–191

binomial interest rate trees,

193–194, 195, 196

callable bond example, 189–

190

call provision, 192–193

convexity, 208–209

option-adjusted spread (OAS),

189, 206, 207–208

price volatility, 207

price-yield relationships,

205–206

pricing, 196–197

pricing callable, 200–204

pricing, risk-neutral, 197–198

recombining and nonrecombin-

ing trees, 198–200

sinking funds, 209–210

spreads, measuring, 206–207

valuation, 191–192

epsilon, 165

equilibrium interest rate models,

79–81

error, 84

eta, 165

Eurex, 139

Eurobonds, 24, 28

European options, 137, 138, 191

excess servicing spread accounts,

265

exchange-traded options, 137–139

expectations hypothesis, 63–65

expiry date, 138

extendable swaps, 120

face value, 5

Federal Home Loan Corporation

(Freddie Mac), 244

Federal National Mortgage Asso-

ciation (Fannie Mae), 244

ﬁ nancial options, 133

Fisher, Irving, 63, 220

Fitch, 174, 175

ﬁ xed-income instruments, deﬁ ned,

3–4

ﬂ at yield, 21

ﬂ oating-rate notes (FRNs), 6, 107

collared, 231

corridor, 231

hedging inverse, 233–234

inverse, 228, 231–233

step-up recovery, 231

variable-rate, 228

ﬂ oorlets, 172

ﬂ oors, 172, 228

forward interest rates, 22, 57–63

calculating, from spot rate dis-

count factors, 113–117

forward rate agreement (FRA),

316

Index 349

forwards

cash ﬂ ow, 96–98

deﬁ ned, 95–96

relationship between futures

prices and, 98–99

spot parity, 99–101

forward start swap, 120

forward yield curve, 59

Fremont Investment and Loan,

276

French OAT (Obligations Assimi-

lable du Trésor) strips, 49, 50

funded credit derivatives, 180

futures

basis and implied repo rate,

101–104

cash ﬂ ow, 96–98

deﬁ ned, 96

relationship between forward

prices and, 98–99

trading, 316–320

gamma, 163–164

Garman-Kohlhagen model, 157

geometric Brownian motion,

68–70

Geske model, 157

gilt options, 137–138

Government National Mortgage

Association (GNMA) (Ginnie

Mae), 244

Grabbe model, 157

Greeks, 161–168

gross basis, 103–104

gross redemption yield, 4, 21, 22

comparisons, 296

concept of, 294–295

Heath-Jarrow-Morton (HJM)

model, 68, 77–79, 188

hedging, 39–40, 104

bond positions, 326–329

delta, 162

dynamic, 162, 167

inverse ﬂ oaters, 233–234

options and, 133

simple, 326–327

swaps and, 127–131

Ho-Lee model, 73, 79

Hull -White model, 70, 72–73

hybrid securities

deﬁ ned, 227

ﬂ oating-rate notes, 228–234

indexed amortizing notes,

234–236

interest differential notes,

238–240

synthetic convertible notes,

237–238

immunization, 297

implied repo rate, 104

indexation, types of, 214–216

indexation lag, 213–214, 223–225

indexed amortizing notes (IANs),

234–236

index swap, 184

inﬂ ation-indexed bonds

cash ﬂ ows and yields, 216–223

coupon frequency, 214

index, choice of, 211–213

indexation, types of, 214–216

indexation lag, 213–214,

223–225

inﬂ ation expectations, 223–226

versus conventional bonds,

222–223

inﬂ ation rate, break-even, 222

interest differential notes (IDNs),

238–240

interest indexation, 214

interest-only (IO) bonds, 245,

250, 261–263, 275, 278

interest rate modeling. See term-

350 Index

structure modeling

interest rate swaps

applications, 124–131

generic, 106–111

non-vanilla, 119–121

interest yield, 21

internal rate of return (IRR),

19–20

International Swaps and De-

rivatives Association (ISDA),

105, 284

in-the-money, 138, 160, 191

intrinsic values, 137, 138, 191

intuitive swap valuation, 112

inverse ﬂ oating-rate notes, 228,

231–233

inverted shape, 49

issuer, 5

Ito’s lemma, 70–71

kappa, 165

lambda, 168

liability-linked swaps, 125

LIBOR (London Interbank Of-

fered Rate), 6, 107, 109–

110, 119–121, 228

LIBOR-in-arrears (back-set) swap,

121

linear interpolation, 86

liquidating trusts, 266

liquidity premium hypothesis, 65

London International Financial Fu-

tures and Options Exchange

(LIFFE), 138, 139

Macaulay’s duration. See duration

macroeconomic prices, 47

margining, 97–98, 229–230

margin swap, 120

martingale process, 54, 144

maturity, 5

maturity value, 5, 118–119

MBNA International, 242

mean reversion, 70

Merton model, 157

Microsoft Excel

Black-Scholes model in,

331–332

MDURATION function, 128

Moody’s Inc., 175

mortgage-backed securities (MBSs)