Choudhry. Fixed Income Securities Derivatives Handbook

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352 Index

put, 138

putable swaps, 120

put-call parity, 149

put option, 191

put provision, 6

put swaption, 122

quasi-coupon periods, 18

random variables, discrete versus

continuous, 68

real estate mortgage investment

conduits (REMICs), 263

recombining trees, 198–200

redemption value, 5

reference entity, 177

reﬁ nancing burnout, 255

reinvestment risk, 215

relative value, 315, 320–326

replicating portfolio, 196

repo rate, 183

reserve funds, 265

return-to-maturity expectations

hypothesis, 64

Reuters, 109, 182

rho, 166–168

risk-neutral price, 54, 197–198

risks

basis, 104, 120

credit derivative, 173, 175

mortgage prepayment and

default, 248–249

reinvestment, 215

roller coasters, 121

Roll model, 157

running cost, 21

running yield, 21, 35

secondary market, 17

securitization

See also mortgage-backed securi-

ties (MBSs)

deﬁ ned, 241

participants in, 242–243

reasons for, 242

segmented markets hypothesis,

65–66

semiannual-coupon bonds, yield to

maturity, 23, 25

senior/subordinated structures,

265

settlement date, 17

short (instantaneous) rate, 52, 193

processes, 68–70

simple interest, 6–7

Singapore International Monetary

Exchange (SIMEX), 139

single monthly mortality (SMM)

rate, 250

single-property/single-borrower

loans, 266

sinking funds, 209–210

smoothing, 84–87

special purpose vehicle (SPV),

242–243, 279, 281, 283–

284

spline-based methods, 88–91

spline estimation, 62

spot interest rates, 47, 59

calculating, 60–63

calculating forward rate from,

113–117

zero-coupon yields and, 300–

304

spot yields, zero-coupon yields

and, 304–307

spread, 315, 318–320

Standard & Poor’s, 175

standard default assumption

(SDA), 254

static cash ﬂ ow model, 268–270

step-up recovery FRNs, 231

sterling markets, 21

stochastic rates, 54–56

Index 353

straight bonds, 5

straight line interpolation, 11

strike price, 138, 191

stripped mortgage-backed securi-

ties

deﬁ ned, 249

interest-only (IO), 250

principal only (PO), 250

strips, 18

anomalies, 308

case study, 311–313

coupon, 304

determining values, 307–308

principal, 304

trading strategies, 309–311

structured notes, deﬁ ned, 227

Svensson model, 91

swaps

accreting (step-up), 121

amortizing, 121

applications, 124–131

basic, 120–121

constant maturity swap (CMS),

121

constant maturity Treasury

(CMT), 121

credit default swap, 178–179

dates and terminology, 107–109

deﬁ ned, 105, 227

differential, 121

extendable, 120

forward-start, 120

generic interest rate, 106–111

hedging and, 127–131

index, 184

LIBOR-in-arrears (back-set),

121

margin, 120

non-vanilla interest rate,

119–121

off-market, 120

putable, 120

spreads and yield curve, 109–

111

total return, 181–183, 187

swaps, generic valuation

calculating forward rate from

spot rate discount factors,

113–117

ﬁ nal maturity discount factor,

118–119

intuitive, 112

key principles of interest rate,

117–118

zero-coupon, 113

swaptions, 122–124, 236

synthetic CDO structures, 283–

284

synthetic convertible notes,

237–238

synthetic-coupon pass-throughs,

262

targeted amortization classes

(TACs), 256, 260

taxes, 215–216

Taylor expansion, 37

technical analysis, 316

term, 5

terminal (future) value, 6–7

term-structure modeling

basic concepts, 67–71

Brennan-Schwartz model, 76

choosing, 79–81

Cox-Ingersoll-Ross (CIR)

model, 74–75

Cox-Ingersoll-Ross (CIR)

model, extended, 76–77

Heath-Jarrow-Morton (HJM)

model, 68, 77–79

Ho-Lee model, 73, 79

Hull and White model, 70,

72–73

inﬂ ation, 225–226

354 Index

Ito’s lemma, 70–71

one-factor, 68, 71–75

short-rate processes, 68–70

two-factor, 68, 75–79

Vasicek model, 71–72

term structure of interest rates,

48–49

expectations hypothesis, 63–65

liquidity premium hypothesis,

segmented markets hypothesis,

65–66

term to maturity, 5, 268

Theory of Interest (Fisher), 220

theta, 165

ticks, 296

time-dependent drift, 73

time values, 6, 137, 138, 159–160,

191

total return swaps (TRS), 181–183,

187

trading

futures, 316–320

low- and high-coupon yield

spreads, 323–326

relative value, 315, 320–326

speculative, 315

spread, 315, 318–320

yield curves, 320–322

tranches, 249

true return, 297–299

trustees, issuer versus security, 243

two-factor term-structure models,

68, 75–79

unfunded credit derivatives, 180

U.K. gilt strips, 49, 50

U.S. Treasuries, 28, 49

U.S. Treasury inﬂ ation-indexed

securities (TIIS), 213

U.S. Treasury inﬂ ation-protected

securities (TIPS), 213,

216–221

valuation. See swaps, generic valu-

ation

value date, 17

variable-rate notes, 228

Vasicek model, 71–72

vega, 165–166

very accurately deﬁ ned maturity

(VADM), 256

volatility, 143

future, 144

historical, 144

implied, 144, 156

option smile, 169–170

stochastic, 156

Weiner process, 68–70, 145

Whaley model, 157

writer, 138, 191

yield

See also gross redemption yield

assessing, on index-linked

bonds, 221–222

beta, 40

calculating, for mortgage-

backed securities, 268–270

curve, 49

money (nominal), 219, 220–

221

real, 219, 220–221

relative value, 315, 320–322

yield curve, ﬁ tting the, 83

comparing curves, 92

cubic polynomials, 87–88

Nelson and Siegel curves,

91–92

non-parametric methods,

88–92

smoothing, 84–87

spline-based methods, 88–91

Index 355

Svensson model, 91

yield to maturity (YTM), 4, 12,

229, 230

calculating, 19–27

yield-to-maturity expectations

hypothesis, 64–65

yield to workout, 20

yield to worst, 189

Z-class, 261

zero-cost collars, 172

zero-coupon bonds, 5–6, 18, 19,

47–49, 299

zero-coupon indexation, 214–215

zero-coupon swap valuation, 113

zero-coupon yields

spot rates and, 300–304

sport yields and, 304–307

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ABOUT THE AUTHOR

Moorad Choudhry is Head of Treasury at KBC Financial Products UK

Limited. His responsibilities cover asset-liability management for the

group’s activities worldwide, including money-market funding, managing

the asset-backed conduit program, and corporate bond repo trading.

He was previously a vice president in structured ﬁ nance services with

JPMorgan Chase Bank in London. Prior to that he worked as a gilt-edged

market maker and treasury trader with ABN Amro Hoare Govett Sterling

Bonds Limited, and as a sterling proprietary trader within the Treasury

division at Hambros Bank Limited.

Dr. Choudhry is a visiting professor at the Department of Econom-

ics, London Metropolitan University, and a senior fellow at the Centre

for Mathematical Trading and Finance, Cass Business School. He was

educated at Claremont Fan Court School in Surrey, the University of

Westminster, the University of Reading, Henley Management College,

and Birkbeck, University of London.

His previous publications include The Bond and Money Markets

(Butterworth Heinemann, 2001), Capital Market Instruments (FT Prentice

Hall, 2001), Analysing and Interpreting the Yield Curve (John Wiley,

2004), Structured Credit Products (John Wiley, 2004), and numerous

articles in academic and trade journals.

His research can be viewed at www.YieldCurve.com.