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Table 10.1: The Cash Flows to a Typical Coupon Bond with Price B (0), Principal L, Coupon C and Maturity T. 0 1 2 … T | | | | B (0) C C … C Coupons L Principal. Time. coupon rate c = 1+C/L. Table 10.2: An Example of a Time 0 Zero-Coupon Bond Price Curve. P(0,4) = .923845

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Presentation Transcript
Table 10.1: The Cash Flows to a Typical Coupon Bond with Price B(0), Principal L, Coupon C and Maturity T

0 1 2 … T

| | | |

B(0) C C … C Coupons

L Principal

Time

coupon rate c = 1+C/L

P(0,4) = .923845

P(0,3) = .942322

P(0,2) = .961169

P(0,1) = .980392

1.054597

.985301

1

1

1.037958

1/2

.967826

1.016031

.984222

1.054597

1

1/2

1/2

.981381

1.02

1

1

.947497

.965127

1.059125

1.017606

.982699

1

.982456

1

1.037958

1

1/2

1/2

1/2

.960529

1

1.020393

B(0)

.980015

1.059125

1

P(0,4)

.923845

1/2

.977778

P(0,3)

1

.942322

1

=

r(0) = 1.02

P(0,2)

.961169

P(0,1)

.980392

1.062869

P(0,0)

1

.983134

1.042854

1/2

1

1

.962414

1/2

1.019193

.981169

1.02

1/2

1.062869

1

1/2

.937148

.978637

1

.957211

1

1.022406

.978085

1

1.068337

.979870

1.042854

1

1/2

1/2

1

.953877

.976147

1.024436

1

1/2

1.068337

.974502

1

1

time 0 1 2 3 4

Figure 10.1: An Example of a One-Factor Bond Price Curve Evolution. Pseudo-Probabilities Are Along Each Branch of the Tree.

time 0 1 2 3 4

Figure 10.2: The Evolution of the Coupon Bond\'s Price for the Example in Table 10.3.The coupon payment at each date is indicated by the nodes. The Synthetic Coupon-Bond Portfolio (n0(t;st), n4(t;st)) in the money market account and four-period zero-coupon bond are given under each node. Pseudo-probabilities along the branches of the Tree.

1.054597

.985301

1

1

1.037958

1/2

.967826

1.016031

.984222

1.054597

1

1/2

1/2

.981381

1.02

1

1

.947497

.965127

1.059125

1.017606

.982699

1

.982456

1

1.037958

1

1/2

1/2

1/2

.960529

1

1.020393

B(0)

.980015

1.059125

1

P(0,4)

.923845

1/2

.977778

P(0,3)

1

.942322

1

=

r(0) = 1.02

P(0,2)

.961169

P(0,1)

.980392

1.062869

P(0,0)

1

.983134

1.042854

1/2

1

1

.962414

1/2

1.019193

.981169

1.02

1/2

1.019193

1

1/2

.937148

.978637

1

.957211

1

1.022406

.978085

1

1.068337

.979870

1.042854

1

1/2

1/2

1

.953877

.976147

1.024436

1

1/2

1.068337

.974502

1

1

time 0 1 2 3 4

Figure 10.1: An Example of a One-Factor Bond Price Curve Evolution. Pseudo-Probabilities Are Along Each Branch of the Tree.

Figure 10.3: A Comparison of HJM Hedging versus Duration Hedging. The Bond Trading Strategy (na(0), nb(0)) is Given.

Investment

Actual Payoff

HJM .56027

Duration .489811

1/2

HJM .549287

(1, -.445825)

Duration .480585

(1, -.52020)

Duration hedge (if corrcct)

1.02(.480585)=.490197

r(0) = 1.02

1/2

HJM .56027

Duration .490581

time 0 1