introduction to the ma thematic is of financial derivatives solution manual - neftci

8/3/2019 Introduction to the Ma Thematic Is of Financial Derivatives Solution Manual - Neftci

1/90

0 2 4 6 8 10 12 14 16 18 2020

15

10

5

0

5

10

15

20short stockshort callcombined position

written call

short stock

short stock + short call


2/90

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5long putlong callput + call

0 2 4 6 8 10 126

4

2

0

2

4

6long put+short callshort put + long callcombined position

K1 K

2


3/90

0 2 4 6 8 10 12 14 16 18 2025

20

15

10

5

0

5

10short stockshort callcombined positionshort stock

written call

short stock + short call

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4long putlong callput + call


4/90

0 1 2 3 4 5 6 7 8 9 106

4

2

0

2

4

6long put+short callshort put+long callcombined position

-

-

-

-

-

- -

-

-

- -


5/90


6/90


7/90


8/90


9/90

St

St+d

St+u

St+2uu

St+2ud

St+2du

St+2dd


10/90


11/90


12/90


13/90


14/90


15/90


16/90


17/90

-

-


18/90


19/90


20/90


21/90


22/90

Binomial Density, n=4

0.0625

0.25

0.375

0.25

0.0625

00.05

0.10.15

0.20.25

0.30.35

0.4

0 1 2 3 4

Number of Successes

Probability


23/90


24/90


25/90


26/90


27/90


28/90


29/90


30/90


31/90


32/90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.8

0.6

0.4

0.2

0

0.2

0.4

0.6

Time

Brownian Motion Path

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.85

0.9

0.95

1

1.05

1.1

Time

Stock Price Path


33/90


34/90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.8

0.6

0.4

0.2

0

0.2

0.4

0.6

Time

Brownian Motion Path

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.85

0.9

0.95

1

1.05

1.1

Time

Stock Price Path


35/90


36/90


37/90


38/90


39/90


40/90


41/90


42/90


43/90


44/90

-


45/90


46/90


47/90


48/90

0 0.5 1 1.5 2 2.5 31

1.1

1.2

1.3

Stock Price Path, Delta = 1

Stoc

kPrice

Time

0 0.5 1 1.5 2 2.5 30.95

1

1.05

1.1

1.15

1.2Stock Price Path, Delta = .5

Stoc

kPrice

Time


49/90

0 0.5 1 1.5 2 2.5 3

0.9

0.95

1

1.05

1.1

1.15Path of Stock Price, Delta = .01, sigma=.1

Time

Stoc

kPrice

0 0.5 1 1.5 2 2.5 30.8

0.9

1

1.1

1.2

1.3Path of Stock Price, Delta = .01, sigma=.1*sqrt(3)

Time

Stoc

kPrice


50/90


51/90


52/90


53/90

Time

x variable

0

.25

.50

.75

1.0

$0 $3 $6 $9 $12

0 0 0 3 6

0

0

0

0

6

6

6

6

0 .4167 3

.0579 .7176 3.0579

.1415 .9510 3.1415

.2342 1.1428 3.2342


54/90


55/90


56/90


57/90

32

10

12

3

3

2

1

0

1

2

3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Rr

f

(R,r

)


58/90

32

10

12

3

3

2

1

0

1

2

3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Rr

f(R

,r)


59/90


60/90


61/90


62/90


63/90

0 0.02 0.04 0.06 0.08 0.1 0.12

2

0

2

4

6

8

10

12

14

16

18

x 103 Caplet Payoff for each $1 of Notional Amount

(Lt3

mon

ths

6

.75%

)*3/12

3 month Libor at start of 3 month period

payoff


64/90

0 20 40 60 80 100 120 140 160

80

60

40

20

0

20

40

60

80

Forward Contract Payoff with Forward Price = $89.5

Price, in 3 months, of a defaultfree discount bond maturing in 18 months

Bon

dprice

in3mon

ths8

9.5

payoff

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160.08

0.06

0.04

0.02

0

0.02

0.04

0.06

0.08Payoff of a Single FRA on 3month Libor with F equal to 7.5%

Libor at the end of each threemonth period

Payo

ff(same

fora

lls

ixagreemen

ts)

payoff


65/90

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140.04

0.03

0.02

0.01

0

0.01

0.02

0.03

0.04Fixed Payer Interest Rate Swap at 6, 12, 18, and 24 Months per $1 Notional

6 month Libor at the start of the 6 month period

(Lt1

/27

.5%)*6/12

payoff

0 0.02 0.04 0.06 0.08 0.1 0.120

0.01

0.02

0.03

0.04

0.05

0.06Payoff of Swaption with 6% Swap Rate

current swap rates

max

(curren

tswapra

te6

%,0

)

payoff


66/90


67/90


68/90

-


69/90


70/90


71/90


72/90


73/90


74/90


75/90


76/90


77/90

- -

-

- - -

-

- - -

-


78/90


79/90


80/90


81/90


82/90


83/90


84/90


85/90


86/90


87/90


88/90


89/90


90/90

1 1.5 2 2.5 3 3.5 40

2

4

6

8

10

12

14

Time

Va

lue

Func

tion

Value Function over Time

introduction to the ma thematic is of financial derivatives solution manual - neftci

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