Introduction to the Ma Thematic Is of Financial Derivatives Solution Manual - Neftci
Transcript of Introduction to the Ma Thematic Is of Financial Derivatives Solution Manual - Neftci
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20short stockshort callcombined position
written call
short stock
short stock + short call
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3.5long putlong callput + call
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6long put+short callshort put + long callcombined position
K1 K
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written call
short stock + short call
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6long put+short callshort put+long callcombined position
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St
St+d
St+u
St+2uu
St+2ud
St+2du
St+2dd
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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
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.8
0.6
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0
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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
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Time
Brownian Motion Path
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0.9
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1
1.05
1.1
Time
Stock Price Path
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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
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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
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Time
x variable
0
.25
.50
.75
1.0
$0 $3 $6 $9 $12
0 0 0 3 6
0
0
0
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6
6
6
0 .4167 3
.0579 .7176 3.0579
.1415 .9510 3.1415
.2342 1.1428 3.2342
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Rr
f
(R,r
)
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f(R
,r)
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0 0.02 0.04 0.06 0.08 0.1 0.12
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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
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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
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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
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.140.04
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6 month Libor at the start of the 6 month period
(Lt1
/27
.5%)*6/12
payoff
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0.06Payoff of Swaption with 6% Swap Rate
current swap rates
max
(curren
tswapra
te6
%,0
)
payoff
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1 1.5 2 2.5 3 3.5 40
2
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Time
Va
lue
Func
tion
Value Function over Time