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Trading real options analysis course - business cases and software applic - Mun P.D.

Mun P.D. Trading real options analysis course - business cases and software applic - Wiley publishing , 2003. - 318 p.
ISBN 047-43001-3
Download (direct link): tradingohnathan2003.pdf
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217
Solutions for European Option
European Option Calculations
-Assumptions-----------------
Asset Value ($) Implementation Cost ($) Maturity (Years) Risk-free Rate (%) Dividends (%)
Volatility (%)
Lattice Steps
$100.00
$100.00
1.00
5.00%
0.00%
25.00%
5
- Intermediate Calculations--------
Stepping-Time (dt)
Up Step-Size (up)
Down Step-Size (down) Risk-neutral Probability (prob)
- Results--------------------------
Lattice Results Black-Scholes Results
$12.79
$12.34
0.20000
1.1183
0.8942
51.69%
Underlying Asset 174.90 |
156.39
139.85 139.85 |
125.06 125.06
111.83 111.83 111.83 |
I 100.00 100.00 100.00
89.42 89.42 89.42 |
79.96 79.96
71.50 71.50 |
63.94
57.18 |
Option Valuation 74.90 I
57.39
41.83 39.85 |
29.17 26.05
19.61 16.23 11.83 |
1 12.79 9.79 6.05
5.77 3.10 0.00 |
1.59 0.00
0.00 0.00 I
0.00
0.00 I
Decision Lattice Execute I
Continue
Continue Execute I
Continue Continue
Continue Continue Execute I
1 Continue Continue Continue
Continue Continue End |
Continue Continue
Continue End |
Continue
End
218
EXERCISE SOLUTIONS
Solutions for American Option
American Option Calculations


Asset Value ($) $100.00 Stepping-Time (dt) 0.6000
Implementation Cost ($) $80.00 Up Step-Size (up) 1.3114
Maturity (Years) 3.00 Down Step-Size (down) 0.7625
Risk-free Rate (%) 5.00% Risk-neutral Probability (prob) 35.77%
Dividends (%) 12.00%
Volatility (%) 35.00%
Lattice Steps 5 Lattice Results $23.47 I
Underlying Asset
131.14
171.9
225.54
131.14
295.78
171.!
387.98
225.54
131.14
100.00
100.00
100.00
76.25
Option Valuation
51.14
76.25
58.15
58.15
44.34
33.81
91.98
145.54
51.14
215.78
91.98
76.25
44.34
25.78
307.89
145.54
51.14
23.47
22.08
20.00
9.17
Decision Lattice
6.94
2.41
0.00
0.00
0.00
Execute
Execute
Execute
Execute
Execute
Execute
0.00
0.00
0.00
Execute
Execute
Execute
Continue
Continue
Execute
Continue
Continue
Continue
Continue
Continue
Continue
End
End
End
Exercise Solutions
219
Solutions for Risk-Neutral Probability Approach Versus Market-Replicating Portfolio
Part I: Risk-Neutral Probability Approach
Stepping Time = 1.00 Up Jump-Size (up) = 1.1052 Down Jump-Size (down) = 0.9048 Risk-Neutral Probability = 0.7309
Option Valuation Lattice
34.99
27.02 :
20.66 :
10.52
15.66 ?
7.31
5.08
0
0
0
Part II: Market-Replicating Portfolio Approach
Step 1: Get the call values at the terminal nodes.
C3VV = 34.99
C3UD = 10.52 C3DU = .0 C3DD = .0
Step 2: Get the hedge ratios for the terminal branches.
h2U = 1.0000 h2M = 0.5250 h2D = 0.0000
Step 3: Get the debt load for the terminal branches.
D2U = 100.0000 D2M = 47.5030 D2L = 0.0000
220
EXERCISE SOLUTIONS
Step 4: Get the call values one node back, t = 2.
C2U = 27.0171 C2M = 7.3137 C2D = 0.0000
Step 5: Get the hedge ratios for the one branch back, t = 1.
h1U = 0.8899 h1D = 0.4034
Step 6: Get the debt load for one branch back, t = 1.
D1U = 81.6753 D1D = 33.0263
Step 7: Get the call values one node back.
C1U = 20.6598 C1D = 5.0840
Step 8: Get the hedge ratios for two branches back, t = 0.
h0 = 0.7772
Step 9: Get the debt load for two branches back, t = 0.
D0 = 65.2363
Step 10: Get the call value at t = 0, the option value of this analysis.
C0 = 15.66
Exercise Solutions
221
Solutions for State-Pricing Approach
European Option Calculations State Pricing Approach
? Intermediate Calculations -
Stepping-Time (dt)
Up Step-Size (up)
Down Step-Size (down) Up Jump Increment Down Jump Increment Up State Price Down State Price
|- Assumptions
Asset Value ($) $100.00
Implementation Cost ($) $100.00
Maturity (Years) 5.00
Risk-free Rate (%) 5.00%
Dividends (%) 0.00%
Volatility (%) 25.00%
Lattice Steps 5
? Results------------------
Lattice Results Black-Scholes Results
1.0000
1.2840
0.7788
28.40%
-22.12%
0.5106
0.4406
$32.71
$32.50
Underlying Asset Lattice 349.03 1
271.83
211.70 211.70 1
164.87 164.87
128.40 128.40 128.40 1
I 100.00 100.00 100.00
77.88 77.88 77.88 1
60.65 60.65
47.24 47.24 1
36.79
28.65 1

State Prices Lattice 249.03 1
176.38
120.70 111.70 1
80.10 69.55
51.76 41.90 28.40 1
1 32.71 24.66 14.50
14.26 7.41 0.00 1
3.78 0.00
0.00 0.00 1
0.00
0.00 1

Decision Lattice Execute 1
Continue
Continue Execute 1
Continue Continue
Continue Continue Execute 1
1 Continue Continue Continue
Continue Continue End 1
Continue Continue
Continue End 1
Continue
End
222
EXERCISE SOLUTIONS
Solutions for Trinomial Lattices
American Option Calculations (Trinomial Lattice)
? Assumptions-----------------
Asset Value ($) Implementation Cost ($) Maturity (Years)
Risk-free Rate (%) Dividends (%)
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